LMFDB - Embedded newform 130.3.r.b.43.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,3,Mod(17,130)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("130.17"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	130.r (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.54224343668$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			43.7
Character	$\chi$	$=$	130.43
Dual form			130.3.r.b.127.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36603 - 0.366025i) q^{2} +(5.53084 - 1.48198i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-4.80922 - 1.36799i) q^{5} +(7.01282 - 4.04885i) q^{6} +(-2.44911 + 9.14020i) q^{7} +(2.00000 - 2.00000i) q^{8} +(20.5996 - 11.8932i) q^{9} +(-7.07024 - 0.108409i) q^{10} +(-9.31429 - 5.37761i) q^{11} +(8.09771 - 8.09771i) q^{12} +(-0.193180 + 12.9986i) q^{13} +13.3822i q^{14} +(-28.6263 - 0.438931i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-21.4878 - 5.75763i) q^{17} +(23.7864 - 23.7864i) q^{18} +(0.639170 + 1.10707i) q^{19} +(-9.69780 + 2.43980i) q^{20} +54.1825i q^{21} +(-14.6919 - 3.93668i) q^{22} +(5.86687 - 1.57202i) q^{23} +(8.09771 - 14.0256i) q^{24} +(21.2572 + 13.1579i) q^{25} +(4.49392 + 17.8271i) q^{26} +(59.8680 - 59.8680i) q^{27} +(4.89822 + 18.2804i) q^{28} +(1.45536 + 0.840250i) q^{29} +(-39.2650 + 9.87838i) q^{30} -9.47101i q^{31} +(1.46410 - 5.46410i) q^{32} +(-59.4853 - 15.9390i) q^{33} -31.4603 q^{34} +(24.2820 - 40.6069i) q^{35} +(23.7864 - 41.1993i) q^{36} +(-3.88977 + 1.04226i) q^{37} +(1.27834 + 1.27834i) q^{38} +(18.1952 + 72.1792i) q^{39} +(-12.3544 + 6.88247i) q^{40} +(44.6273 + 25.7656i) q^{41} +(19.8322 + 74.0146i) q^{42} +(-7.19635 + 26.8571i) q^{43} -21.5104 q^{44} +(-115.338 + 29.0170i) q^{45} +(7.43889 - 4.29484i) q^{46} +(-19.1125 - 19.1125i) q^{47} +(5.92793 - 22.1233i) q^{48} +(-35.1099 - 20.2707i) q^{49} +(33.8540 + 10.1934i) q^{50} -127.378 q^{51} +(12.6640 + 22.7074i) q^{52} +(28.6938 + 28.6938i) q^{53} +(59.8680 - 103.694i) q^{54} +(37.4380 + 38.6039i) q^{55} +(13.3822 + 23.1786i) q^{56} +(5.17581 + 5.17581i) q^{57} +(2.29561 + 0.615106i) q^{58} +(-33.4478 - 57.9332i) q^{59} +(-50.0212 + 27.8661i) q^{60} +(-55.5573 - 96.2281i) q^{61} +(-3.46663 - 12.9376i) q^{62} +(58.2555 + 217.413i) q^{63} -8.00000i q^{64} +(18.7109 - 62.2487i) q^{65} -87.0925 q^{66} +(10.5120 - 2.81667i) q^{67} +(-42.9756 + 11.5153i) q^{68} +(30.1190 - 17.3892i) q^{69} +(18.3067 - 64.3579i) q^{70} +(5.08817 - 2.93766i) q^{71} +(17.4129 - 64.9857i) q^{72} +(26.4931 - 26.4931i) q^{73} +(-4.93203 + 2.84751i) q^{74} +(137.070 + 41.2714i) q^{75} +(2.21415 + 1.27834i) q^{76} +(71.9641 - 71.9641i) q^{77} +(51.2745 + 91.9387i) q^{78} -4.59103i q^{79} +(-14.3573 + 13.9237i) q^{80} +(135.358 - 234.447i) q^{81} +(70.3929 + 18.8617i) q^{82} +(-35.2497 + 35.2497i) q^{83} +(54.1825 + 93.8468i) q^{84} +(95.4631 + 57.0847i) q^{85} +39.3216i q^{86} +(9.29457 + 2.49047i) q^{87} +(-29.3838 + 7.87336i) q^{88} +(30.9180 - 53.5516i) q^{89} +(-146.934 + 81.8546i) q^{90} +(-118.336 - 33.6006i) q^{91} +(8.58969 - 8.58969i) q^{92} +(-14.0359 - 52.3826i) q^{93} +(-33.1038 - 19.1125i) q^{94} +(-1.55944 - 6.19854i) q^{95} -32.3908i q^{96} +(0.954724 - 3.56308i) q^{97} +(-55.3806 - 14.8392i) q^{98} -255.828 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{2} - 8 q^{5} - 4 q^{7} + 56 q^{8} + 48 q^{9} + 6 q^{10} - 12 q^{11} - 18 q^{13} - 10 q^{15} + 56 q^{16} - 40 q^{17} + 92 q^{18} + 36 q^{19} + 4 q^{20} - 12 q^{22} - 28 q^{23} - 6 q^{25} + 42 q^{26}+ \cdots - 16 q^{99}+O(q^{100}) $ 28 * q + 14 * q^2 - 8 * q^5 - 4 * q^7 + 56 * q^8 + 48 * q^9 + 6 * q^10 - 12 * q^11 - 18 * q^13 - 10 * q^15 + 56 * q^16 - 40 * q^17 + 92 * q^18 + 36 * q^19 + 4 * q^20 - 12 * q^22 - 28 * q^23 - 6 * q^25 + 42 * q^26 - 24 * q^27 + 8 * q^28 - 186 * q^29 - 60 * q^30 - 56 * q^32 - 196 * q^33 + 20 * q^34 - 66 * q^35 + 92 * q^36 - 30 * q^37 + 72 * q^38 - 156 * q^39 - 20 * q^40 + 48 * q^41 + 108 * q^42 + 80 * q^43 + 4 * q^45 - 96 * q^46 - 104 * q^47 - 96 * q^49 - 60 * q^50 - 336 * q^51 - 24 * q^52 + 126 * q^53 - 24 * q^54 + 362 * q^55 - 16 * q^56 - 160 * q^57 - 242 * q^58 - 80 * q^59 - 136 * q^60 - 336 * q^61 - 60 * q^62 + 516 * q^63 + 236 * q^65 - 64 * q^66 - 16 * q^67 - 80 * q^68 - 264 * q^69 - 200 * q^70 - 60 * q^71 + 4 * q^72 + 286 * q^73 - 6 * q^74 + 672 * q^75 + 24 * q^76 + 424 * q^77 + 160 * q^78 + 8 * q^80 + 86 * q^81 + 138 * q^82 + 64 * q^83 + 96 * q^84 + 280 * q^85 + 528 * q^87 - 24 * q^88 + 348 * q^89 - 294 * q^90 + 192 * q^91 + 80 * q^92 - 240 * q^93 - 432 * q^94 - 50 * q^95 + 14 * q^97 - 110 * q^98 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.36603	−	0.366025i	0.683013	−	0.183013i
$2$	1.36603	−	0.366025i	0.683013	−	0.183013i
$3$	5.53084	−	1.48198i	1.84361	−	0.493994i	0.844477	−	0.535591i	$-0.179911\pi$
$3$	5.53084	−	1.48198i	1.84361	−	0.493994i	0.999134	+	0.0415970i	$0.0132446\pi$
$4$	1.73205	−	1.00000i	0.433013	−	0.250000i
$5$	−4.80922	−	1.36799i	−0.961844	−	0.273598i
$5$	−4.80922	−	1.36799i	−0.961844	−	0.273598i
$6$	7.01282	−	4.04885i	1.16880	−	0.674809i
$7$	−2.44911	+	9.14020i	−0.349873	+	1.30574i	0.536943	+	0.843619i	$0.319579\pi$
$7$	−2.44911	+	9.14020i	−0.349873	+	1.30574i	−0.886815	+	0.462124i	$0.847087\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	20.5996	−	11.8932i	2.28885	−	1.32147i
$10$	−7.07024	−	0.108409i	−0.707024	−	0.0108409i
$11$	−9.31429	−	5.37761i	−0.846753	−	0.488873i	0.0128007	−	0.999918i	$-0.495925\pi$
$11$	−9.31429	−	5.37761i	−0.846753	−	0.488873i	−0.859554	+	0.511045i	$0.829259\pi$
$12$	8.09771	−	8.09771i	0.674809	−	0.674809i
$13$	−0.193180	+	12.9986i	−0.0148600	+	0.999890i
$13$	−0.193180	+	12.9986i	−0.0148600	+	0.999890i
$14$			13.3822i			0.955870i
$15$	−28.6263	−	0.438931i	−1.90842	−	0.0292621i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	−21.4878	−	5.75763i	−1.26399	−	0.338684i	−0.436263	−	0.899819i	$-0.643698\pi$
$17$	−21.4878	−	5.75763i	−1.26399	−	0.338684i	−0.827724	+	0.561135i	$0.810365\pi$
$18$	23.7864	−	23.7864i	1.32147	−	1.32147i
$19$	0.639170	+	1.10707i	0.0336405	+	0.0582671i	0.882355	−	0.470583i	$-0.155957\pi$
$19$	0.639170	+	1.10707i	0.0336405	+	0.0582671i	−0.848715	+	0.528851i	$0.822623\pi$
$20$	−9.69780	+	2.43980i	−0.484890	+	0.121990i
$21$			54.1825i			2.58012i
$22$	−14.6919	−	3.93668i	−0.667813	−	0.178940i
$23$	5.86687	−	1.57202i	0.255081	−	0.0683488i	−0.129012	−	0.991643i	$-0.541181\pi$
$23$	5.86687	−	1.57202i	0.255081	−	0.0683488i	0.384094	+	0.923294i	$0.374514\pi$
$24$	8.09771	−	14.0256i	0.337404	−	0.584402i
$25$	21.2572	+	13.1579i	0.850289	+	0.526316i
$26$	4.49392	+	17.8271i	0.172843	+	0.685657i
$27$	59.8680	−	59.8680i	2.21733	−	2.21733i
$28$	4.89822	+	18.2804i	0.174936	+	0.652871i
$29$	1.45536	+	0.840250i	0.0501847	+	0.0289742i	0.524882	−	0.851175i	$-0.324109\pi$
$29$	1.45536	+	0.840250i	0.0501847	+	0.0289742i	−0.474698	+	0.880149i	$0.657443\pi$
$30$	−39.2650	+	9.87838i	−1.30883	+	0.329279i
$31$		−	9.47101i		−	0.305517i	−0.988264	−	0.152758i	$-0.951184\pi$
$31$		−	9.47101i		−	0.305517i	0.988264	−	0.152758i	$-0.0488156\pi$
$32$	1.46410	−	5.46410i	0.0457532	−	0.170753i
$33$	−59.4853	−	15.9390i	−1.80259	−	0.483001i
$34$	−31.4603			−0.925303
$35$	24.2820	−	40.6069i	0.693771	−	1.16020i
$36$	23.7864	−	41.1993i	0.660734	−	1.14442i
$37$	−3.88977	+	1.04226i	−0.105129	+	0.0281692i	−0.311000	−	0.950410i	$-0.600664\pi$
$37$	−3.88977	+	1.04226i	−0.105129	+	0.0281692i	0.205871	+	0.978579i	$0.433997\pi$
$38$	1.27834	+	1.27834i	0.0336405	+	0.0336405i
$39$	18.1952	+	72.1792i	0.466544	+	1.85075i
$40$	−12.3544	+	6.88247i	−0.308860	+	0.172062i
$41$	44.6273	+	25.7656i	1.08847	+	0.628429i	0.933169	−	0.359438i	$-0.117031\pi$
$41$	44.6273	+	25.7656i	1.08847	+	0.628429i	0.155302	+	0.987867i	$0.450365\pi$
$42$	19.8322	+	74.0146i	0.472194	+	1.76225i
$43$	−7.19635	+	26.8571i	−0.167357	+	0.624584i	0.830371	+	0.557211i	$0.188129\pi$
$43$	−7.19635	+	26.8571i	−0.167357	+	0.624584i	−0.997728	+	0.0673734i	$0.978538\pi$
$44$	−21.5104			−0.488873
$45$	−115.338	+	29.0170i	−2.56307	+	0.644822i
$46$	7.43889	−	4.29484i	0.161715	−	0.0933662i
$47$	−19.1125	−	19.1125i	−0.406649	−	0.406649i	0.473919	−	0.880568i	$-0.342839\pi$
$47$	−19.1125	−	19.1125i	−0.406649	−	0.406649i	−0.880568	+	0.473919i	$0.842839\pi$
$48$	5.92793	−	22.1233i	0.123499	−	0.460903i
$49$	−35.1099	−	20.2707i	−0.716528	−	0.413688i
$50$	33.8540	+	10.1934i	0.677081	+	0.203867i
$51$	−127.378			−2.49761
$52$	12.6640	+	22.7074i	0.243538	+	0.436680i
$53$	28.6938	+	28.6938i	0.541393	+	0.541393i	0.923937	−	0.382544i	$-0.124952\pi$
$53$	28.6938	+	28.6938i	0.541393	+	0.541393i	−0.382544	+	0.923937i	$0.624952\pi$
$54$	59.8680	−	103.694i	1.10867	−	1.92027i
$55$	37.4380	+	38.6039i	0.680690	+	0.701890i
$56$	13.3822	+	23.1786i	0.238968	+	0.413904i
$57$	5.17581	+	5.17581i	0.0908036	+	0.0908036i
$58$	2.29561	+	0.615106i	0.0395794	+	0.0106053i
$59$	−33.4478	−	57.9332i	−0.566911	−	0.981919i	−0.996869	−	0.0790703i	$-0.974805\pi$
$59$	−33.4478	−	57.9332i	−0.566911	−	0.981919i	0.429958	−	0.902849i	$-0.358528\pi$
$60$	−50.0212	+	27.8661i	−0.833687	+	0.464435i
$61$	−55.5573	−	96.2281i	−0.910776	−	1.57751i	−0.812971	−	0.582304i	$-0.802151\pi$
$61$	−55.5573	−	96.2281i	−0.910776	−	1.57751i	−0.0978047	−	0.995206i	$-0.531182\pi$
$62$	−3.46663	−	12.9376i	−0.0559134	−	0.208672i
