LMFDB - Embedded newform 130.3.r.b.127.7

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			127.7
Character	$\chi$	$=$	130.127
Dual form			130.3.r.b.43.7

$q$-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 $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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	0.999134	−	0.0415970i	$-0.0132446\pi$
$3$	5.53084	+	1.48198i	1.84361	+	0.493994i	0.844477	+	0.535591i	$0.179911\pi$
$4$	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	−0.886815	−	0.462124i	$-0.847087\pi$
$7$	−2.44911	−	9.14020i	−0.349873	−	1.30574i	0.536943	−	0.843619i	$-0.319579\pi$
$8$	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	−0.859554	−	0.511045i	$-0.829259\pi$
$11$	−9.31429	+	5.37761i	−0.846753	+	0.488873i	0.0128007	+	0.999918i	$0.495925\pi$
$12$	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	−0.827724	−	0.561135i	$-0.810365\pi$
$17$	−21.4878	+	5.75763i	−1.26399	+	0.338684i	−0.436263	+	0.899819i	$0.643698\pi$
$18$	23.7864	+	23.7864i	1.32147	+	1.32147i
$19$	0.639170	−	1.10707i	0.0336405	−	0.0582671i	−0.848715	−	0.528851i	$-0.822623\pi$
$19$	0.639170	−	1.10707i	0.0336405	−	0.0582671i	0.882355	+	0.470583i	$0.155957\pi$
$20$	−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	0.384094	−	0.923294i	$-0.374514\pi$
$23$	5.86687	+	1.57202i	0.255081	+	0.0683488i	−0.129012	+	0.991643i	$0.541181\pi$
$24$	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	−0.474698	−	0.880149i	$-0.657443\pi$
$29$	1.45536	−	0.840250i	0.0501847	−	0.0289742i	0.524882	+	0.851175i	$0.324109\pi$
$30$	−39.2650	−	9.87838i	−1.30883	−	0.329279i
$31$			9.47101i			0.305517i	0.988264	+	0.152758i	$0.0488156\pi$
$31$			9.47101i			0.305517i	−0.988264	+	0.152758i	$0.951184\pi$
$32$	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	0.205871	−	0.978579i	$-0.433997\pi$
$37$	−3.88977	−	1.04226i	−0.105129	−	0.0281692i	−0.311000	+	0.950410i	$0.600664\pi$
$38$	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	0.155302	−	0.987867i	$-0.450365\pi$
$41$	44.6273	−	25.7656i	1.08847	−	0.628429i	0.933169	+	0.359438i	$0.117031\pi$
$42$	19.8322	−	74.0146i	0.472194	−	1.76225i
$43$	−7.19635	−	26.8571i	−0.167357	−	0.624584i	−0.997728	−	0.0673734i	$-0.978538\pi$
$43$	−7.19635	−	26.8571i	−0.167357	−	0.624584i	0.830371	−	0.557211i	$-0.188129\pi$
$44$	−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	−0.880568	−	0.473919i	$-0.842839\pi$
$47$	−19.1125	+	19.1125i	−0.406649	+	0.406649i	0.473919	+	0.880568i	$0.342839\pi$
$48$	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	−0.382544	−	0.923937i	$-0.624952\pi$
$53$	28.6938	−	28.6938i	0.541393	−	0.541393i	0.923937	+	0.382544i	$0.124952\pi$
$54$	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	0.429958	+	0.902849i	$0.358528\pi$
$59$	−33.4478	+	57.9332i	−0.566911	+	0.981919i	−0.996869	+	0.0790703i	$0.974805\pi$
$60$	−50.0212	−	27.8661i	−0.833687	−	0.464435i
$61$	−55.5573	+	96.2281i	−0.910776	+	1.57751i	−0.0978047	+	0.995206i	$0.531182\pi$
$61$	−55.5573	+	96.2281i	−0.910776	+	1.57751i	−0.812971	+	0.582304i	$0.802151\pi$
$62$	−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	0.336411	−	0.941715i	$-0.390787\pi$
$67$	10.5120	+	2.81667i	0.156895	+	0.0420398i	−0.179517	+	0.983755i	$0.557453\pi$
$68$	−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	0.535404	−	0.844596i	$-0.320159\pi$
$71$	5.08817	+	2.93766i	0.0716644	+	0.0413755i	−0.463740	+	0.885972i	$0.653493\pi$
$72$	17.4129	+	64.9857i	0.241845	+	0.902579i
$73$	26.4931	+	26.4931i	0.362920	+	0.362920i	0.864887	−	0.501967i	$-0.167390\pi$
$73$	26.4931	+	26.4931i	0.362920	+	0.362920i	−0.501967	+	0.864887i	$0.667390\pi$