$63$	58.2555	+	217.413i	0.924691	+	3.45099i
$64$		−	8.00000i		−	0.125000i
$65$	18.7109	−	62.2487i	0.287860	−	0.957672i
$66$	−87.0925			−1.31958
$67$	10.5120	−	2.81667i	0.156895	−	0.0420398i	−0.179517	−	0.983755i	$-0.557453\pi$
$67$	10.5120	−	2.81667i	0.156895	−	0.0420398i	0.336411	+	0.941715i	$0.390787\pi$
$68$	−42.9756	+	11.5153i	−0.631993	+	0.169342i
$69$	30.1190	−	17.3892i	0.436507	−	0.252017i
$70$	18.3067	−	64.3579i	0.261524	−	0.919398i
$71$	5.08817	−	2.93766i	0.0716644	−	0.0413755i	−0.463740	−	0.885972i	$-0.653493\pi$
$71$	5.08817	−	2.93766i	0.0716644	−	0.0413755i	0.535404	+	0.844596i	$0.320159\pi$
$72$	17.4129	−	64.9857i	0.241845	−	0.902579i
$73$	26.4931	−	26.4931i	0.362920	−	0.362920i	−0.501967	−	0.864887i	$-0.667390\pi$
$73$	26.4931	−	26.4931i	0.362920	−	0.362920i	0.864887	+	0.501967i	$0.167390\pi$
$74$	−4.93203	+	2.84751i	−0.0666491	+	0.0384799i
$75$	137.070	+	41.2714i	1.82760	+	0.550285i
$76$	2.21415	+	1.27834i	0.0291335	+	0.0168203i
$77$	71.9641	−	71.9641i	0.934599	−	0.934599i
$78$	51.2745	+	91.9387i	0.657366	+	1.17870i
$79$		−	4.59103i		−	0.0581143i	−0.999578	−	0.0290572i	$-0.990750\pi$
$79$		−	4.59103i		−	0.0581143i	0.999578	−	0.0290572i	$-0.00925049\pi$
$80$	−14.3573	+	13.9237i	−0.179466	+	0.174046i
$81$	135.358	−	234.447i	1.67108	−	2.89440i
$82$	70.3929	+	18.8617i	0.858451	+	0.230021i
$83$	−35.2497	+	35.2497i	−0.424695	+	0.424695i	−0.886817	−	0.462122i	$-0.847088\pi$
$83$	−35.2497	+	35.2497i	−0.424695	+	0.424695i	0.462122	+	0.886817i	$0.347088\pi$
$84$	54.1825	+	93.8468i	0.645030	+	1.11722i
$85$	95.4631	+	57.0847i	1.12310	+	0.671585i
$86$			39.3216i			0.457227i
$87$	9.29457	+	2.49047i	0.106834	+	0.0286261i
$88$	−29.3838	+	7.87336i	−0.333907	+	0.0894700i
$89$	30.9180	−	53.5516i	0.347393	−	0.601703i	−0.638392	−	0.769711i	$-0.720400\pi$
$89$	30.9180	−	53.5516i	0.347393	−	0.601703i	0.985786	+	0.168008i	$0.0537335\pi$
$90$	−146.934	+	81.8546i	−1.63260	+	0.909496i
$91$	−118.336	−	33.6006i	−1.30040	−	0.369237i
$92$	8.58969	−	8.58969i	0.0933662	−	0.0933662i
$93$	−14.0359	−	52.3826i	−0.150923	−	0.563254i
$94$	−33.1038	−	19.1125i	−0.352168	−	0.203324i
$95$	−1.55944	−	6.19854i	−0.0164152	−	0.0652478i
$96$		−	32.3908i		−	0.337404i
$97$	0.954724	−	3.56308i	0.00984251	−	0.0367328i	−0.960830	−	0.277139i	$-0.910614\pi$
$97$	0.954724	−	3.56308i	0.00984251	−	0.0367328i	0.970672	+	0.240406i	$0.0772805\pi$
$98$	−55.3806	−	14.8392i	−0.565108	−	0.151420i
$99$	−255.828			−2.58412
$100$	49.9765	+	1.53295i	0.499765	+	0.0153295i
$101$	−63.0678	+	109.237i	−0.624433	+	1.08155i	0.364217	+	0.931314i	$0.381337\pi$
$101$	−63.0678	+	109.237i	−0.624433	+	1.08155i	−0.988650	+	0.150236i	$0.951997\pi$
$102$	−174.002	+	46.6236i	−1.70590	+	0.457094i
$103$	63.1318	+	63.1318i	0.612930	+	0.612930i	0.943709	−	0.330778i	$-0.107311\pi$
$103$	63.1318	+	63.1318i	0.612930	+	0.612930i	−0.330778	+	0.943709i	$0.607311\pi$
$104$	25.6108	+	26.3835i	0.246257	+	0.253687i
$105$	74.1210	−	260.576i	0.705914	−	2.48167i
$106$	49.6991	+	28.6938i	0.468860	+	0.270696i
$107$	12.3428	+	46.0640i	0.115353	+	0.430505i	0.999313	−	0.0370584i	$-0.0117987\pi$
$107$	12.3428	+	46.0640i	0.115353	+	0.430505i	−0.883960	+	0.467563i	$0.845132\pi$
$108$	43.8264	−	163.562i	0.405800	−	1.51447i
$109$	145.298			1.33301			0.666503	−	0.745502i	$-0.267790\pi$
$109$	145.298			1.33301			0.666503	+	0.745502i	$0.267790\pi$
$110$	65.2712	+	39.0307i	0.593375	+	0.354825i
$111$	−19.9691	+	11.5292i	−0.179902	+	0.103866i
$112$	26.7644	+	26.7644i	0.238968	+	0.238968i
$113$	44.1247	−	164.676i	0.390484	−	1.45731i	−0.438854	−	0.898558i	$-0.644615\pi$
$113$	44.1247	−	164.676i	0.390484	−	1.45731i	0.829338	−	0.558747i	$-0.188718\pi$
$114$	8.96476	+	5.17581i	0.0786382	+	0.0454018i
$115$	−30.3656	−	0.465599i	−0.264048	−	0.00404869i
$116$	3.36100			0.0289742
$117$	150.615	+	270.063i	1.28731	+	2.30823i
$118$	−66.8955	−	66.8955i	−0.566911	−	0.566911i
$119$	105.252	−	182.302i	0.884469	−	1.53195i
$120$	−58.1306	+	56.3748i	−0.484421	+	0.469790i
$121$	−2.66271	−	4.61194i	−0.0220058	−	0.0381152i
$122$	−111.115	−	111.115i	−0.910776	−	0.910776i
$123$	285.011	+	76.3684i	2.31716	+	0.620881i
$124$	−9.47101	−	16.4043i	−0.0763791	−	0.132293i
$125$	−84.2308	−	92.3589i	−0.673846	−	0.738871i
$126$	159.157	+	275.668i	1.26315	+	2.18784i
$127$	5.25548	+	19.6137i	0.0413817	+	0.154439i	0.983525	−	0.180771i	$-0.0578594\pi$
$127$	5.25548	+	19.6137i	0.0413817	+	0.154439i	−0.942143	+	0.335210i	$0.891193\pi$
$128$	−2.92820	−	10.9282i	−0.0228766	−	0.0853766i
$129$			159.207i			1.23416i
$130$	2.77499	−	91.8820i	0.0213461	−	0.706785i
$131$	158.906			1.21302			0.606512	−	0.795075i	$-0.292568\pi$
$131$	158.906			1.21302			0.606512	+	0.795075i	$0.292568\pi$
$132$	−118.971	+	31.8781i	−0.901293	+	0.241501i
$133$	−11.6843	+	3.13079i	−0.0878517	+	0.0235398i
$134$	13.3286	−	7.69528i	0.0994673	−	0.0574275i
$135$	−369.817	+	206.020i	−2.73939	+	1.52607i
$136$	−54.4908	+	31.4603i	−0.400668	+	0.231326i
$137$	−13.8504	+	51.6905i	−0.101098	+	0.377303i	−0.997873	−	0.0651835i	$-0.979237\pi$
$137$	−13.8504	+	51.6905i	−0.101098	+	0.377303i	0.896775	+	0.442486i	$0.145903\pi$
$138$	34.7784	−	34.7784i	0.252017	−	0.252017i
$139$	−228.938	+	132.177i	−1.64704	+	0.950917i	−0.668795	+	0.743447i	$0.733190\pi$
$139$	−228.938	+	132.177i	−1.64704	+	0.950917i	−0.978241	+	0.207470i	$0.933477\pi$
$140$	1.45075	−	94.6152i	0.0103625	−	0.675823i
$141$	−134.032	−	77.3837i	−0.950585	−	0.548820i
$142$	5.87531	−	5.87531i	0.0413755	−	0.0413755i
$143$	71.7005	−	120.034i	0.501402	−	0.839395i
$144$		−	95.1457i		−	0.660734i
$145$	−5.84968	−	6.03186i	−0.0403426	−	0.0415990i
$146$	26.4931	−	45.8875i	0.181460	−	0.314298i
$147$	−224.228	−	60.0816i	−1.52536	−	0.408719i
$148$	−5.69502	+	5.69502i	−0.0384799	+	0.0384799i
$149$	−102.289	−	177.170i	−0.686504	−	1.18906i	−0.972961	−	0.230968i	$-0.925811\pi$
$149$	−102.289	−	177.170i	−0.686504	−	1.18906i	0.286457	−	0.958093i	$-0.407522\pi$
$150$	202.347	+	6.20670i	1.34898	+	0.0413780i
$151$			140.695i			0.931754i	0.884850	+	0.465877i	$0.154261\pi$
$151$			140.695i			0.931754i	−0.884850	+	0.465877i	$0.845739\pi$
$152$	3.49249	+	0.935809i	0.0229769	+	0.00615664i
$153$	−511.117	+	136.953i	−3.34064	+	0.895121i
$154$	71.9641	−	124.645i	0.467299	−	0.809386i
$155$	−12.9562	+	45.5482i	−0.0835886	+	0.293859i
$156$	103.694	+	106.823i	0.664707	+	0.684762i
$157$	−87.9079	+	87.9079i	−0.559923	+	0.559923i	−0.929285	−	0.369363i	$-0.879576\pi$
$157$	−87.9079	+	87.9079i	−0.559923	+	0.559923i	0.369363	+	0.929285i	$0.379576\pi$
$158$	−1.68043	−	6.27147i	−0.0106357	−	0.0396928i
$159$	201.224	+	116.177i	1.26556	+	0.730673i
$160$	−14.5160	+	24.2752i	−0.0907251	+	0.151720i
$161$			57.4744i			0.356984i
$162$	99.0888	−	369.805i	0.611659	−	2.28274i
$163$	150.580	+	40.3478i	0.923804	+	0.247532i	0.689210	−	0.724561i	$-0.257958\pi$
$163$	150.580	+	40.3478i	0.923804	+	0.247532i	0.234593	+	0.972094i	$0.424624\pi$
$164$	103.062			0.628429
$165$	264.274	+	158.030i	1.60166	+	0.957755i
$166$	−35.2497	+	61.0543i	−0.212348	+	0.367797i
$167$	144.361	−	38.6814i	0.864438	−	0.231625i	0.200757	−	0.979641i	$-0.435660\pi$
$167$	144.361	−	38.6814i	0.864438	−	0.231625i	0.663681	+	0.748016i	$0.268993\pi$
$168$	108.365	+	108.365i	0.645030	+	0.645030i
$169$	−168.925	−	5.02213i	−0.999558	−	0.0297167i
$170$	151.300	+	43.0373i	0.889997	+	0.253161i
$171$	26.3333	+	15.2036i	0.153996	+	0.0889097i
$172$	14.3927	+	53.7143i	0.0836784	+	0.312292i
$173$	−2.26738	+	8.46197i	−0.0131062	+	0.0489131i	−0.972169	−	0.234280i	$-0.924727\pi$
$173$	−2.26738	+	8.46197i	−0.0131062	+	0.0489131i	0.959063	+	0.283193i	$0.0913936\pi$
$174$	13.6082			0.0782080
$175$	−172.327	+	162.070i	−0.984727	+	0.926115i
$176$	−37.2571	+	21.5104i	−0.211688	+	0.122218i
$177$	−270.850	−	270.850i	−1.53023	−	1.53023i
$178$	22.6336	−	84.4696i	0.127155	−	0.474548i
$179$	−67.2238	−	38.8117i	−0.375552	−	0.216825i	0.300329	−	0.953836i	$-0.402903\pi$
$179$	−67.2238	−	38.8117i	−0.375552	−	0.216825i	−0.675881	+	0.737011i	$0.736237\pi$
$180$	−170.754	+	165.597i	−0.948635	+	0.919983i
$181$	−67.2118			−0.371336			−0.185668	−	0.982613i	$-0.559445\pi$
$181$	−67.2118			−0.371336			−0.185668	+	0.982613i	$0.559445\pi$
$182$	−173.949	−	2.58517i	−0.955765	−	0.0142042i
$183$	−449.887	−	449.887i	−2.45840	−	2.45840i
$184$	8.58969	−	14.8778i	0.0466831	−	0.0808575i
$185$	20.1326	+	0.308695i	0.108825	+	0.00166862i
$186$	−38.3467	−	66.4185i	−0.206165	−	0.357089i
$187$	169.181	+	169.181i	0.904712	+	0.904712i
$188$	−52.2163	−	13.9913i	−0.277746	−	0.0744219i
$189$	400.582	+	693.829i	2.11948	+	3.67105i
$190$	−4.39906	−	7.89657i	−0.0231530	−	0.0415609i
$191$	77.7526	+	134.671i	0.407082	+	0.705086i	0.994561	−	0.104153i	$-0.0332131\pi$
$191$	77.7526	+	134.671i	0.407082	+	0.705086i	−0.587480	+	0.809239i	$0.699880\pi$
$192$	−11.8559	−	44.2467i	−0.0617493	−	0.230451i
$193$	−28.5204	−	106.440i	−0.147774	−	0.551501i	−0.999616	−	0.0277019i	$-0.991181\pi$
$193$	−28.5204	−	106.440i	−0.147774	−	0.551501i	0.851842	−	0.523799i	$-0.175486\pi$
$194$		−	5.21671i		−	0.0268902i
$195$	11.2355	−	372.017i	0.0576180	−	1.90778i
$196$	−81.0828			−0.413688
$197$	52.1908	−	13.9845i	0.264928	−	0.0709872i	−0.123910	−	0.992293i	$-0.539543\pi$
$197$	52.1908	−	13.9845i	0.264928	−	0.0709872i	0.388838	+	0.921306i	$0.372877\pi$
$198$	−349.467	+	93.6395i	−1.76499	+	0.472927i
$199$	86.1019	−	49.7110i	0.432673	−	0.249804i	−0.267812	−	0.963471i	$-0.586301\pi$
$199$	86.1019	−	49.7110i	0.432673	−	0.249804i	0.700485	+	0.713667i	$0.252967\pi$
$200$	68.8303	−	16.1986i	0.344151	−	0.0809931i
$201$	53.9656	−	31.1571i	0.268486	−	0.155010i
$202$	−46.1688	+	172.304i	−0.228558	+	0.852992i
$203$	−11.2444	+	11.2444i	−0.0553911	+	0.0553911i
$204$	−220.625	+	127.378i	−1.08150	+	0.624402i
$205$	−179.376	−	184.962i	−0.875003	−	0.902254i
$206$	109.348	+	63.1318i	0.530813	+	0.306465i
$207$	102.159	−	102.159i	0.493521	−	0.493521i
$208$	44.6420	+	26.6663i	0.214625	+	0.128203i
$209$		−	13.7488i		−	0.0657838i
$210$	5.87386	−	383.083i	0.0279708	−	1.82420i
$211$	−187.438	+	324.653i	−0.888334	+	1.53864i	−0.0464896	+	0.998919i	$0.514803\pi$
$211$	−187.438	+	324.653i	−0.888334	+	1.53864i	−0.841844	+	0.539721i	$0.818530\pi$
$212$	78.3929	+	21.0053i	0.369778	+	0.0990817i
$213$	23.7883	−	23.7883i	0.111682	−	0.111682i
$214$	33.7212	+	58.4068i	0.157576	+	0.272929i
$215$	71.3490	−	119.317i	0.331856	−	0.554964i
$216$		−	239.472i		−	1.10867i
$217$	86.5669	+	23.1955i	0.398926	+	0.106892i
$218$	198.480	−	53.1826i	0.910460	−	0.243957i
$219$	107.267	−	185.792i	0.489803	−	0.848363i
$220$	103.448	+	29.4260i	0.470220	+	0.133755i
$221$	78.9920	−	278.198i	0.357430	−	1.25881i
$222$	−23.0583	+	23.0583i	−0.103866	+	0.103866i
$223$	97.2233	+	362.842i	0.435979	+	1.62710i	0.738713	+	0.674020i	$0.235434\pi$
$223$	97.2233	+	362.842i	0.435979	+	1.62710i	−0.302734	+	0.953075i	$0.597899\pi$
$224$	46.3572	+	26.7644i	0.206952	+	0.119484i
$225$	594.381	+	18.2317i	2.64169	+	0.0810298i
$226$		−	241.102i		−	1.06682i
$227$	−82.6042	+	308.283i	−0.363895	+	1.35807i	0.505018	+	0.863109i	$0.331486\pi$
$227$	−82.6042	+	308.283i	−0.363895	+	1.35807i	−0.868913	+	0.494965i	$0.835181\pi$
$228$	14.1406	+	3.78895i	0.0620200	+	0.0166182i
$229$	−238.311			−1.04066			−0.520330	−	0.853965i	$-0.674191\pi$
$229$	−238.311			−1.04066			−0.520330	+	0.853965i	$0.674191\pi$
$230$	−41.6506	+	10.4785i	−0.181089	+	0.0455589i
$231$	291.372	−	504.671i	1.26135	−	2.18472i
$232$	4.59121	−	1.23021i	0.0197897	−	0.00530264i
$233$	244.087	+	244.087i	1.04758	+	1.04758i	0.998810	+	0.0487732i	$0.0155311\pi$
$233$	244.087	+	244.087i	1.04758	+	1.04758i	0.0487732	+	0.998810i	$0.484469\pi$
$234$	304.594	+	313.784i	1.30168	+	1.34096i
$235$	65.7706	+	118.062i	0.279875	+	0.502391i
$236$	−115.866	−	66.8955i	−0.490960	−	0.283456i
$237$	−6.80383	−	25.3922i	−0.0287081	−	0.107140i
$238$	77.0497	−	287.553i	0.323738	−	1.20821i
$239$	−321.683			−1.34595			−0.672977	−	0.739663i	$-0.734985\pi$
$239$	−321.683			−1.34595			−0.672977	+	0.739663i	$0.734985\pi$
$240$	−58.7732	+	98.2867i	−0.244888	+	0.409528i
$241$	280.135	−	161.736i	1.16239	−	0.671105i	0.210513	−	0.977591i	$-0.432487\pi$
$241$	280.135	−	161.736i	1.16239	−	0.671105i	0.951875	+	0.306486i	$0.0991533\pi$
$242$	−5.32541	−	5.32541i	−0.0220058	−	0.0220058i
$243$	203.977	−	761.253i	0.839412	−	3.13273i
$244$	−192.456	−	111.115i	−0.788755	−	0.455388i
$245$	141.121	+	145.516i	0.576004	+	0.593943i
$246$	417.285			1.69628
$247$	−14.5138	+	8.09442i	−0.0587605	+	0.0327709i
$248$	−18.9420	−	18.9420i	−0.0763791	−	0.0763791i
$249$	−142.721	+	247.200i	−0.573176	+	0.992770i
$250$	−148.867	−	95.3340i	−0.595469	−	0.381336i
$251$	−23.9973	−	41.5646i	−0.0956069	−	0.165596i	0.814255	−	0.580508i	$-0.197146\pi$
$251$	−23.9973	−	41.5646i	−0.0956069	−	0.165596i	−0.909862	+	0.414912i	$0.863813\pi$
$252$	318.314	+	318.314i	1.26315	+	1.26315i
$253$	−63.0994	−	16.9074i	−0.249405	−	0.0668278i
$254$	14.3582	+	24.8692i	0.0565285	+	0.0979102i
$255$	612.589	+	174.252i	2.40231	+	0.683340i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−47.5426	−	177.431i	−0.184991	−	0.690395i	−0.994633	−	0.103471i	$-0.967005\pi$
$257$	−47.5426	−	177.431i	−0.184991	−	0.690395i	0.809642	−	0.586924i	$-0.199661\pi$
$258$	58.2739	+	217.481i	0.225868	+	0.842950i
$259$		−	38.1059i		−	0.147127i
$260$	−29.8404	−	126.529i	−0.114771	−	0.486649i
$261$	39.9731			0.153154
$262$	217.070	−	58.1637i	0.828510	−	0.221999i
$263$	180.289	−	48.3082i	0.685508	−	0.183681i	0.100777	−	0.994909i	$-0.467867\pi$
$263$	180.289	−	48.3082i	0.685508	−	0.183681i	0.584730	+	0.811228i	$0.301200\pi$
$264$	−150.849	+	87.0925i	−0.571397	+	0.329896i
$265$	−98.7421	−	177.248i	−0.372612	−	0.668859i
$266$	−14.8151	+	8.55348i	−0.0556957	+	0.0321560i
$267$	91.6399	−	342.005i	0.343221	−	1.28092i
$268$	15.3906	−	15.3906i	0.0574275	−	0.0574275i
$269$	−214.275	+	123.712i	−0.796561	+	0.459895i	−0.842267	−	0.539060i	$-0.818779\pi$
$269$	−214.275	+	123.712i	−0.796561	+	0.459895i	0.0457064	+	0.998955i	$0.485446\pi$
$270$	−429.771	+	416.791i	−1.59175	+	1.54367i
$271$	−198.642	−	114.686i	−0.732997	−	0.423196i	0.0865208	−	0.996250i	$-0.472425\pi$
$271$	−198.642	−	114.686i	−0.732997	−	0.423196i	−0.819517	+	0.573054i	$0.805758\pi$
$272$	−62.9206	+	62.9206i	−0.231326	+	0.231326i
$273$	−704.294	−	10.4670i	−2.57983	−	0.0383406i
$274$			75.6801i			0.276205i
$275$	−127.238	−	236.870i	−0.462683	−	0.861344i
$276$	34.7784	−	60.2379i	0.126009	−	0.218253i
$277$	192.295	+	51.5254i	0.694207	+	0.186012i	0.588635	−	0.808399i	$-0.299666\pi$
$277$	192.295	+	51.5254i	0.694207	+	0.186012i	0.105573	+	0.994412i	$0.466332\pi$
$278$	−264.355	+	264.355i	−0.950917	+	0.950917i
$279$	−112.641	−	195.099i	−0.403730	−	0.699281i
$280$	−32.6498	−	129.778i	−0.116606	−	0.463492i
$281$			508.362i			1.80912i	0.426350	+	0.904558i	$0.359799\pi$
$281$			508.362i			1.80912i	−0.426350	+	0.904558i	$0.640201\pi$
$282$	−211.416	−	56.6488i	−0.749703	−	0.200882i
$283$	221.794	−	59.4296i	0.783725	−	0.209999i	0.155299	−	0.987868i	$-0.450366\pi$
$283$	221.794	−	59.4296i	0.783725	−	0.209999i	0.628427	+	0.777869i	$0.283699\pi$
$284$	5.87531	−	10.1763i	0.0206877	−	0.0358322i
$285$	−17.8112	−	31.9720i	−0.0624953	−	0.112183i
$286$	54.0094	−	190.213i	0.188844	−	0.665081i
$287$	−344.800	+	344.800i	−1.20139	+	1.20139i
$288$	−34.8257	−	129.971i	−0.120923	−	0.451290i
$289$	178.293	+	102.937i	0.616931	+	0.356185i
$290$	−10.1986	−	6.09854i	−0.0351677	−	0.0210295i
$291$		−	21.1217i		−	0.0725831i
$292$	19.3943	−	72.3806i	0.0664189	−	0.247879i
$293$	−410.129	−	109.894i	−1.39976	−	0.375064i	−0.521501	−	0.853251i	$-0.674628\pi$
$293$	−410.129	−	109.894i	−1.39976	−	0.375064i	−0.878258	+	0.478186i	$0.841294\pi$
$294$	−328.292			−1.11664
$295$	81.6058	+	324.370i	0.276630	+	1.09956i
$296$	−5.69502	+	9.86407i	−0.0192399	+	0.0333246i
$297$	−879.574	+	235.681i	−2.96153	+	0.793540i
$298$	−204.578	−	204.578i	−0.686504	−	0.686504i
$299$	19.3007	+	76.5645i	0.0645507	+	0.256069i
$300$	278.684	−	65.5858i	0.928945	−	0.218619i
$301$	−227.855	−	131.552i	−0.756993	−	0.437050i
$302$	51.4979	+	192.193i	0.170523	+	0.636400i
$303$	−186.931	+	697.635i	−0.616933	+	2.30243i
$304$	5.11336			0.0168203
$305$	135.549	+	538.784i	0.444422	+	1.76650i
$306$	−648.071	+	374.164i	−2.11788	+	1.22276i
$307$	−188.905	−	188.905i	−0.615324	−	0.615324i	0.329004	−	0.944328i	$-0.393287\pi$
$307$	−188.905	−	188.905i	−0.615324	−	0.615324i	−0.944328	+	0.329004i	$0.893287\pi$
$308$	52.6814	−	196.610i	0.171043	−	0.638343i
$309$	442.732	+	255.612i	1.43279	+	0.827222i
$310$	−1.02674	+	66.9623i	−0.00331207	+	0.216007i
$311$	−473.159			−1.52141			−0.760706	−	0.649097i	$-0.775147\pi$
$311$	−473.159			−1.52141			−0.760706	+	0.649097i	$0.775147\pi$
$312$	180.749	+	107.968i	0.579323	+	0.346051i
$313$	235.894	+	235.894i	0.753655	+	0.753655i	0.975159	−	0.221505i	$-0.0710968\pi$
$313$	235.894	+	235.894i	0.753655	+	0.753655i	−0.221505	+	0.975159i	$0.571097\pi$
$314$	−87.9079	+	152.261i	−0.279961	+	0.484907i
$315$	17.2540	−	1125.28i	0.0547747	−	3.57231i
$316$	−4.59103	−	7.95190i	−0.0145286	−	0.0251642i
$317$	−211.063	−	211.063i	−0.665814	−	0.665814i	0.290930	−	0.956744i	$-0.406035\pi$
$317$	−211.063	−	211.063i	−0.665814	−	0.665814i	−0.956744	+	0.290930i	$0.906035\pi$
$318$	317.401	+	85.0475i	0.998118	+	0.267445i
$319$	−9.03707	−	15.6527i	−0.0283294	−	0.0490679i
$320$	−10.9439	+	38.4738i	−0.0341997	+	0.120231i
$321$	136.532	+	236.481i	0.425334	+	0.736700i
$322$	21.0371	+	78.5115i	0.0653326	+	0.243824i
$323$	−7.36021	−	27.4687i	−0.0227870	−	0.0850423i
$324$		−	541.431i		−	1.67108i
$325$	−175.140	+	273.771i	−0.538894	+	0.842374i
$326$	220.464			0.676271
$327$	803.618	−	215.329i	2.45755	−	0.658498i
$328$	140.786	−	37.7235i	0.429225	−	0.115011i
$329$	221.501	−	127.883i	0.673254	−	0.388704i
$330$	418.847	+	119.142i	1.26923	+	0.361035i
$331$	111.208	−	64.2061i	0.335976	−	0.193976i	−0.322515	−	0.946564i	$-0.604528\pi$
$331$	111.208	−	64.2061i	0.335976	−	0.193976i	0.658491	+	0.752588i	$0.271195\pi$
$332$	−25.8046	+	96.3040i	−0.0777246	+	0.290072i
$333$	−67.7321	+	67.7321i	−0.203400	+	0.203400i
$334$	183.043	−	105.680i	0.548032	−	0.316406i
$335$	−54.4075	−	0.834236i	−0.162410	−	0.00249026i
$336$	187.694	+	108.365i	0.558612	+	0.322515i
$337$	109.270	−	109.270i	0.324244	−	0.324244i	−0.526149	−	0.850393i	$-0.676365\pi$
$337$	109.270	−	109.270i	0.324244	−	0.324244i	0.850393	+	0.526149i	$0.176365\pi$
$338$	−232.595	+	54.9706i	−0.688150	+	0.162635i
$339$		−	976.185i		−	2.87960i
$340$	222.432	+	3.41057i	0.654211	+	0.0100311i
$341$	−50.9314	+	88.2157i	−0.149359	+	0.258697i
$342$	41.5369	+	11.1298i	0.121453	+	0.0325432i