$74$	−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	$0.00925049\pi$
$79$			4.59103i			0.0581143i	−0.999578	+	0.0290572i	$0.990750\pi$
$80$	−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	0.462122	−	0.886817i	$-0.347088\pi$
$83$	−35.2497	−	35.2497i	−0.424695	−	0.424695i	−0.886817	+	0.462122i	$0.847088\pi$
$84$	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	0.985786	−	0.168008i	$-0.0537335\pi$
$89$	30.9180	+	53.5516i	0.347393	+	0.601703i	−0.638392	+	0.769711i	$0.720400\pi$
$90$	−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	0.970672	−	0.240406i	$-0.0772805\pi$
$97$	0.954724	+	3.56308i	0.00984251	+	0.0367328i	−0.960830	+	0.277139i	$0.910614\pi$
$98$	−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	−0.988650	−	0.150236i	$-0.951997\pi$
$101$	−63.0678	−	109.237i	−0.624433	−	1.08155i	0.364217	−	0.931314i	$-0.381337\pi$
$102$	−174.002	−	46.6236i	−1.70590	−	0.457094i
$103$	63.1318	−	63.1318i	0.612930	−	0.612930i	−0.330778	−	0.943709i	$-0.607311\pi$
$103$	63.1318	−	63.1318i	0.612930	−	0.612930i	0.943709	+	0.330778i	$0.107311\pi$
$104$	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	−0.883960	−	0.467563i	$-0.845132\pi$
$107$	12.3428	−	46.0640i	0.115353	−	0.430505i	0.999313	+	0.0370584i	$0.0117987\pi$
$108$	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	0.829338	+	0.558747i	$0.188718\pi$
$113$	44.1247	+	164.676i	0.390484	+	1.45731i	−0.438854	+	0.898558i	$0.644615\pi$
$114$	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	−0.942143	−	0.335210i	$-0.891193\pi$
$127$	5.25548	−	19.6137i	0.0413817	−	0.154439i	0.983525	+	0.180771i	$0.0578594\pi$
$128$	−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	0.896775	−	0.442486i	$-0.145903\pi$
$137$	−13.8504	−	51.6905i	−0.101098	−	0.377303i	−0.997873	+	0.0651835i	$0.979237\pi$
$138$	34.7784	+	34.7784i	0.252017	+	0.252017i
$139$	−228.938	−	132.177i	−1.64704	−	0.950917i	−0.978241	−	0.207470i	$-0.933477\pi$
$139$	−228.938	−	132.177i	−1.64704	−	0.950917i	−0.668795	−	0.743447i	$-0.733190\pi$
$140$	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	0.286457	+	0.958093i	$0.407522\pi$
$149$	−102.289	+	177.170i	−0.686504	+	1.18906i	−0.972961	+	0.230968i	$0.925811\pi$
$150$	202.347	−	6.20670i	1.34898	−	0.0413780i
$151$		−	140.695i		−	0.931754i	−0.884850	−	0.465877i	$-0.845739\pi$
$151$		−	140.695i		−	0.931754i	0.884850	−	0.465877i	$-0.154261\pi$
$152$	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	0.369363	−	0.929285i	$-0.379576\pi$
$157$	−87.9079	−	87.9079i	−0.559923	−	0.559923i	−0.929285	+	0.369363i	$0.879576\pi$
$158$	−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	0.234593	−	0.972094i	$-0.424624\pi$
$163$	150.580	−	40.3478i	0.923804	−	0.247532i	0.689210	+	0.724561i	$0.257958\pi$
$164$	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	0.663681	−	0.748016i	$-0.268993\pi$
$167$	144.361	+	38.6814i	0.864438	+	0.231625i	0.200757	+	0.979641i	$0.435660\pi$
$168$	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	0.959063	−	0.283193i	$-0.0913936\pi$
$173$	−2.26738	−	8.46197i	−0.0131062	−	0.0489131i	−0.972169	+	0.234280i	$0.924727\pi$
$174$	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	−0.675881	−	0.737011i	$-0.736237\pi$
$179$	−67.2238	+	38.8117i	−0.375552	+	0.216825i	0.300329	+	0.953836i	$0.402903\pi$
$180$	−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	−0.587480	−	0.809239i	$-0.699880\pi$
$191$	77.7526	−	134.671i	0.407082	−	0.705086i	0.994561	+	0.104153i	$0.0332131\pi$
$192$	−11.8559	+	44.2467i	−0.0617493	+	0.230451i