$343$	−56.5973	+	56.5973i	−0.165007	+	0.165007i
$344$	39.3216	+	68.1069i	0.114307	+	0.197985i
$345$	−168.637	+	42.4261i	−0.488803	+	0.122974i
$346$			12.3892i			0.0358069i
$347$	−168.363	−	45.1128i	−0.485197	−	0.130008i	0.00792445	−	0.999969i	$-0.497478\pi$
$347$	−168.363	−	45.1128i	−0.485197	−	0.130008i	−0.493122	+	0.869960i	$0.664144\pi$
$348$	18.5891	−	4.98095i	0.0534171	−	0.0143131i
$349$	−102.293	+	177.176i	−0.293103	+	0.507669i	−0.974542	−	0.224206i	$-0.928021\pi$
$349$	−102.293	+	177.176i	−0.293103	+	0.507669i	0.681439	+	0.731875i	$0.261354\pi$
$350$	−176.082	+	284.468i	−0.503090	+	0.812766i
$351$	766.633	+	789.763i	2.18414	+	2.25004i
$352$	−43.0208	+	43.0208i	−0.122218	+	0.122218i
$353$	75.5982	+	282.136i	0.214159	+	0.799253i	0.986461	+	0.163997i	$0.0524387\pi$
$353$	75.5982	+	282.136i	0.214159	+	0.799253i	−0.772302	+	0.635256i	$0.780895\pi$
$354$	−469.126	−	270.850i	−1.32522	−	0.765114i
$355$	−28.4888	+	7.16729i	−0.0802502	+	0.0201895i
$356$		−	123.672i		−	0.347393i
$357$	311.963	−	1164.26i	0.873845	−	3.26124i
$358$	−106.036	−	28.4121i	−0.296189	−	0.0793635i
$359$	−167.177			−0.465674			−0.232837	−	0.972516i	$-0.574801\pi$
$359$	−167.177			−0.465674			−0.232837	+	0.972516i	$0.574801\pi$
$360$	−172.642	+	288.710i	−0.479561	+	0.801972i
$361$	179.683	−	311.220i	0.497737	−	0.862105i
$362$	−91.8130	+	24.6012i	−0.253627	+	0.0679592i
$363$	−21.5618	−	21.5618i	−0.0593989	−	0.0593989i
$364$	−238.565	+	60.1384i	−0.655399	+	0.165215i
$365$	−163.654	+	91.1691i	−0.448366	+	0.249778i
$366$	−779.227	−	449.887i	−2.12903	−	1.22920i
$367$	132.450	+	494.309i	0.360898	+	1.34689i	0.872897	+	0.487905i	$0.162239\pi$
$367$	132.450	+	494.309i	0.360898	+	1.34689i	−0.511999	+	0.858986i	$0.671095\pi$
$368$	6.28809	−	23.4675i	0.0170872	−	0.0637703i
$369$	1225.74			3.32180
$370$	27.6146	−	6.94735i	0.0746341	−	0.0187766i
$371$	−332.541	+	191.993i	−0.896338	+	0.517501i
$372$	−76.6935	−	76.6935i	−0.206165	−	0.206165i
$373$	117.842	−	439.793i	0.315931	−	1.17907i	−0.607188	−	0.794558i	$-0.707703\pi$
$373$	117.842	−	439.793i	0.315931	−	1.17907i	0.923120	−	0.384513i	$-0.125631\pi$
$374$	293.030	+	169.181i	0.783503	+	0.452356i
$375$	−602.741	−	385.993i	−1.60731	−	1.02932i
$376$	−76.4500			−0.203324
$377$	−11.2032	+	18.7552i	−0.0297167	+	0.0497486i
$378$	801.165	+	801.165i	2.11948	+	2.11948i
$379$	−121.154	+	209.844i	−0.319667	+	0.553679i	−0.980418	−	0.196925i	$-0.936904\pi$
$379$	−121.154	+	209.844i	−0.319667	+	0.553679i	0.660752	+	0.750605i	$0.270238\pi$
$380$	−8.89958	−	9.17674i	−0.0234199	−	0.0241493i
$381$	58.1344	+	100.692i	0.152584	+	0.264283i
$382$	155.505	+	155.505i	0.407082	+	0.407082i
$383$	−141.713	−	37.9718i	−0.370007	−	0.0991430i	0.0690242	−	0.997615i	$-0.478011\pi$
$383$	−141.713	−	37.9718i	−0.370007	−	0.0991430i	−0.439031	+	0.898472i	$0.644678\pi$
$384$	−32.3908	−	56.1025i	−0.0843511	−	0.146100i
$385$	−444.537	+	247.645i	−1.15464	+	0.643234i
$386$	−77.9192	−	134.960i	−0.201863	−	0.349637i
$387$	171.175	+	638.835i	0.442313	+	1.65074i
$388$	−1.90945	−	7.12616i	−0.00492126	−	0.0183664i
$389$		−	703.661i		−	1.80890i	−0.426582	−	0.904449i	$-0.640282\pi$
$389$		−	703.661i		−	1.80890i	0.426582	−	0.904449i	$-0.359718\pi$
$390$	−120.820	−	512.297i	−0.309794	−	1.31358i
$391$	−135.117			−0.345568
$392$	−110.761	+	29.6784i	−0.282554	+	0.0757101i
$393$	878.883	−	235.496i	2.23634	−	0.599227i
$394$	66.1753	−	38.2063i	0.167958	−	0.0969704i
$395$	−6.28048	+	22.0793i	−0.0158999	+	0.0558969i
$396$	−443.107	+	255.828i	−1.11896	+	0.646030i
$397$	56.3735	−	210.389i	0.141999	−	0.529946i	−0.857872	−	0.513863i	$-0.828214\pi$
$397$	56.3735	−	210.389i	0.141999	−	0.529946i	0.999871	−	0.0160828i	$-0.00511955\pi$
$398$	99.4219	−	99.4219i	0.249804	−	0.249804i
$399$	−59.9840	+	34.6318i	−0.150336	+	0.0867965i
$400$	88.0948	−	47.3213i	0.220237	−	0.118303i
$401$	602.874	+	348.070i	1.50343	+	0.868004i	0.999992	+	0.00397127i	$0.00126410\pi$
$401$	602.874	+	348.070i	1.50343	+	0.868004i	0.503435	+	0.864033i	$0.332069\pi$
$402$	62.3141	−	62.3141i	0.155010	−	0.155010i
$403$	123.110	+	1.82961i	0.305483	+	0.00453998i
$404$			252.271i			0.624433i
$405$	−971.686	+	942.338i	−2.39923	+	2.32676i
$406$	−11.2444	+	19.4758i	−0.0276955	+	0.0479701i
$407$	41.8353	+	11.2097i	0.102790	+	0.0275424i
$408$	−254.756	+	254.756i	−0.624402	+	0.624402i
$409$	−350.975	−	607.906i	−0.858129	−	1.48632i	−0.873712	−	0.486444i	$-0.838294\pi$
$409$	−350.975	−	607.906i	−0.858129	−	1.48632i	0.0155826	−	0.999879i	$-0.495040\pi$
$410$	−312.733	−	187.007i	−0.762762	−	0.456114i
$411$			306.417i			0.745541i
$412$	172.479	+	46.2157i	0.418639	+	0.112174i
$413$	611.439	−	163.835i	1.48048	−	0.396694i
$414$	102.159	−	176.944i	0.246761	−	0.427402i
$415$	217.745	−	121.302i	0.524686	−	0.292295i
$416$	70.7426	+	20.0868i	0.170054	+	0.0482855i
$417$	−1070.33	+	1070.33i	−2.56675	+	2.56675i
$418$	−5.03241	−	18.7812i	−0.0120393	−	0.0449312i
$419$	503.791	+	290.864i	1.20237	+	0.694186i	0.961080	−	0.276269i	$-0.0890979\pi$
$419$	503.791	+	290.864i	1.20237	+	0.694186i	0.241285	+	0.970454i	$0.422431\pi$
$420$	−132.194	−	525.451i	−0.314748	−	1.25107i
$421$		−	360.258i		−	0.855721i	−0.903845	−	0.427860i	$-0.859268\pi$
$421$		−	360.258i		−	0.855721i	0.903845	−	0.427860i	$-0.140732\pi$
$422$	−137.214	+	512.091i	−0.325153	+	1.21349i
$423$	−621.019	−	166.402i	−1.46813	−	0.393385i
$424$	114.775			0.270696
$425$	−381.012	−	405.126i	−0.896499	−	0.953237i
$426$	23.7883	−	41.2025i	0.0558410	−	0.0967195i
$427$	1015.61	−	272.132i	2.37848	−	0.637311i
$428$	67.4424	+	67.4424i	0.157576	+	0.157576i
$429$	218.676	−	770.145i	0.509734	−	1.79521i
$430$	53.7914	−	189.106i	0.125096	−	0.439782i
$431$	417.479	+	241.032i	0.968629	+	0.559238i	0.898818	−	0.438322i	$-0.144427\pi$
$431$	417.479	+	241.032i	0.968629	+	0.559238i	0.0698108	+	0.997560i	$0.477760\pi$
$432$	−87.6528	−	327.125i	−0.202900	−	0.757234i
$433$	60.7377	−	226.676i	0.140272	−	0.523501i	−0.859649	−	0.510886i	$-0.829318\pi$
$433$	60.7377	−	226.676i	0.140272	−	0.523501i	0.999920	−	0.0126157i	$-0.00401582\pi$
$434$	126.743			0.292034
$435$	−41.2927	−	24.6921i	−0.0949258	−	0.0567634i
$436$	251.663	−	145.298i	0.577209	−	0.333252i
$437$	5.49027	+	5.49027i	0.0125635	+	0.0125635i
$438$	78.5247	−	293.058i	0.179280	−	0.669083i
$439$	−311.341	−	179.753i	−0.709204	−	0.409459i	0.101562	−	0.994829i	$-0.467616\pi$
$439$	−311.341	−	179.753i	−0.709204	−	0.409459i	−0.810766	+	0.585370i	$0.800949\pi$
$440$	152.084	+	2.33192i	0.345645	+	0.00529982i
$441$	−964.334			−2.18670
$442$	6.07750	−	408.939i	0.0137500	−	0.925201i
$443$	−199.318	−	199.318i	−0.449929	−	0.449929i	0.445402	−	0.895331i	$-0.353061\pi$
$443$	−199.318	−	199.318i	−0.449929	−	0.449929i	−0.895331	+	0.445402i	$0.853061\pi$
$444$	−23.0583	+	39.9382i	−0.0519331	+	0.0899508i
$445$	−221.949	+	215.246i	−0.498763	+	0.483699i
$446$	265.619	+	460.066i	0.595558	+	1.03154i
$447$	−828.307	−	828.307i	−1.85304	−	1.85304i
$448$	73.1216	+	19.5929i	0.163218	+	0.0437341i
$449$	166.720	+	288.768i	0.371314	+	0.643135i	0.989768	−	0.142686i	$-0.0455739\pi$
$449$	166.720	+	288.768i	0.371314	+	0.643135i	−0.618454	+	0.785821i	$0.712241\pi$
$450$	818.613	−	192.653i	1.81914	−	0.428119i
$451$	−277.115	−	479.976i	−0.614445	−	1.06425i
$452$	−88.2494	−	329.351i	−0.195242	−	0.728653i
$453$	208.507	+	778.160i	0.460281	+	1.71779i
$454$			451.357i			0.994179i
$455$	523.141	+	323.475i	1.14976	+	0.710935i
$456$	20.7032			0.0454018
$457$	47.4764	−	12.7213i	0.103887	−	0.0278365i	−0.206501	−	0.978446i	$-0.566208\pi$
$457$	47.4764	−	12.7213i	0.103887	−	0.0278365i	0.310388	+	0.950610i	$0.399541\pi$
$458$	−325.539	+	87.2279i	−0.710784	+	0.190454i
$459$	−1631.13	+	941.732i	−3.55366	+	2.05170i
$460$	−53.0603	+	29.5591i	−0.115348	+	0.0642590i
$461$	−210.116	+	121.311i	−0.455784	+	0.263147i	−0.710270	−	0.703930i	$-0.751427\pi$
$461$	−210.116	+	121.311i	−0.455784	+	0.263147i	0.254486	+	0.967076i	$0.418094\pi$
$462$	213.299	−	796.043i	0.461686	−	1.72304i
$463$	544.140	−	544.140i	1.17525	−	1.17525i	0.194307	−	0.980941i	$-0.437754\pi$
$463$	544.140	−	544.140i	1.17525	−	1.17525i	0.980941	−	0.194307i	$-0.0622459\pi$
$464$	5.82143	−	3.36100i	0.0125462	−	0.00724354i
$465$	−4.15712	+	271.120i	−0.00894005	+	0.583055i
$466$	422.771	+	244.087i	0.907234	+	0.523792i
$467$	−53.0807	+	53.0807i	−0.113663	+	0.113663i	−0.761651	−	0.647988i	$-0.775611\pi$
$467$	−53.0807	+	53.0807i	−0.113663	+	0.113663i	0.647988	+	0.761651i	$0.275611\pi$
$468$	530.936	+	317.148i	1.13448	+	0.677667i
$469$			102.980i			0.219573i
$470$	133.058	+	137.202i	0.283102	+	0.291919i
$471$	−355.926	+	616.482i	−0.755682	+	1.30888i
$472$	−182.762	−	48.9709i	−0.387208	−	0.103752i
$473$	211.456	−	211.456i	0.447053	−	0.447053i
$474$	−18.5884	−	32.1961i	−0.0392161	−	0.0679242i
$475$	−0.979816	+	31.9435i	−0.00206277	+	0.0672494i
$476$		−	421.007i		−	0.884469i
$477$	932.343	+	249.821i	1.95460	+	0.523733i
$478$	−439.427	+	117.744i	−0.919304	+	0.246327i
$479$	273.994	−	474.571i	0.572012	−	0.990754i	−0.424347	−	0.905500i	$-0.639496\pi$
$479$	273.994	−	474.571i	0.572012	−	0.990754i	0.996359	−	0.0852542i	$-0.0271702\pi$
$480$	−44.3102	+	155.775i	−0.0923130	+	0.324530i
$481$	−12.7965	−	50.7628i	−0.0266039	−	0.105536i
$482$	323.473	−	323.473i	0.671105	−	0.671105i
$483$	85.1761	+	317.881i	0.176348	+	0.658140i