$193$	−28.5204	+	106.440i	−0.147774	+	0.551501i	0.851842	+	0.523799i	$0.175486\pi$
$193$	−28.5204	+	106.440i	−0.147774	+	0.551501i	−0.999616	+	0.0277019i	$0.991181\pi$
$194$			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	0.388838	−	0.921306i	$-0.372877\pi$
$197$	52.1908	+	13.9845i	0.264928	+	0.0709872i	−0.123910	+	0.992293i	$0.539543\pi$
$198$	−349.467	−	93.6395i	−1.76499	−	0.472927i
$199$	86.1019	+	49.7110i	0.432673	+	0.249804i	0.700485	−	0.713667i	$-0.252967\pi$
$199$	86.1019	+	49.7110i	0.432673	+	0.249804i	−0.267812	+	0.963471i	$0.586301\pi$
$200$	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	−0.841844	−	0.539721i	$-0.818530\pi$
$211$	−187.438	−	324.653i	−0.888334	−	1.53864i	−0.0464896	−	0.998919i	$-0.514803\pi$
$212$	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	−0.302734	−	0.953075i	$-0.597899\pi$
$223$	97.2233	−	362.842i	0.435979	−	1.62710i	0.738713	−	0.674020i	$-0.235434\pi$
$224$	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	−0.868913	−	0.494965i	$-0.835181\pi$
$227$	−82.6042	−	308.283i	−0.363895	−	1.35807i	0.505018	−	0.863109i	$-0.331486\pi$
$228$	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	0.0487732	−	0.998810i	$-0.484469\pi$
$233$	244.087	−	244.087i	1.04758	−	1.04758i	0.998810	−	0.0487732i	$-0.0155311\pi$
$234$	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	0.951875	−	0.306486i	$-0.0991533\pi$
$241$	280.135	+	161.736i	1.16239	+	0.671105i	0.210513	+	0.977591i	$0.432487\pi$
$242$	−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	−0.909862	−	0.414912i	$-0.863813\pi$
$251$	−23.9973	+	41.5646i	−0.0956069	+	0.165596i	0.814255	+	0.580508i	$0.197146\pi$
$252$	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	0.809642	+	0.586924i	$0.199661\pi$
$257$	−47.5426	+	177.431i	−0.184991	+	0.690395i	−0.994633	+	0.103471i	$0.967005\pi$
$258$	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	0.584730	−	0.811228i	$-0.301200\pi$
$263$	180.289	+	48.3082i	0.685508	+	0.183681i	0.100777	+	0.994909i	$0.467867\pi$
$264$	−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	0.0457064	−	0.998955i	$-0.485446\pi$
$269$	−214.275	−	123.712i	−0.796561	−	0.459895i	−0.842267	+	0.539060i	$0.818779\pi$
$270$	−429.771	−	416.791i	−1.59175	−	1.54367i
$271$	−198.642	+	114.686i	−0.732997	+	0.423196i	−0.819517	−	0.573054i	$-0.805758\pi$
$271$	−198.642	+	114.686i	−0.732997	+	0.423196i	0.0865208	+	0.996250i	$0.472425\pi$
$272$	−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	0.105573	−	0.994412i	$-0.466332\pi$
$277$	192.295	−	51.5254i	0.694207	−	0.186012i	0.588635	+	0.808399i	$0.299666\pi$
$278$	−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	$-0.640201\pi$
$281$		−	508.362i		−	1.80912i	0.426350	−	0.904558i	$-0.359799\pi$
$282$	−211.416	+	56.6488i	−0.749703	+	0.200882i
$283$	221.794	+	59.4296i	0.783725	+	0.209999i	0.628427	−	0.777869i	$-0.283699\pi$
$283$	221.794	+	59.4296i	0.783725	+	0.209999i	0.155299	+	0.987868i	$0.450366\pi$
$284$	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	−0.878258	−	0.478186i	$-0.841294\pi$
$293$	−410.129	+	109.894i	−1.39976	+	0.375064i	−0.521501	+	0.853251i	$0.674628\pi$
$294$	−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	−0.944328	−	0.329004i	$-0.893287\pi$
$307$	−188.905	+	188.905i	−0.615324	+	0.615324i	0.329004	+	0.944328i	$0.393287\pi$
$308$	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	−0.221505	−	0.975159i	$-0.571097\pi$
$313$	235.894	−	235.894i	0.753655	−	0.753655i	0.975159	+	0.221505i	$0.0710968\pi$
$314$	−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	−0.956744	−	0.290930i	$-0.906035\pi$