$484$	−9.22388	−	5.32541i	−0.0190576	−	0.0110029i
$485$	−9.46573	+	15.8296i	−0.0195170	+	0.0326383i
$486$		−	1114.55i		−	2.29332i
$487$	−30.2836	+	113.020i	−0.0621840	+	0.232074i	−0.990023	−	0.140908i	$-0.954998\pi$
$487$	−30.2836	+	113.020i	−0.0621840	+	0.232074i	0.927839	+	0.372982i	$0.121665\pi$
$488$	−303.571	−	81.3416i	−0.622071	−	0.166684i
$489$	892.628			1.82541
$490$	246.038	+	147.125i	0.502118	+	0.300255i
$491$	166.770	−	288.854i	0.339654	−	0.588298i	−0.644714	−	0.764424i	$-0.723023\pi$
$491$	166.770	−	288.854i	0.339654	−	0.588298i	0.984368	+	0.176126i	$0.0563567\pi$
$492$	570.021	−	152.737i	1.15858	−	0.310441i
$493$	−26.4345	−	26.4345i	−0.0536197	−	0.0536197i
$494$	−16.8635	+	16.3696i	−0.0341367	+	0.0331369i
$495$	1230.33	+	349.969i	2.48552	+	0.707009i
$496$	−32.8085	−	18.9420i	−0.0661463	−	0.0381896i
$497$	14.3893	+	53.7016i	0.0289523	+	0.108051i
$498$	−104.479	+	389.920i	−0.209797	+	0.782973i
$499$	763.563			1.53019			0.765094	−	0.643919i	$-0.222693\pi$
$499$	763.563			1.53019			0.765094	+	0.643919i	$0.222693\pi$
$500$	−238.251	−	75.7395i	−0.476502	−	0.151479i
$501$	741.112	−	427.881i	1.47927	−	0.854055i
$502$	−47.9947	−	47.9947i	−0.0956069	−	0.0956069i
$503$	−58.4965	+	218.312i	−0.116295	+	0.434020i	−0.999381	−	0.0351926i	$-0.988796\pi$
$503$	−58.4965	+	218.312i	−0.116295	+	0.434020i	0.883085	+	0.469213i	$0.155462\pi$
$504$	551.336	+	318.314i	1.09392	+	0.631576i
$505$	452.741	−	439.067i	0.896517	−	0.869439i
$506$	−92.3839			−0.182577
$507$	−941.741	+	222.568i	−1.85748	+	0.438990i
$508$	28.7165	+	28.7165i	0.0565285	+	0.0565285i
$509$	139.196	−	241.095i	0.273470	−	0.473664i	−0.696278	−	0.717772i	$-0.745162\pi$
$509$	139.196	−	241.095i	0.273470	−	0.473664i	0.969748	+	0.244108i	$0.0784953\pi$
$510$	900.593	+	13.8089i	1.76587	+	0.0270763i
$511$	177.268	+	307.037i	0.346904	+	0.600855i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	104.544	+	28.0125i	0.203790	+	0.0546053i
$514$	−129.889	−	224.974i	−0.252702	−	0.437693i
$515$	−217.251	−	389.979i	−0.421847	−	0.757240i
$516$	159.207	+	275.755i	0.308541	+	0.534409i
$517$	75.2398	+	280.799i	0.145532	+	0.543131i
$518$	−13.9477	−	52.0536i	−0.0269261	−	0.100490i
$519$			50.1620i			0.0966512i
$520$	−87.0756	−	161.919i	−0.167453	−	0.311383i
$521$	−931.649			−1.78819			−0.894097	−	0.447874i	$-0.852181\pi$
$521$	−931.649			−1.78819			−0.894097	+	0.447874i	$0.852181\pi$
$522$	54.6043	−	14.6312i	0.104606	−	0.0280291i
$523$	−373.000	+	99.9451i	−0.713193	+	0.191100i	−0.597133	−	0.802143i	$-0.703693\pi$
$523$	−373.000	+	99.9451i	−0.713193	+	0.191100i	−0.116061	+	0.993242i	$0.537027\pi$
$524$	275.233	−	158.906i	0.525255	−	0.303256i
$525$	−712.928	+	1151.77i	−1.35796	+	2.19385i
$526$	228.597	−	131.980i	0.434595	−	0.250913i
$527$	−54.5306	+	203.511i	−0.103474	+	0.386169i
$528$	−174.185	+	174.185i	−0.329896	+	0.329896i
$529$	−426.179	+	246.054i	−0.805631	+	0.465131i
$530$	−199.761	−	205.983i	−0.376908	−	0.388647i
$531$	−1378.02	−	795.603i	−2.59515	−	1.49831i
$532$	−17.1070	+	17.1070i	−0.0321560	+	0.0321560i
$533$	−343.537	+	575.114i	−0.644535	+	1.07901i
$534$		−	500.730i		−	0.937696i
$535$	3.65567	−	238.417i	0.00683304	−	0.445639i
$536$	15.3906	−	26.6572i	0.0287137	−	0.0497337i
$537$	−429.322	−	115.037i	−0.799483	−	0.214221i
$538$	−247.423	+	247.423i	−0.459895	+	0.459895i
$539$	218.016	+	377.614i	0.404482	+	0.700583i
$540$	−434.522	+	726.654i	−0.804671	+	1.34566i
$541$		−	854.714i		−	1.57988i	−0.613186	−	0.789939i	$-0.710112\pi$
$541$		−	854.714i		−	1.57988i	0.613186	−	0.789939i	$-0.289888\pi$
$542$	−313.328	−	83.9560i	−0.578096	−	0.154900i
$543$	−371.737	+	99.6067i	−0.684599	+	0.183438i
$544$	−62.9206	+	108.982i	−0.115663	+	0.200334i
$545$	−698.769	−	198.765i	−1.28214	−	0.364707i
$546$	−965.915	+	243.492i	−1.76908	+	0.445955i
$547$	298.170	−	298.170i	0.545100	−	0.545100i	−0.379919	−	0.925020i	$-0.624048\pi$
$547$	298.170	−	298.170i	0.545100	−	0.545100i	0.925020	+	0.379919i	$0.124048\pi$
$548$	27.7008	+	103.381i	0.0505490	+	0.188651i
$549$	−2288.92	−	1321.51i	−4.16926	−	2.40712i
$550$	−260.510	−	276.998i	−0.473655	−	0.503632i
$551$			2.14825i			0.00389882i
$552$	25.4595	−	95.0163i	0.0461224	−	0.172131i
$553$	41.9630	+	11.2439i	0.0758824	+	0.0203326i
$554$	281.540			0.508195
$555$	111.807	−	28.1288i	0.201455	−	0.0506825i
$556$	−264.355	+	457.876i	−0.475458	+	0.823518i
$557$	602.072	−	161.325i	1.08092	−	0.289632i	0.325947	−	0.945388i	$-0.394317\pi$
$557$	602.072	−	161.325i	1.08092	−	0.289632i	0.754973	+	0.655756i	$0.227650\pi$
$558$	−225.281	−	225.281i	−0.403730	−	0.403730i
$559$	−347.714	−	98.7304i	−0.622028	−	0.176620i
$560$	−92.1024	−	165.329i	−0.164469	−	0.295230i
$561$	1186.44	+	684.989i	2.11486	+	1.22101i
$562$	186.073	+	694.435i	0.331091	+	1.23565i
$563$	50.9552	−	190.167i	0.0905066	−	0.337775i	−0.905793	−	0.423720i	$-0.860724\pi$
$563$	50.9552	−	190.167i	0.0905066	−	0.337775i	0.996300	+	0.0859447i	$0.0273908\pi$
$564$	−309.535			−0.548820
$565$	−437.479	+	731.599i	−0.774300	+	1.29487i
$566$	281.224	−	162.365i	0.496862	−	0.286863i
$567$	1811.38	+	1811.38i	3.19468	+	3.19468i
$568$	4.30103	−	16.0517i	0.00757223	−	0.0282600i
$569$	431.859	+	249.334i	0.758980	+	0.438197i	0.828929	−	0.559353i	$-0.188950\pi$
$569$	431.859	+	249.334i	0.758980	+	0.438197i	−0.0699496	+	0.997551i	$0.522284\pi$
$570$	−36.0331	−	37.1553i	−0.0632159	−	0.0651847i
$571$	969.122			1.69724			0.848618	−	0.529006i	$-0.177435\pi$
$571$	969.122			1.69724			0.848618	+	0.529006i	$0.177435\pi$
$572$	4.15539	−	279.605i	0.00726466	−	0.488819i
$573$	629.618	+	629.618i	1.09881	+	1.09881i
$574$	−344.800	+	597.211i	−0.600697	+	1.04044i
$575$	145.398	+	43.7789i	0.252866	+	0.0761372i
$576$	−95.1457	−	164.797i	−0.165183	−	0.286106i
$577$	309.490	+	309.490i	0.536378	+	0.536378i	0.922463	−	0.386085i	$-0.126173\pi$
$577$	309.490	+	309.490i	0.536378	+	0.536378i	−0.386085	+	0.922463i	$0.626173\pi$
$578$	281.230	+	75.3555i	0.486558	+	0.130373i
$579$	−315.483	−	546.433i	−0.544876	−	0.943753i
$580$	−16.1638	−	4.59781i	−0.0278686	−	0.00792726i
$581$	−235.859	−	408.520i	−0.405953	−	0.703132i
$582$	−7.73107	−	28.8528i	−0.0132836	−	0.0495752i
$583$	−112.958	−	421.566i	−0.193754	−	0.723098i
$584$		−	105.973i		−	0.181460i
$585$	−354.898	−	1504.83i	−0.606664	−	2.57237i
$586$	−600.471			−1.02469
$587$	−623.550	+	167.080i	−1.06227	+	0.284633i	−0.747312	−	0.664474i	$-0.768656\pi$
$587$	−623.550	+	167.080i	−1.06227	+	0.284633i	−0.314954	+	0.949107i	$0.601989\pi$
$588$	−448.456	+	120.163i	−0.762679	+	0.204359i
$589$	10.4851	−	6.05358i	0.0178016	−	0.0102777i
$590$	230.203	+	413.228i	0.390175	+	0.700386i
$591$	267.934	−	154.692i	0.453357	−	0.261746i
$592$	−4.16905	+	15.5591i	−0.00704231	+	0.0262822i
$593$	−536.796	+	536.796i	−0.905221	+	0.905221i	−0.995882	−	0.0906604i	$-0.971102\pi$
$593$	−536.796	+	536.796i	−0.905221	+	0.905221i	0.0906604	+	0.995882i	$0.471102\pi$
$594$	−1115.26	+	643.893i	−1.87753	+	1.08400i
$595$	−755.566	+	732.745i	−1.26986	+	1.23150i
$596$	−354.340	−	204.578i	−0.594530	−	0.343252i
$597$	402.545	−	402.545i	0.674279	−	0.674279i
$598$	54.3898	+	97.5246i	0.0909528	+	0.163085i
$599$			698.216i			1.16564i	0.812602	+	0.582818i	$0.198050\pi$
$599$			698.216i			1.16564i	−0.812602	+	0.582818i	$0.801950\pi$
$600$	356.683	−	191.597i	0.594471	−	0.319329i
$601$	435.765	−	754.767i	0.725066	−	1.25585i	−0.233881	−	0.972265i	$-0.575142\pi$
$601$	435.765	−	754.767i	0.725066	−	1.25585i	0.958947	−	0.283586i	$-0.0915242\pi$
$602$	−359.407	−	96.3028i	−0.597022	−	0.159971i
$603$	183.043	−	183.043i	0.303554	−	0.303554i
$604$	140.695	+	243.691i	0.232938	+	0.403461i
$605$	6.49646	+	25.8224i	0.0107380	+	0.0426816i
$606$			1021.41i			1.68549i
$607$	18.8959	+	5.06313i	0.0311299	+	0.00834123i	0.274350	−	0.961630i	$-0.411537\pi$
$607$	18.8959	+	5.06313i	0.0311299	+	0.00834123i	−0.243220	+	0.969971i	$0.578204\pi$
$608$	6.98497	−	1.87162i	0.0114884	−	0.00307832i
$609$	−45.5268	+	78.8548i	−0.0747567	+	0.129482i
$610$	382.371	+	686.378i	0.626838	+	1.12521i
$611$	252.127	−	244.743i	0.412647	−	0.400561i
$612$	−748.327	+	748.327i	−1.22276	+	1.22276i
$613$	−197.196	−	735.947i	−0.321691	−	1.20057i	−0.917597	−	0.397512i	$-0.869874\pi$
$613$	−197.196	−	735.947i	−0.321691	−	1.20057i	0.595906	−	0.803054i	$-0.296793\pi$
$614$	−327.192	−	188.905i	−0.532886	−	0.307662i
$615$	−1266.21	−	757.163i	−2.05888	−	1.23116i
$616$		−	287.856i		−	0.467299i
$617$	221.597	−	827.010i	0.359152	−	1.34037i	−0.516027	−	0.856573i	$-0.672589\pi$
$617$	221.597	−	827.010i	0.359152	−	1.34037i	0.875178	−	0.483800i	$-0.160744\pi$
$618$	698.344	+	187.121i	1.13001	+	0.302784i
$619$	904.370			1.46102			0.730509	−	0.682903i	$-0.239283\pi$
$619$	904.370			1.46102			0.730509	+	0.682903i	$0.239283\pi$
$620$	23.1073	+	91.8480i	0.0372699	+	0.148142i
$621$	257.124	−	445.351i	0.414048	−	0.717152i
$622$	−646.347	+	173.188i	−1.03914	+	0.278438i
$623$	413.750	+	413.750i	0.664126	+	0.664126i
$624$	286.427	+	81.3284i	0.459017	+	0.130334i
$625$	278.739	+	559.401i	0.445982	+	0.895042i
$626$	408.580	+	235.894i	0.652684	+	0.376827i
$627$	−20.3755	−	76.0424i	−0.0324968	−	0.121280i
$628$	−64.3530	+	240.169i	−0.102473	+	0.382434i
$629$	89.5835			0.142422
$630$	−388.311	−	1543.47i	−0.616367	−	2.44996i
$631$	461.063	−	266.195i	0.730686	−	0.421861i	−0.0879874	−	0.996122i	$-0.528044\pi$
$631$	461.063	−	266.195i	0.730686	−	0.421861i	0.818673	+	0.574260i	$0.194710\pi$
$632$	−9.18206	−	9.18206i	−0.0145286	−	0.0145286i
$633$	−555.561	+	2073.38i	−0.877664	+	3.27549i
$634$	−365.572	−	211.063i	−0.576612	−	0.332907i
$635$	1.55656	−	101.516i	0.00245128	−	0.159868i
$636$	464.708			0.730673
$637$	270.272	−	452.462i	0.424290	−	0.710302i
$638$	−18.0741	−	18.0741i	−0.0283294	−	0.0283294i
$639$	69.8763	−	121.029i	0.109353	−	0.189404i
$640$	−0.867270	+	56.5619i	−0.00135511	+	0.0883780i
$641$	304.484	+	527.382i	0.475015	+	0.822749i	0.999591	−	0.0286143i	$-0.00910946\pi$
$641$	304.484	+	527.382i	0.475015	+	0.822749i	−0.524576	+	0.851364i	$0.675776\pi$
$642$	273.064	+	273.064i	0.425334	+	0.425334i
$643$	−794.150	−	212.792i	−1.23507	−	0.330936i	−0.418519	−	0.908208i	$-0.637451\pi$
$643$	−794.150	−	212.792i	−1.23507	−	0.330936i	−0.816552	+	0.577272i	$0.804117\pi$
$644$	57.4744	+	99.5486i	0.0892459	+	0.154579i
$645$	217.794	−	765.663i	0.337664	−	1.18707i
$646$	−20.1085	−	34.8289i	−0.0311276	−	0.0539147i
$647$	−202.193	−	754.596i	−0.312509	−	1.16630i	−0.926286	−	0.376821i	$-0.877017\pi$
$647$	−202.193	−	754.596i	−0.312509	−	1.16630i	0.613777	−	0.789480i	$-0.289649\pi$
$648$	−198.178	−	739.609i	−0.305830	−	1.14137i
$649$			719.476i			1.10859i
$650$	−139.039	+	438.085i	−0.213906	+	0.673976i
$651$	513.163			0.788269
$652$	301.160	−	80.6956i	0.461902	−	0.123766i
$653$	377.721	−	101.210i	0.578439	−	0.154992i	0.0422748	−	0.999106i	$-0.486540\pi$
$653$	377.721	−	101.210i	0.578439	−	0.154992i	0.536164	+	0.844114i	$0.319873\pi$
$654$	1018.95	−	588.289i	1.55802	−	0.899524i
$655$	−764.215	−	217.382i	−1.16674	−	0.331880i
$656$	178.509	−	103.062i	0.272118	−	0.157107i
$657$	230.661	−	860.837i	0.351082	−	1.31025i
$658$	255.767	−	255.767i	0.388704	−	0.388704i
$659$	−597.928	+	345.214i	−0.907326	+	0.523845i	−0.879570	−	0.475770i	$-0.842169\pi$
$659$	−597.928	+	345.214i	−0.907326	+	0.523845i	−0.0277560	+	0.999615i	$0.508836\pi$
$660$	615.765	+	9.44160i	0.932977	+	0.0143055i
$661$	−686.512	−	396.358i	−1.03860	−	0.599634i	−0.119161	−	0.992875i	$-0.538020\pi$
$661$	−686.512	−	396.358i	−1.03860	−	0.599634i	−0.919435	+	0.393241i	$0.871354\pi$
$662$	128.412	−	128.412i	0.193976	−	0.193976i
$663$	24.6069	−	1655.73i	0.0371145	−	2.49733i
$664$			140.999i			0.212348i
$665$	60.4751	+	0.927273i	0.0909401	+	0.00139440i
$666$	−67.7321	+	117.315i	−0.101700	+	0.176149i
$667$	9.85927	+	2.64178i	0.0147815	+	0.00396070i
$668$	211.359	−	211.359i	0.316406	−	0.316406i
$669$	1075.45	+	1862.74i	1.60755	+	2.78436i
$670$	−74.6273	+	18.7749i	−0.111384	+	0.0280223i
$671$			1195.06i			1.78102i
$672$	296.059	+	79.3287i	0.440563	+	0.118049i
$673$	−637.376	+	170.784i	−0.947067	+	0.253766i	−0.699117	−	0.715007i	$-0.746423\pi$
$673$	−637.376	+	170.784i	−0.947067	+	0.253766i	−0.247950	+	0.968773i	$0.579757\pi$
$674$	109.270	−	189.261i	0.162122	−	0.280803i
$675$	2060.37	−	484.889i	3.05239	−	0.718355i
$676$	−297.609	+	160.227i	−0.440251	+	0.237022i
$677$	647.655	−	647.655i	0.956655	−	0.956655i	−0.0424438	−	0.999099i	$-0.513514\pi$
$677$	647.655	−	647.655i	0.956655	−	0.956655i	0.999099	+	0.0424438i	$0.0135143\pi$
$678$	−357.309	−	1333.49i	−0.527004	−	1.96681i
$679$	30.2290	+	17.4527i	0.0445199	+	0.0257036i
$680$	305.096	−	76.7567i	0.448670	−	0.112878i
$681$			1827.48i			2.68352i
$682$	−37.2844	+	139.147i	−0.0546691	+	0.204028i
$683$	−125.098	−	33.5199i	−0.183160	−	0.0490774i	0.166073	−	0.986113i	$-0.446891\pi$
$683$	−125.098	−	33.5199i	−0.183160	−	0.0490774i	−0.349233	+	0.937036i	$0.613558\pi$
$684$	60.8142			0.0889097
$685$	137.322	−	229.644i	0.200470	−	0.335246i
$686$	−56.5973	+	98.0294i	−0.0825034	+	0.142900i
$687$	−1318.06	+	353.173i	−1.91857	+	0.514080i
$688$	78.6431	+	78.6431i	0.114307	+	0.114307i
$689$	−378.521	+	367.435i	−0.549378	+	0.533288i
$690$	−214.833	+	119.681i	−0.311353	+	0.173450i
$691$	52.5682	+	30.3503i	0.0760755	+	0.0439222i	0.537555	−	0.843229i	$-0.319348\pi$
$691$	52.5682	+	30.3503i	0.0760755	+	0.0439222i	−0.461480	+	0.887151i	$0.652681\pi$
$692$	4.53476	+	16.9239i	0.00655311	+	0.0244566i
$693$	626.551	−	2338.32i	0.904113	−	3.37420i
$694$	−246.501			−0.355189
$695$	1281.83	−	322.486i	1.84436	−	0.464009i
$696$	23.5701	−	13.6082i	0.0338651	−	0.0195520i
$697$	−810.593	−	810.593i	−1.16297	−	1.16297i
$698$	−74.8836	+	279.469i	−0.107283	+	0.400386i
$699$	1711.74	+	988.272i	2.44884	+	1.41384i
$700$	−136.409	+	453.041i	−0.194871	+	0.647201i
$701$	−1093.57			−1.56001			−0.780006	−	0.625772i	$-0.784784\pi$
$701$	−1093.57			−1.56001			−0.780006	+	0.625772i	$0.784784\pi$
$702$	1336.31	+	798.230i	1.90358	+	1.13708i
$703$	−3.64009	−	3.64009i	−0.00517793	−	0.00517793i
$704$	−43.0208	+	74.5143i	−0.0611092	+	0.105844i
$705$	538.732	+	555.510i	0.764159	+	0.787957i
$706$	206.538	+	357.734i	0.292547	+	0.506706i
$707$	−843.984	−	843.984i	−1.19375	−	1.19375i
$708$	−739.977	−	198.276i	−1.04516	−	0.280051i
$709$	296.125	+	512.904i	0.417666	+	0.723419i	0.995704	−	0.0925905i	$-0.0295147\pi$
$709$	296.125	+	512.904i	0.417666	+	0.723419i	−0.578038	+	0.816010i	$0.696181\pi$
$710$	−36.2930	+	20.2183i	−0.0511170	+	0.0284765i
$711$	−54.6021	−	94.5736i	−0.0767962	−	0.133015i
$712$	−45.2671	−	168.939i	−0.0635774	−	0.237274i
$713$	−14.8886	−	55.5652i	−0.0208817	−	0.0779315i
$714$		−	1704.60i		−	2.38739i
$715$	−509.028	+	479.182i	−0.711927	+	0.670185i
$716$	−155.247			−0.216825
$717$	−1779.18	+	476.729i	−2.48142	+	0.664894i
$718$	−228.368	+	61.1910i	−0.318061	+	0.0852242i
$719$	−349.555	+	201.816i	−0.486169	+	0.280690i	−0.722984	−	0.690865i	$-0.757230\pi$
$719$	−349.555	+	201.816i	−0.486169	+	0.280690i	0.236815	+	0.971555i	$0.423896\pi$
$720$	−130.158	+	457.577i	−0.180775	+	0.635523i
$721$	−731.654	+	422.421i	−1.01478	+	0.585882i
$722$	131.537	−	490.903i	0.182184	−	0.679921i
$723$	1309.69	−	1309.69i	1.81147	−	1.81147i
$724$	−116.414	+	67.2118i	−0.160793	+	0.0928340i
$725$	19.8809	+	37.0108i	0.0274219	+	0.0510494i
$726$	−37.3461	−	21.5618i	−0.0514410	−	0.0296995i
$727$	−931.292	+	931.292i	−1.28101	+	1.28101i	−0.340912	+	0.940095i	$0.610736\pi$
$727$	−931.292	+	931.292i	−1.28101	+	1.28101i	−0.940095	+	0.340912i	$0.889264\pi$
$728$	−303.874	+	169.472i	−0.417409	+	0.232791i
$729$		−	2076.22i		−	2.84803i
$730$	−190.185	+	184.441i	−0.260527	+	0.252658i
$731$	309.267	−	535.666i	0.423074	−	0.732785i
$732$	−1229.11	−	329.340i	−1.67912	−	0.449918i
$733$	72.7371	−	72.7371i	0.0992321	−	0.0992321i	−0.655748	−	0.754980i	$-0.727647\pi$
$733$	72.7371	−	72.7371i	0.0992321	−	0.0992321i	0.754980	+	0.655748i	$0.227647\pi$
$734$	361.859	+	626.759i	0.492996	+	0.853895i
$735$	996.170	+	595.687i	1.35533	+	0.810458i
$736$		−	34.3588i		−	0.0466831i
$737$	−113.058	−	30.2939i	−0.153403	−	0.0411043i
$738$	1674.40	−	448.653i	2.26883	−	0.607931i
$739$	374.607	−	648.839i	0.506911	−	0.877996i	−0.493057	−	0.869997i	$-0.664121\pi$
$739$	374.607	−	648.839i	0.506911	−	0.877996i	0.999968	−	0.00799871i	$-0.00254610\pi$
$740$	35.1793	−	19.5979i	0.0475397	−	0.0264837i
$741$	−68.2779	+	66.2782i	−0.0921429	+	0.0894443i
$742$	−383.986	+	383.986i	−0.517501	+	0.517501i
$743$	−107.249	−	400.259i	−0.144346	−	0.538706i	−0.999784	−	0.0208006i	$-0.993378\pi$
$743$	−107.249	−	400.259i	−0.144346	−	0.538706i	0.855438	−	0.517906i	$-0.173288\pi$
$744$	−132.837	−	76.6935i	−0.178544	−	0.103083i
$745$	249.565	+	991.980i	0.334986	+	1.33152i
$746$		−	643.902i		−	0.863140i
$747$	−306.899	+	1145.36i	−0.410842	+	1.53328i
$748$	462.211	+	123.849i	0.617929	+	0.165574i
$749$	−451.263			−0.602487
$750$	−964.643	−	306.658i	−1.28619	−	0.408878i
$751$	−514.646	+	891.393i	−0.685281	+	1.18694i	0.288068	+	0.957610i	$0.406987\pi$
$751$	−514.646	+	891.393i	−0.685281	+	1.18694i	−0.973348	+	0.229331i	$0.926346\pi$
$752$	−104.433	+	27.9826i	−0.138873	+	0.0372110i
$753$	−194.323	−	194.323i	−0.258066	−	0.258066i
$754$	−8.43896	+	29.7208i	−0.0111923	+	0.0394175i
$755$	192.469	−	676.632i	0.254925	−	0.896202i
$756$	1387.66	+	801.165i	1.83553	+	1.05974i
$757$	217.431	+	811.462i	0.287227	+	1.07194i	0.947197	+	0.320653i	$0.103902\pi$
$757$	217.431	+	811.462i	0.287227	+	1.07194i	−0.659970	+	0.751292i	$0.729431\pi$
$758$	−88.6907	+	330.998i	−0.117006	+	0.436673i
$759$	−374.049			−0.492818
$760$	−15.5160	−	9.27819i	−0.0204157	−	0.0122081i
$761$	352.995	−	203.802i	0.463857	−	0.267808i	−0.249807	−	0.968296i	$-0.580367\pi$
$761$	352.995	−	203.802i	0.463857	−	0.267808i	0.713665	+	0.700487i	$0.247034\pi$
$762$	116.269	+	116.269i	0.152584	+	0.152584i
$763$	−355.850	+	1328.05i	−0.466383	+	1.74056i
$764$	269.343	+	155.505i	0.352543	+	0.203541i
$765$	2645.43	+	40.5626i	3.45807	+	0.0530231i
$766$	−207.482			−0.270864
$767$	759.510	−	423.582i	0.990235	−	0.552257i
$768$	−64.7816	−	64.7816i	−0.0843511	−	0.0843511i
$769$	396.676	−	687.062i	0.515833	−	0.893449i	−0.483998	−	0.875069i	$-0.660816\pi$
$769$	396.676	−	687.062i	0.515833	−	0.893449i	0.999831	−	0.0183801i	$-0.00585090\pi$
$770$	−516.605	+	501.002i	−0.670915	+	0.650652i
$771$	−525.901	−	910.887i	−0.682102	−	1.18144i
$772$	−155.838	−	155.838i	−0.201863	−	0.201863i
$773$	−828.928	−	222.111i	−1.07235	−	0.287336i	−0.320893	−	0.947116i	$-0.603983\pi$
$773$	−828.928	−	222.111i	−1.07235	−	0.287336i	−0.751459	+	0.659780i	$0.770650\pi$
$774$	467.659	+	810.010i	0.604211	+	1.04652i
$775$	124.619	−	201.327i	0.160798	−	0.259777i