$317$	−211.063	+	211.063i	−0.665814	+	0.665814i	0.290930	+	0.956744i	$0.406035\pi$
$318$	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	0.658491	−	0.752588i	$-0.271195\pi$
$331$	111.208	+	64.2061i	0.335976	+	0.193976i	−0.322515	+	0.946564i	$0.604528\pi$
$332$	−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	0.850393	−	0.526149i	$-0.176365\pi$
$337$	109.270	+	109.270i	0.324244	+	0.324244i	−0.526149	+	0.850393i	$0.676365\pi$
$338$	−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	−0.493122	−	0.869960i	$-0.664144\pi$
$347$	−168.363	+	45.1128i	−0.485197	+	0.130008i	0.00792445	+	0.999969i	$0.497478\pi$
$348$	18.5891	+	4.98095i	0.0534171	+	0.0143131i
$349$	−102.293	−	177.176i	−0.293103	−	0.507669i	0.681439	−	0.731875i	$-0.261354\pi$
$349$	−102.293	−	177.176i	−0.293103	−	0.507669i	−0.974542	+	0.224206i	$0.928021\pi$
$350$	−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	−0.772302	−	0.635256i	$-0.780895\pi$
$353$	75.5982	−	282.136i	0.214159	−	0.799253i	0.986461	−	0.163997i	$-0.0524387\pi$
$354$	−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	−0.511999	−	0.858986i	$-0.671095\pi$
$367$	132.450	−	494.309i	0.360898	−	1.34689i	0.872897	−	0.487905i	$-0.162239\pi$
$368$	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	0.923120	+	0.384513i	$0.125631\pi$
$373$	117.842	+	439.793i	0.315931	+	1.17907i	−0.607188	+	0.794558i	$0.707703\pi$
$374$	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	0.660752	−	0.750605i	$-0.270238\pi$
$379$	−121.154	−	209.844i	−0.319667	−	0.553679i	−0.980418	+	0.196925i	$0.936904\pi$
$380$	−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	−0.439031	−	0.898472i	$-0.644678\pi$
$383$	−141.713	+	37.9718i	−0.370007	+	0.0991430i	0.0690242	+	0.997615i	$0.478011\pi$
$384$	−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	$0.359718\pi$
$389$			703.661i			1.80890i	−0.426582	+	0.904449i	$0.640282\pi$
$390$	−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	0.999871	+	0.0160828i	$0.00511955\pi$
$397$	56.3735	+	210.389i	0.141999	+	0.529946i	−0.857872	+	0.513863i	$0.828214\pi$
$398$	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	0.503435	−	0.864033i	$-0.332069\pi$
$401$	602.874	−	348.070i	1.50343	−	0.868004i	0.999992	−	0.00397127i	$-0.00126410\pi$
$402$	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	0.0155826	+	0.999879i	$0.495040\pi$
$409$	−350.975	+	607.906i	−0.858129	+	1.48632i	−0.873712	+	0.486444i	$0.838294\pi$
$410$	−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	0.241285	−	0.970454i	$-0.422431\pi$
$419$	503.791	−	290.864i	1.20237	−	0.694186i	0.961080	+	0.276269i	$0.0890979\pi$
$420$	−132.194	+	525.451i	−0.314748	+	1.25107i
$421$			360.258i			0.855721i	0.903845	+	0.427860i	$0.140732\pi$
$421$			360.258i			0.855721i	−0.903845	+	0.427860i	$0.859268\pi$
$422$	−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	0.0698108	−	0.997560i	$-0.477760\pi$
$431$	417.479	−	241.032i	0.968629	−	0.559238i	0.898818	+	0.438322i	$0.144427\pi$
$432$	−87.6528	+	327.125i	−0.202900	+	0.757234i
$433$	60.7377	+	226.676i	0.140272	+	0.523501i	0.999920	+	0.0126157i	$0.00401582\pi$
$433$	60.7377	+	226.676i	0.140272	+	0.523501i	−0.859649	+	0.510886i	$0.829318\pi$
$434$	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	−0.810766	−	0.585370i	$-0.800949\pi$
$439$	−311.341	+	179.753i	−0.709204	+	0.409459i	0.101562	+	0.994829i	$0.467616\pi$
$440$	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	−0.895331	−	0.445402i	$-0.853061\pi$
$443$	−199.318	+	199.318i	−0.449929	+	0.449929i	0.445402	+	0.895331i	$0.353061\pi$