$776$	−5.21671	−	9.03560i	−0.00672256	−	0.0116438i
$777$	−56.4723	−	210.758i	−0.0726799	−	0.271245i
$778$	−257.558	−	961.219i	−0.331051	−	1.23550i
$779$			65.8744i			0.0845627i
$780$	−352.556	−	655.587i	−0.451995	−	0.840496i
$781$	−63.1903			−0.0809094
$782$	−184.573	+	49.4563i	−0.236027	+	0.0632433i
$783$	137.433	−	36.8252i	0.175522	−	0.0470309i
$784$	−140.439	+	81.0828i	−0.179132	+	0.103422i
$785$	543.025	−	302.512i	0.691752	−	0.385365i
$786$	1114.38	−	643.387i	1.41779	−	0.818559i
$787$	156.560	−	584.289i	0.198932	−	0.742426i	−0.792281	−	0.610156i	$-0.791107\pi$
$787$	156.560	−	584.289i	0.198932	−	0.742426i	0.991214	−	0.132270i	$-0.0422265\pi$
$788$	76.4127	−	76.4127i	0.0969704	−	0.0969704i
$789$	925.554	−	534.369i	1.17307	−	0.677274i
$790$	−0.497708	+	32.4597i	−0.000630011	+	0.0410882i
$791$	1397.10	+	806.617i	1.76625	+	1.01974i
$792$	−511.656	+	511.656i	−0.646030	+	0.646030i
$793$	1261.56	−	703.576i	1.59087	−	0.887233i
$794$		−	308.030i		−	0.387948i
$795$	−808.804	−	833.993i	−1.01736	−	1.04905i
$796$	99.4219	−	172.204i	0.124902	−	0.216336i
$797$	1268.00	+	339.759i	1.59096	+	0.426297i	0.942298	−	0.334776i	$-0.108661\pi$
$797$	1268.00	+	339.759i	1.59096	+	0.426297i	0.648666	+	0.761073i	$0.275327\pi$
$798$	−69.2636	+	69.2636i	−0.0867965	+	0.0867965i
$799$	300.642	+	520.728i	0.376273	+	0.651724i
$800$	103.019	−	96.8871i	0.128774	−	0.121109i
$801$		−	1470.86i		−	1.83628i
$802$	950.944	+	254.805i	1.18572	+	0.317712i
$803$	−389.234	+	104.295i	−0.484725	+	0.129882i
$804$	62.3141	−	107.931i	0.0775051	−	0.134243i
$805$	78.6243	−	276.407i	0.0976699	−	0.343363i
$806$	168.840	−	42.5619i	0.209480	−	0.0528064i
$807$	−1001.78	+	1001.78i	−1.24136	+	1.24136i
$808$	92.3376	+	344.609i	0.114279	+	0.426496i
$809$	−886.121	−	511.602i	−1.09533	−	0.632388i	−0.160338	−	0.987062i	$-0.551259\pi$
$809$	−886.121	−	511.602i	−1.09533	−	0.632388i	−0.934990	+	0.354674i	$0.884592\pi$
$810$	−982.428	+	1642.92i	−1.21287	+	2.02830i
$811$			1301.46i			1.60476i	0.596810	+	0.802382i	$0.296434\pi$
$811$			1301.46i			1.60476i	−0.596810	+	0.802382i	$0.703566\pi$
$812$	−8.23146	+	30.7202i	−0.0101373	+	0.0378328i
$813$	−1268.62	−	339.926i	−1.56042	−	0.418113i
$814$	61.2512			0.0752471
$815$	−668.977	−	400.033i	−0.820831	−	0.490838i
$816$	−254.756	+	441.251i	−0.312201	+	0.540748i
$817$	−34.3325	+	9.19937i	−0.0420227	+	0.0112599i
$818$	−701.949	−	701.949i	−0.858129	−	0.858129i
$819$	−2837.31	+	715.238i	−3.46435	+	0.873307i
$820$	−495.650	−	140.988i	−0.604451	−	0.171937i
$821$	187.633	+	108.330i	0.228542	+	0.131949i	0.609899	−	0.792479i	$-0.291210\pi$
$821$	187.633	+	108.330i	0.228542	+	0.131949i	−0.381357	+	0.924428i	$0.624543\pi$
$822$	112.157	+	418.574i	0.136444	+	0.509214i
$823$	−388.594	+	1450.25i	−0.472168	+	1.76216i	0.159788	+	0.987151i	$0.448919\pi$
$823$	−388.594	+	1450.25i	−0.472168	+	1.76216i	−0.631956	+	0.775004i	$0.717748\pi$
$824$	252.527			0.306465
$825$	−1054.77	−	1121.52i	−1.27851	−	1.35942i
$826$	775.273	−	447.604i	0.938587	−	0.541894i
$827$	−230.849	−	230.849i	−0.279140	−	0.279140i	0.553626	−	0.832766i	$-0.313244\pi$
$827$	−230.849	−	230.849i	−0.279140	−	0.279140i	−0.832766	+	0.553626i	$0.813244\pi$
$828$	74.7855	−	279.103i	0.0903207	−	0.337081i
$829$	151.614	+	87.5347i	0.182888	+	0.105591i	0.588649	−	0.808389i	$-0.299660\pi$
$829$	151.614	+	87.5347i	0.182888	+	0.105591i	−0.405761	+	0.913979i	$0.632993\pi$
$830$	253.045	−	245.402i	0.304874	−	0.295665i
$831$	1139.91			1.37174
$832$	103.989	+	1.54544i	0.124986	+	0.00185750i
$833$	637.722	+	637.722i	0.765573	+	0.765573i
$834$	−1070.33	+	1853.87i	−1.28337	+	2.22287i
$835$	−747.180	−	11.4566i	−0.894827	−	0.0137205i
$836$	−13.7488	−	23.8136i	−0.0164459	−	0.0284852i
$837$	−567.011	−	567.011i	−0.677432	−	0.677432i
$838$	794.655	+	212.927i	0.948276	+	0.254090i
$839$	−187.023	−	323.933i	−0.222911	−	0.386094i	0.732779	−	0.680466i	$-0.238223\pi$
$839$	−187.023	−	323.933i	−0.222911	−	0.386094i	−0.955691	+	0.294373i	$0.904889\pi$
$840$	−372.909	−	669.393i	−0.443939	−	0.796896i
$841$	−419.088	−	725.882i	−0.498321	−	0.863117i
$842$	−131.864	−	492.122i	−0.156608	−	0.584468i
$843$	753.384	+	2811.67i	0.893693	+	3.33531i
$844$			749.754i			0.888334i
$845$	805.529	+	255.240i	0.953289	+	0.302060i
$846$	−909.236			−1.07475
$847$	48.6753	−	13.0425i	0.0574679	−	0.0153985i
$848$	156.786	−	42.0106i	0.184889	−	0.0495409i
$849$	1138.63	−	657.391i	1.34115	−	0.774312i
$850$	−668.758	−	413.952i	−0.786774	−	0.487002i
$851$	−21.1823	+	12.2296i	−0.0248911	+	0.0143709i
$852$	17.4142	−	64.9908i	0.0204392	−	0.0762803i
$853$	−185.625	+	185.625i	−0.217614	+	0.217614i	−0.807492	−	0.589878i	$-0.799176\pi$
$853$	−185.625	+	185.625i	−0.217614	+	0.217614i	0.589878	+	0.807492i	$0.299176\pi$
$854$	1287.74	−	743.478i	1.50789	−	0.870583i
$855$	−105.845	−	109.141i	−0.123795	−	0.127650i
$856$	116.814	+	67.4424i	0.136465	+	0.0787878i
$857$	−429.506	+	429.506i	−0.501173	+	0.501173i	−0.911802	−	0.410629i	$-0.865309\pi$
$857$	−429.506	+	429.506i	−0.501173	+	0.501173i	0.410629	+	0.911802i	$0.365309\pi$
$858$	16.8246	−	1132.08i	0.0196090	−	1.31944i
$859$		−	159.919i		−	0.186169i	−0.995658	−	0.0930846i	$-0.970327\pi$
$859$		−	159.919i		−	0.186169i	0.995658	−	0.0930846i	$-0.0296727\pi$
$860$	4.26280	−	278.013i	0.00495675	−	0.323271i
$861$	−1396.04	+	2418.02i	−1.62142	+	2.80839i
$862$	658.511	+	176.447i	0.763933	+	0.204695i
$863$	594.605	−	594.605i	0.688997	−	0.688997i	−0.273013	−	0.962010i	$-0.588020\pi$
$863$	594.605	−	594.605i	0.688997	−	0.688997i	0.962010	+	0.273013i	$0.0880202\pi$
$864$	−239.472	−	414.778i	−0.277167	−	0.480067i
$865$	22.4802	−	37.5937i	0.0259887	−	0.0434610i
$866$		−	331.877i		−	0.383230i
$867$	1138.66	+	305.103i	1.31333	+	0.351907i
$868$	173.134	−	46.3911i	0.199463	−	0.0534460i
$869$	−24.6888	+	42.7622i	−0.0284105	+	0.0492085i
$870$	−65.4448	−	18.6158i	−0.0752240	−	0.0213975i
$871$	34.5820	+	137.184i	0.0397037	+	0.157502i
$872$	290.595	−	290.595i	0.333252	−	0.333252i
$873$	−22.7095	−	84.7528i	−0.0260131	−	0.0970823i
$874$	9.50942	+	5.49027i	0.0108803	+	0.00628177i
$875$	1050.47	−	543.689i	1.20054	−	0.621359i
$876$		−	429.067i		−	0.489803i
$877$	84.6508	−	315.921i	0.0965231	−	0.360229i	−0.900723	−	0.434394i	$-0.856962\pi$
$877$	84.6508	−	315.921i	0.0965231	−	0.360229i	0.997246	+	0.0741650i	$0.0236291\pi$
$878$	−491.093	−	131.588i	−0.559332	−	0.149873i
$879$	−2431.22			−2.76589
$880$	208.604	−	52.4811i	0.237050	−	0.0596376i
$881$	490.625	−	849.787i	0.556896	−	0.964571i	−0.440858	−	0.897577i	$-0.645326\pi$
$881$	490.625	−	849.787i	0.556896	−	0.964571i	0.997753	−	0.0669945i	$-0.0213410\pi$
$882$	−1317.31	+	352.971i	−1.49354	+	0.400194i
$883$	−1202.77	−	1202.77i	−1.36214	−	1.36214i	−0.871182	−	0.490960i	$-0.836646\pi$
$883$	−1202.77	−	1202.77i	−1.36214	−	1.36214i	−0.490960	−	0.871182i	$-0.663354\pi$
$884$	−141.380	−	560.845i	−0.159932	−	0.634440i
$885$	932.059	+	1673.10i	1.05317	+	1.89051i
$886$	−345.230	−	199.318i	−0.389650	−	0.224964i
$887$	−11.9189	−	44.4819i	−0.0134373	−	0.0501487i	0.958882	−	0.283806i	$-0.0915972\pi$
$887$	−11.9189	−	44.4819i	−0.0134373	−	0.0501487i	−0.972319	+	0.233657i	$0.924931\pi$
$888$	−16.8799	+	62.9965i	−0.0190088	+	0.0709420i
$889$	−192.145			−0.216136
$890$	−224.403	+	375.270i	−0.252138	+	0.421652i
$891$	−2521.52	+	1455.80i	−2.82999	+	1.63390i
$892$	531.238	+	531.238i	0.595558	+	0.595558i
$893$	8.94283	−	33.3751i	0.0100144	−	0.0373741i
$894$	−1434.67	−	828.307i	−1.60478	−	0.926518i
$895$	270.200	+	278.615i	0.301900	+	0.311302i
$896$	107.057			0.119484
$897$	220.216	+	394.863i	0.245503	+	0.440204i
$898$	333.440	+	333.440i	0.371314	+	0.371314i
$899$	7.95802	−	13.7837i	0.00885208	−	0.0153323i
$900$	1047.73	−	562.803i	1.16414	−	0.625336i
$901$	−451.358	−	781.775i	−0.500952	−	0.867674i
$902$	−554.229	−	554.229i	−0.614445	−	0.614445i
$903$	−1455.19	−	389.916i	−1.61150	−	0.431800i
$904$	−241.102	−	417.600i	−0.266705	−	0.461947i
$905$	323.236	+	91.9449i	0.357167	+	0.101597i
$906$	569.652	+	986.667i	0.628755	+	1.08904i
$907$	−188.478	−	703.409i	−0.207804	−	0.775533i	−0.988577	−	0.150719i	$-0.951841\pi$
$907$	−188.478	−	703.409i	−0.207804	−	0.775533i	0.780773	−	0.624815i	$-0.214825\pi$
$908$	165.208	+	616.566i	0.181947	+	0.679037i
$909$			3000.31i			3.30067i
$910$	833.023	+	250.393i	0.915410	+	0.275157i
$911$	−395.554			−0.434198			−0.217099	−	0.976150i	$-0.569659\pi$
$911$	−395.554			−0.434198			−0.217099	+	0.976150i	$0.569659\pi$
$912$	28.2811	−	7.57791i	0.0310100	−	0.00830911i
$913$	517.885	−	138.767i	0.567234	−	0.151990i
$914$	60.1977	−	34.7552i	0.0658618	−	0.0380253i
$915$	1548.17	+	2779.04i	1.69198	+	3.03721i
$916$	−412.767	+	238.311i	−0.450619	+	0.260165i
$917$	−389.178	+	1452.43i	−0.424404	+	1.58390i
$918$	−1883.46	+	1883.46i	−2.05170	+	2.05170i
$919$	−32.2144	+	18.5990i	−0.0350538	+	0.0202383i	−0.517424	−	0.855729i	$-0.673109\pi$
$919$	−32.2144	+	18.5990i	−0.0350538	+	0.0202383i	0.482371	+	0.875967i	$0.339776\pi$
$920$	−61.6623	+	59.7999i	−0.0670243	+	0.0649999i
$921$	−1324.75	−	764.846i	−1.43839	−	0.830452i
$922$	−242.621	+	242.621i	−0.263147	+	0.263147i
$923$	37.2024	+	66.7064i	0.0403060	+	0.0722713i
$924$		−	1165.49i		−	1.26135i
$925$	−96.3997	−	29.0257i	−0.104216	−	0.0313791i
$926$	544.140	−	942.478i	0.587624	−	1.01779i
$927$	2051.33	+	549.653i	2.21287	+	0.592937i
$928$	6.72200	−	6.72200i	0.00724354	−	0.00724354i
$929$	−642.011	−	1112.00i	−0.691077	−	1.19698i	−0.971485	−	0.237100i	$-0.923803\pi$
$929$	−642.011	−	1112.00i	−0.691077	−	1.19698i	0.280408	−	0.959881i	$-0.409530\pi$
$930$	93.5582	+	371.879i	0.100600	+	0.399870i
$931$		−	51.8256i		−	0.0556666i
$932$	666.858	+	178.684i	0.715513	+	0.191721i
$933$	−2616.97	+	701.214i	−2.80489	+	0.751569i
$934$	−53.0807	+	91.9385i	−0.0568316	+	0.0984352i
$935$	−582.192	−	1045.07i	−0.622665	−	1.11772i
$936$	841.357	+	238.896i	0.898886	+	0.255231i
$937$	434.462	−	434.462i	0.463673	−	0.463673i	−0.436184	−	0.899857i	$-0.643670\pi$
$937$	434.462	−	434.462i	0.463673	−	0.463673i	0.899857	+	0.436184i	$0.143670\pi$
$938$	37.6932	+	140.673i	0.0401846	+	0.149971i
$939$	1654.28	+	955.100i	1.76175	+	1.01715i
$940$	231.980	+	138.719i	0.246787	+	0.147573i
$941$		−	1108.22i		−	1.17770i	−0.808242	−	0.588850i	$-0.799581\pi$
$941$		−	1108.22i		−	1.17770i	0.808242	−	0.588850i	$-0.200419\pi$
$942$	−260.556	+	972.408i	−0.276599	+	1.03228i
$943$	302.327	+	81.0082i	0.320601	+	0.0859048i
$944$	−267.582			−0.283456
$945$	−977.339	−	3884.77i	−1.03422	−	4.11087i
$946$	211.456	−	366.252i	0.223526	−	0.387159i
$947$	−807.757	+	216.438i	−0.852964	+	0.228551i	−0.658707	−	0.752400i	$-0.728896\pi$
$947$	−807.757	+	216.438i	−0.852964	+	0.228551i	−0.194257	+	0.980951i	$0.562230\pi$
$948$	−37.1768	−	37.1768i	−0.0392161	−	0.0392161i
$949$	339.255	+	349.491i	0.357487	+	0.368273i
$950$	10.3537	+	43.9942i	0.0108986	+	0.0463097i
$951$	−1480.15	−	854.564i	−1.55641	−	0.898595i
$952$	−154.099	−	575.107i	−0.161869	−	0.604104i
$953$	−478.486	+	1785.74i	−0.502084	+	1.87380i	−0.0160386	+	0.999871i	$0.505105\pi$
$953$	−478.486	+	1785.74i	−0.502084	+	1.87380i	−0.486046	+	0.873933i	$0.661561\pi$
$954$	1365.05			1.43087
$955$	−189.701	−	754.030i	−0.198639	−	0.789560i
$956$	−557.171	+	321.683i	−0.582815	+	0.336488i
$957$	−73.1795	−	73.1795i	−0.0764676	−	0.0764676i
$958$	200.577	−	748.565i	0.209371	−	0.781383i
$959$	−438.540	−	253.191i	−0.457289	−	0.264016i
$960$	−3.51145	+	229.011i	−0.00365776	+	0.238553i
$961$	871.300			0.906660
$962$	−36.0608	−	64.6594i	−0.0374852	−	0.0672136i
$963$	802.106	+	802.106i	0.832924	+	0.832924i
$964$	323.473	−	560.271i	0.335552	−	0.581194i
$965$	−8.44713	+	550.907i	−0.00875350	+	0.570888i
$966$	232.705	+	403.057i	0.240896	+	0.417244i
$967$	916.655	+	916.655i	0.947937	+	0.947937i	0.998710	−	0.0507735i	$-0.0161686\pi$
$967$	916.655	+	916.655i	0.947937	+	0.947937i	−0.0507735	+	0.998710i	$0.516169\pi$
$968$	−14.5493	−	3.89847i	−0.0150303	−	0.00402735i
$969$	−81.4162	−	141.017i	−0.0840208	−	0.145528i
$970$	−7.13639	+	25.0883i	−0.00735711	+	0.0258642i
$971$	−224.321	−	388.536i	−0.231021	−	0.400140i	0.727088	−	0.686544i	$-0.240873\pi$
$971$	−224.321	−	388.536i	−0.231021	−	0.400140i	−0.958109	+	0.286405i	$0.907540\pi$
$972$	−407.954	−	1522.51i	−0.419706	−	1.56636i
$973$	−647.434	−	2416.26i	−0.665400	−	2.48331i
$974$			165.473i			0.169890i
$975$	−562.948	+	1773.74i	−0.577383	+	1.81922i
$976$	−444.459			−0.455388
$977$	56.8819	−	15.2415i	0.0582210	−	0.0156003i	−0.229591	−	0.973287i	$-0.573739\pi$
$977$	56.8819	−	15.2415i	0.0582210	−	0.0156003i	0.287812	+	0.957687i	$0.407072\pi$
$978$	1219.35	−	326.724i	1.24678	−	0.334074i
$979$	−575.958	+	332.530i	−0.588313	+	0.339663i
$980$	389.945	+	110.920i	0.397903	+	0.113184i
$981$	2993.08	−	1728.06i	3.05105	−	1.76152i
$982$	122.084	−	455.624i	0.124322	−	0.463976i
$983$	−698.348	+	698.348i	−0.710425	+	0.710425i	−0.966624	−	0.256199i	$-0.917530\pi$
$983$	−698.348	+	698.348i	−0.710425	+	0.710425i	0.256199	+	0.966624i	$0.417530\pi$
$984$	722.758	−	417.285i	0.734510	−	0.424070i
$985$	−270.128	−	4.14190i	−0.274241	−	0.00420498i
$986$	−45.7859	−	26.4345i	−0.0464360	−	0.0268099i
$987$	1035.56	−	1035.56i	1.04920	−	1.04920i
$988$	−17.0443	+	28.5338i	−0.0172513	+	0.0288804i
$989$			168.880i			0.170758i
$990$	1808.76	+	27.7340i	1.82703	+	0.0280141i
$991$	504.962	−	874.620i	0.509548	−	0.882563i	−0.490391	−	0.871503i	$-0.663146\pi$
$991$	504.962	−	874.620i	0.509548	−	0.882563i	0.999939	−	0.0110606i	$-0.00352077\pi$
$992$	−51.7506	−	13.8665i	−0.0521679	−	0.0139784i
$993$	519.922	−	519.922i	0.523587	−	0.523587i
$994$	39.3123	+	68.0908i	0.0395496	+	0.0685019i
$995$	−482.087	+	121.285i	−0.484510	+	0.121894i
$996$			570.883i			0.573176i
$997$	850.405	+	227.865i	0.852964	+	0.228551i	0.658707	−	0.752400i	$-0.271104\pi$
$997$	850.405	+	227.865i	0.852964	+	0.228551i	0.194257	+	0.980951i	$0.437770\pi$
$998$	1043.05	−	279.484i	1.04514	−	0.280044i
$999$	−170.475	+	295.271i	−0.170645	+	0.295567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.3.r.b.43.7	yes	28
5.2	odd	4		130.3.r.a.17.1	✓	28
13.10	even	6		130.3.r.a.23.1	yes	28
65.62	odd	12	inner	130.3.r.b.127.7	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.3.r.a.17.1	✓	28	5.2	odd	4
130.3.r.a.23.1	yes	28	13.10	even	6
130.3.r.b.43.7	yes	28	1.1	even	1	trivial
130.3.r.b.127.7	yes	28	65.62	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	130.r (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 0.366025i) q^{2} +(5.53084 - 1.48198i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-4.80922 - 1.36799i) q^{5} +(7.01282 - 4.04885i) q^{6} +(-2.44911 + 9.14020i) q^{7} +(2.00000 - 2.00000i) q^{8} +(20.5996 - 11.8932i) q^{9} +(-7.07024 - 0.108409i) q^{10} +(-9.31429 - 5.37761i) q^{11} +(8.09771 - 8.09771i) q^{12} +(-0.193180 + 12.9986i) q^{13} +13.3822i q^{14} +(-28.6263 - 0.438931i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-21.4878 - 5.75763i) q^{17} +(23.7864 - 23.7864i) q^{18} +(0.639170 + 1.10707i) q^{19} +(-9.69780 + 2.43980i) q^{20} +54.1825i q^{21} +(-14.6919 - 3.93668i) q^{22} +(5.86687 - 1.57202i) q^{23} +(8.09771 - 14.0256i) q^{24} +(21.2572 + 13.1579i) q^{25} +(4.49392 + 17.8271i) q^{26} +(59.8680 - 59.8680i) q^{27} +(4.89822 + 18.2804i) q^{28} +(1.45536 + 0.840250i) q^{29} +(-39.2650 + 9.87838i) q^{30} -9.47101i q^{31} +(1.46410 - 5.46410i) q^{32} +(-59.4853 - 15.9390i) q^{33} -31.4603 q^{34} +(24.2820 - 40.6069i) q^{35} +(23.7864 - 41.1993i) q^{36} +(-3.88977 + 1.04226i) q^{37} +(1.27834 + 1.27834i) q^{38} +(18.1952 + 72.1792i) q^{39} +(-12.3544 + 6.88247i) q^{40} +(44.6273 + 25.7656i) q^{41} +(19.8322 + 74.0146i) q^{42} +(-7.19635 + 26.8571i) q^{43} -21.5104 q^{44} +(-115.338 + 29.0170i) q^{45} +(7.43889 - 4.29484i) q^{46} +(-19.1125 - 19.1125i) q^{47} +(5.92793 - 22.1233i) q^{48} +(-35.1099 - 20.2707i) q^{49} +(33.8540 + 10.1934i) q^{50} -127.378 q^{51} +(12.6640 + 22.7074i) q^{52} +(28.6938 + 28.6938i) q^{53} +(59.8680 - 103.694i) q^{54} +(37.4380 + 38.6039i) q^{55} +(13.3822 + 23.1786i) q^{56} +(5.17581 + 5.17581i) q^{57} +(2.29561 + 0.615106i) q^{58} +(-33.4478 - 57.9332i) q^{59} +(-50.0212 + 27.8661i) q^{60} +(-55.5573 - 96.2281i) q^{61} +(-3.46663 - 12.9376i) q^{62} +(58.2555 + 217.413i) q^{63} -8.00000i q^{64} +(18.7109 - 62.2487i) q^{65} -87.0925 q^{66} +(10.5120 - 2.81667i) q^{67} +(-42.9756 + 11.5153i) q^{68} +(30.1190 - 17.3892i) q^{69} +(18.3067 - 64.3579i) q^{70} +(5.08817 - 2.93766i) q^{71} +(17.4129 - 64.9857i) q^{72} +(26.4931 - 26.4931i) q^{73} +(-4.93203 + 2.84751i) q^{74} +(137.070 + 41.2714i) q^{75} +(2.21415 + 1.27834i) q^{76} +(71.9641 - 71.9641i) q^{77} +(51.2745 + 91.9387i) q^{78} -4.59103i q^{79} +(-14.3573 + 13.9237i) q^{80} +(135.358 - 234.447i) q^{81} +(70.3929 + 18.8617i) q^{82} +(-35.2497 + 35.2497i) q^{83} +(54.1825 + 93.8468i) q^{84} +(95.4631 + 57.0847i) q^{85} +39.3216i q^{86} +(9.29457 + 2.49047i) q^{87} +(-29.3838 + 7.87336i) q^{88} +(30.9180 - 53.5516i) q^{89} +(-146.934 + 81.8546i) q^{90} +(-118.336 - 33.6006i) q^{91} +(8.58969 - 8.58969i) q^{92} +(-14.0359 - 52.3826i) q^{93} +(-33.1038 - 19.1125i) q^{94} +(-1.55944 - 6.19854i) q^{95} -32.3908i q^{96} +(0.954724 - 3.56308i) q^{97} +(-55.3806 - 14.8392i) q^{98} -255.828 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{2} - 8 q^{5} - 4 q^{7} + 56 q^{8} + 48 q^{9} + 6 q^{10} - 12 q^{11} - 18 q^{13} - 10 q^{15} + 56 q^{16} - 40 q^{17} + 92 q^{18} + 36 q^{19} + 4 q^{20} - 12 q^{22} - 28 q^{23} - 6 q^{25} + 42 q^{26}+ \cdots - 16 q^{99}+O(q^{100}) \) 28 * q + 14 * q^2 - 8 * q^5 - 4 * q^7 + 56 * q^8 + 48 * q^9 + 6 * q^10 - 12 * q^11 - 18 * q^13 - 10 * q^15 + 56 * q^16 - 40 * q^17 + 92 * q^18 + 36 * q^19 + 4 * q^20 - 12 * q^22 - 28 * q^23 - 6 * q^25 + 42 * q^26 - 24 * q^27 + 8 * q^28 - 186 * q^29 - 60 * q^30 - 56 * q^32 - 196 * q^33 + 20 * q^34 - 66 * q^35 + 92 * q^36 - 30 * q^37 + 72 * q^38 - 156 * q^39 - 20 * q^40 + 48 * q^41 + 108 * q^42 + 80 * q^43 + 4 * q^45 - 96 * q^46 - 104 * q^47 - 96 * q^49 - 60 * q^50 - 336 * q^51 - 24 * q^52 + 126 * q^53 - 24 * q^54 + 362 * q^55 - 16 * q^56 - 160 * q^57 - 242 * q^58 - 80 * q^59 - 136 * q^60 - 336 * q^61 - 60 * q^62 + 516 * q^63 + 236 * q^65 - 64 * q^66 - 16 * q^67 - 80 * q^68 - 264 * q^69 - 200 * q^70 - 60 * q^71 + 4 * q^72 + 286 * q^73 - 6 * q^74 + 672 * q^75 + 24 * q^76 + 424 * q^77 + 160 * q^78 + 8 * q^80 + 86 * q^81 + 138 * q^82 + 64 * q^83 + 96 * q^84 + 280 * q^85 + 528 * q^87 - 24 * q^88 + 348 * q^89 - 294 * q^90 + 192 * q^91 + 80 * q^92 - 240 * q^93 - 432 * q^94 - 50 * q^95 + 14 * q^97 - 110 * q^98 - 16 * q^99

Introduction

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