$444$	−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	−0.618454	−	0.785821i	$-0.712241\pi$
$449$	166.720	−	288.768i	0.371314	−	0.643135i	0.989768	+	0.142686i	$0.0455739\pi$
$450$	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	0.310388	−	0.950610i	$-0.399541\pi$
$457$	47.4764	+	12.7213i	0.103887	+	0.0278365i	−0.206501	+	0.978446i	$0.566208\pi$
$458$	−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	0.254486	−	0.967076i	$-0.418094\pi$
$461$	−210.116	−	121.311i	−0.455784	−	0.263147i	−0.710270	+	0.703930i	$0.751427\pi$
$462$	213.299	+	796.043i	0.461686	+	1.72304i
$463$	544.140	+	544.140i	1.17525	+	1.17525i	0.980941	+	0.194307i	$0.0622459\pi$
$463$	544.140	+	544.140i	1.17525	+	1.17525i	0.194307	+	0.980941i	$0.437754\pi$
$464$	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	0.647988	−	0.761651i	$-0.275611\pi$
$467$	−53.0807	−	53.0807i	−0.113663	−	0.113663i	−0.761651	+	0.647988i	$0.775611\pi$
$468$	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	0.996359	+	0.0852542i	$0.0271702\pi$
$479$	273.994	+	474.571i	0.572012	+	0.990754i	−0.424347	+	0.905500i	$0.639496\pi$
$480$	−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	0.927839	−	0.372982i	$-0.121665\pi$
$487$	−30.2836	−	113.020i	−0.0621840	−	0.232074i	−0.990023	+	0.140908i	$0.954998\pi$
$488$	−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	0.984368	−	0.176126i	$-0.0563567\pi$
$491$	166.770	+	288.854i	0.339654	+	0.588298i	−0.644714	+	0.764424i	$0.723023\pi$
$492$	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	0.883085	−	0.469213i	$-0.155462\pi$
$503$	−58.4965	−	218.312i	−0.116295	−	0.434020i	−0.999381	+	0.0351926i	$0.988796\pi$
$504$	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	0.969748	−	0.244108i	$-0.0784953\pi$
$509$	139.196	+	241.095i	0.273470	+	0.473664i	−0.696278	+	0.717772i	$0.745162\pi$
$510$	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	−0.116061	−	0.993242i	$-0.537027\pi$
$523$	−373.000	−	99.9451i	−0.713193	−	0.191100i	−0.597133	+	0.802143i	$0.703693\pi$
$524$	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	$0.289888\pi$
$541$			854.714i			1.57988i	−0.613186	+	0.789939i	$0.710112\pi$
$542$	−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	0.925020	−	0.379919i	$-0.124048\pi$
$547$	298.170	+	298.170i	0.545100	+	0.545100i	−0.379919	+	0.925020i	$0.624048\pi$
$548$	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	0.754973	−	0.655756i	$-0.227650\pi$
$557$	602.072	+	161.325i	1.08092	+	0.289632i	0.325947	+	0.945388i	$0.394317\pi$
$558$	−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	0.996300	−	0.0859447i	$-0.0273908\pi$
$563$	50.9552	+	190.167i	0.0905066	+	0.337775i	−0.905793	+	0.423720i	$0.860724\pi$
$564$	−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	−0.0699496	−	0.997551i	$-0.522284\pi$
$569$	431.859	−	249.334i	0.758980	−	0.438197i	0.828929	+	0.559353i	$0.188950\pi$
$570$	−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	−0.386085	−	0.922463i	$-0.626173\pi$
$577$	309.490	−	309.490i	0.536378	−	0.536378i	0.922463	+	0.386085i	$0.126173\pi$
$578$	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	−0.314954	−	0.949107i	$-0.601989\pi$
$587$	−623.550	−	167.080i	−1.06227	−	0.284633i	−0.747312	+	0.664474i	$0.768656\pi$
$588$	−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	0.0906604	−	0.995882i	$-0.471102\pi$
$593$	−536.796	−	536.796i	−0.905221	−	0.905221i	−0.995882	+	0.0906604i	$0.971102\pi$
$594$	−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	$-0.801950\pi$
$599$		−	698.216i		−	1.16564i	0.812602	−	0.582818i	$-0.198050\pi$
$600$	356.683	+	191.597i	0.594471	+	0.319329i
$601$	435.765	+	754.767i	0.725066	+	1.25585i	0.958947	+	0.283586i	$0.0915242\pi$
$601$	435.765	+	754.767i	0.725066	+	1.25585i	−0.233881	+	0.972265i	$0.575142\pi$
$602$	−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	−0.243220	−	0.969971i	$-0.578204\pi$
$607$	18.8959	−	5.06313i	0.0311299	−	0.00834123i	0.274350	+	0.961630i	$0.411537\pi$
$608$	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	0.595906	+	0.803054i	$0.296793\pi$
$613$	−197.196	+	735.947i	−0.321691	+	1.20057i	−0.917597	+	0.397512i	$0.869874\pi$
$614$	−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	0.875178	+	0.483800i	$0.160744\pi$
$617$	221.597	+	827.010i	0.359152	+	1.34037i	−0.516027	+	0.856573i	$0.672589\pi$
$618$	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	0.818673	−	0.574260i	$-0.194710\pi$
$631$	461.063	+	266.195i	0.730686	+	0.421861i	−0.0879874	+	0.996122i	$0.528044\pi$
$632$	−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	−0.524576	−	0.851364i	$-0.675776\pi$
$641$	304.484	−	527.382i	0.475015	−	0.822749i	0.999591	+	0.0286143i	$0.00910946\pi$
$642$	273.064	−	273.064i	0.425334	−	0.425334i
$643$	−794.150	+	212.792i	−1.23507	+	0.330936i	−0.816552	−	0.577272i	$-0.804117\pi$
$643$	−794.150	+	212.792i	−1.23507	+	0.330936i	−0.418519	+	0.908208i	$0.637451\pi$
$644$	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	0.613777	+	0.789480i	$0.289649\pi$
$647$	−202.193	+	754.596i	−0.312509	+	1.16630i	−0.926286	+	0.376821i	$0.877017\pi$
$648$	−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	0.536164	−	0.844114i	$-0.319873\pi$
$653$	377.721	+	101.210i	0.578439	+	0.154992i	0.0422748	+	0.999106i	$0.486540\pi$
$654$	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	−0.0277560	−	0.999615i	$-0.508836\pi$
$659$	−597.928	−	345.214i	−0.907326	−	0.523845i	−0.879570	+	0.475770i	$0.842169\pi$
$660$	615.765	−	9.44160i	0.932977	−	0.0143055i
$661$	−686.512	+	396.358i	−1.03860	+	0.599634i	−0.919435	−	0.393241i	$-0.871354\pi$
$661$	−686.512	+	396.358i	−1.03860	+	0.599634i	−0.119161	+	0.992875i	$0.538020\pi$
$662$	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	−0.247950	−	0.968773i	$-0.579757\pi$
$673$	−637.376	−	170.784i	−0.947067	−	0.253766i	−0.699117	+	0.715007i	$0.746423\pi$
$674$	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	0.999099	−	0.0424438i	$-0.0135143\pi$
$677$	647.655	+	647.655i	0.956655	+	0.956655i	−0.0424438	+	0.999099i	$0.513514\pi$
$678$	−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	−0.349233	−	0.937036i	$-0.613558\pi$
$683$	−125.098	+	33.5199i	−0.183160	+	0.0490774i	0.166073	+	0.986113i	$0.446891\pi$
$684$	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	−0.461480	−	0.887151i	$-0.652681\pi$
$691$	52.5682	−	30.3503i	0.0760755	−	0.0439222i	0.537555	+	0.843229i	$0.319348\pi$
$692$	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	−0.578038	−	0.816010i	$-0.696181\pi$
$709$	296.125	−	512.904i	0.417666	−	0.723419i	0.995704	+	0.0925905i	$0.0295147\pi$
$710$	−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	0.236815	−	0.971555i	$-0.423896\pi$
$719$	−349.555	−	201.816i	−0.486169	−	0.280690i	−0.722984	+	0.690865i	$0.757230\pi$
$720$	−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	−0.940095	−	0.340912i	$-0.889264\pi$
$727$	−931.292	−	931.292i	−1.28101	−	1.28101i	−0.340912	−	0.940095i	$-0.610736\pi$
$728$	−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	0.754980	−	0.655748i	$-0.227647\pi$
$733$	72.7371	+	72.7371i	0.0992321	+	0.0992321i	−0.655748	+	0.754980i	$0.727647\pi$
$734$	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	0.999968	+	0.00799871i	$0.00254610\pi$
$739$	374.607	+	648.839i	0.506911	+	0.877996i	−0.493057	+	0.869997i	$0.664121\pi$
$740$	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	0.855438	+	0.517906i	$0.173288\pi$
$743$	−107.249	+	400.259i	−0.144346	+	0.538706i	−0.999784	+	0.0208006i	$0.993378\pi$
$744$	−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	−0.973348	−	0.229331i	$-0.926346\pi$
$751$	−514.646	−	891.393i	−0.685281	−	1.18694i	0.288068	−	0.957610i	$-0.406987\pi$
$752$	−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	−0.659970	−	0.751292i	$-0.729431\pi$
$757$	217.431	−	811.462i	0.287227	−	1.07194i	0.947197	−	0.320653i	$-0.103902\pi$
$758$	−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	0.713665	−	0.700487i	$-0.247034\pi$
$761$	352.995	+	203.802i	0.463857	+	0.267808i	−0.249807	+	0.968296i	$0.580367\pi$
$762$	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	0.999831	+	0.0183801i	$0.00585090\pi$
$769$	396.676	+	687.062i	0.515833	+	0.893449i	−0.483998	+	0.875069i	$0.660816\pi$
$770$	−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	−0.751459	−	0.659780i	$-0.770650\pi$
$773$	−828.928	+	222.111i	−1.07235	+	0.287336i	−0.320893	+	0.947116i	$0.603983\pi$
$774$	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	0.991214	+	0.132270i	$0.0422265\pi$
$787$	156.560	+	584.289i	0.198932	+	0.742426i	−0.792281	+	0.610156i	$0.791107\pi$
$788$	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	0.648666	−	0.761073i	$-0.275327\pi$
$797$	1268.00	−	339.759i	1.59096	−	0.426297i	0.942298	+	0.334776i	$0.108661\pi$
$798$	−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	−0.934990	−	0.354674i	$-0.884592\pi$
$809$	−886.121	+	511.602i	−1.09533	+	0.632388i	−0.160338	+	0.987062i	$0.551259\pi$
$810$	−982.428	−	1642.92i	−1.21287	−	2.02830i
$811$		−	1301.46i		−	1.60476i	−0.596810	−	0.802382i	$-0.703566\pi$
$811$		−	1301.46i		−	1.60476i	0.596810	−	0.802382i	$-0.296434\pi$
$812$	−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	−0.381357	−	0.924428i	$-0.624543\pi$
$821$	187.633	−	108.330i	0.228542	−	0.131949i	0.609899	+	0.792479i	$0.291210\pi$
$822$	112.157	−	418.574i	0.136444	−	0.509214i
$823$	−388.594	−	1450.25i	−0.472168	−	1.76216i	−0.631956	−	0.775004i	$-0.717748\pi$
$823$	−388.594	−	1450.25i	−0.472168	−	1.76216i	0.159788	−	0.987151i	$-0.448919\pi$
$824$	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	−0.832766	−	0.553626i	$-0.813244\pi$
$827$	−230.849	+	230.849i	−0.279140	+	0.279140i	0.553626	+	0.832766i	$0.313244\pi$
$828$	74.7855	+	279.103i	0.0903207	+	0.337081i
$829$	151.614	−	87.5347i	0.182888	−	0.105591i	−0.405761	−	0.913979i	$-0.632993\pi$
$829$	151.614	−	87.5347i	0.182888	−	0.105591i	0.588649	+	0.808389i	$0.299660\pi$
$830$	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	−0.955691	−	0.294373i	$-0.904889\pi$
$839$	−187.023	+	323.933i	−0.222911	+	0.386094i	0.732779	+	0.680466i	$0.238223\pi$
$840$	−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	0.589878	−	0.807492i	$-0.299176\pi$
$853$	−185.625	−	185.625i	−0.217614	−	0.217614i	−0.807492	+	0.589878i	$0.799176\pi$
$854$	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	0.410629	−	0.911802i	$-0.365309\pi$
$857$	−429.506	−	429.506i	−0.501173	−	0.501173i	−0.911802	+	0.410629i	$0.865309\pi$
$858$	16.8246	+	1132.08i	0.0196090	+	1.31944i
$859$			159.919i			0.186169i	0.995658	+	0.0930846i	$0.0296727\pi$
$859$			159.919i			0.186169i	−0.995658	+	0.0930846i	$0.970327\pi$
$860$	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	0.962010	−	0.273013i	$-0.0880202\pi$
$863$	594.605	+	594.605i	0.688997	+	0.688997i	−0.273013	+	0.962010i	$0.588020\pi$
$864$	−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	0.997246	−	0.0741650i	$-0.0236291\pi$
$877$	84.6508	+	315.921i	0.0965231	+	0.360229i	−0.900723	+	0.434394i	$0.856962\pi$
$878$	−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	0.997753	+	0.0669945i	$0.0213410\pi$
$881$	490.625	+	849.787i	0.556896	+	0.964571i	−0.440858	+	0.897577i	$0.645326\pi$
$882$	−1317.31	−	352.971i	−1.49354	−	0.400194i
$883$	−1202.77	+	1202.77i	−1.36214	+	1.36214i	−0.490960	+	0.871182i	$0.663354\pi$
$883$	−1202.77	+	1202.77i	−1.36214	+	1.36214i	−0.871182	+	0.490960i	$0.836646\pi$
$884$	−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	−0.972319	−	0.233657i	$-0.924931\pi$
$887$	−11.9189	+	44.4819i	−0.0134373	+	0.0501487i	0.958882	+	0.283806i	$0.0915972\pi$
$888$	−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	0.780773	+	0.624815i	$0.214825\pi$
$907$	−188.478	+	703.409i	−0.207804	+	0.775533i	−0.988577	+	0.150719i	$0.951841\pi$
$908$	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	0.482371	−	0.875967i	$-0.339776\pi$
$919$	−32.2144	−	18.5990i	−0.0350538	−	0.0202383i	−0.517424	+	0.855729i	$0.673109\pi$
$920$	−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	0.280408	+	0.959881i	$0.409530\pi$
$929$	−642.011	+	1112.00i	−0.691077	+	1.19698i	−0.971485	+	0.237100i	$0.923803\pi$
$930$	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	0.899857	−	0.436184i	$-0.143670\pi$
$937$	434.462	+	434.462i	0.463673	+	0.463673i	−0.436184	+	0.899857i	$0.643670\pi$
$938$	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	$0.200419\pi$
$941$			1108.22i			1.17770i	−0.808242	+	0.588850i	$0.799581\pi$
$942$	−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	−0.194257	−	0.980951i	$-0.562230\pi$
$947$	−807.757	−	216.438i	−0.852964	−	0.228551i	−0.658707	+	0.752400i	$0.728896\pi$
$948$	−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	−0.486046	−	0.873933i	$-0.661561\pi$
$953$	−478.486	−	1785.74i	−0.502084	−	1.87380i	−0.0160386	−	0.999871i	$-0.505105\pi$
$954$	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	−0.0507735	−	0.998710i	$-0.516169\pi$
$967$	916.655	−	916.655i	0.947937	−	0.947937i	0.998710	+	0.0507735i	$0.0161686\pi$
$968$	−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	−0.958109	−	0.286405i	$-0.907540\pi$
$971$	−224.321	+	388.536i	−0.231021	+	0.400140i	0.727088	+	0.686544i	$0.240873\pi$
$972$	−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	0.287812	−	0.957687i	$-0.407072\pi$
$977$	56.8819	+	15.2415i	0.0582210	+	0.0156003i	−0.229591	+	0.973287i	$0.573739\pi$
$978$	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	0.256199	−	0.966624i	$-0.417530\pi$
$983$	−698.348	−	698.348i	−0.710425	−	0.710425i	−0.966624	+	0.256199i	$0.917530\pi$
$984$	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	0.999939	+	0.0110606i	$0.00352077\pi$
$991$	504.962	+	874.620i	0.509548	+	0.882563i	−0.490391	+	0.871503i	$0.663146\pi$
$992$	−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	0.194257	−	0.980951i	$-0.437770\pi$
$997$	850.405	−	227.865i	0.852964	−	0.228551i	0.658707	+	0.752400i	$0.271104\pi$
$998$	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.127.7	yes	28
5.3	odd	4		130.3.r.a.23.1	yes	28
13.4	even	6		130.3.r.a.17.1	✓	28
65.43	odd	12	inner	130.3.r.b.43.7	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.3.r.a.17.1	✓	28	13.4	even	6
130.3.r.a.23.1	yes	28	5.3	odd	4
130.3.r.b.43.7	yes	28	65.43	odd	12	inner
130.3.r.b.127.7	yes	28	1.1	even	1	trivial

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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