LMFDB - Embedded newform 63.4.f.c.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(22,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("63.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 6 x^{16} - 23 x^{15} - 6 x^{14} + 255 x^{13} - 56 x^{12} - 81 x^{11} + \cdots + 387420489 $ x^18 - 3x^17 + 6x^16 - 23x^15 - 6x^14 + 255x^13 - 56x^12 - 81x^11 + 5832x^10 - 32373x^9 + 52488x^8 - 6561x^7 - 40824x^6 + 1673055x^5 - 354294x^4 - 12223143x^3 + 28697814x^2 - 129140163*x + 387420489
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			43.2
Root			$-2.90795 + 0.737429i$ of defining polynomial
Character	$\chi$	$=$	63.43
Dual form			63.4.f.c.22.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61753 + 2.80164i) q^{2} +(-5.00056 + 1.41222i) q^{3} +(-1.23279 - 2.13526i) q^{4} +(-4.95111 - 8.57557i) q^{5} +(4.13202 - 16.2941i) q^{6} +(-3.50000 + 6.06218i) q^{7} -17.9041 q^{8} +(23.0113 - 14.1238i) q^{9} +O(q^{10})$	\(q+(-1.61753 + 2.80164i) q^{2} +(-5.00056 + 1.41222i) q^{3} +(-1.23279 - 2.13526i) q^{4} +(-4.95111 - 8.57557i) q^{5} +(4.13202 - 16.2941i) q^{6} +(-3.50000 + 6.06218i) q^{7} -17.9041 q^{8} +(23.0113 - 14.1238i) q^{9} +32.0342 q^{10} +(35.3649 - 61.2538i) q^{11} +(9.18012 + 8.93654i) q^{12} +(12.1938 + 21.1204i) q^{13} +(-11.3227 - 19.6115i) q^{14} +(36.8689 + 35.8906i) q^{15} +(38.8228 - 67.2430i) q^{16} -112.622 q^{17} +(2.34838 + 87.3149i) q^{18} -87.5650 q^{19} +(-12.2074 + 21.1438i) q^{20} +(8.94085 - 35.2571i) q^{21} +(114.407 + 198.160i) q^{22} +(-66.6293 - 115.405i) q^{23} +(89.5308 - 25.2846i) q^{24} +(13.4731 - 23.3360i) q^{25} -78.8956 q^{26} +(-95.1235 + 103.124i) q^{27} +17.2591 q^{28} +(-98.4166 + 170.462i) q^{29} +(-160.189 + 45.2393i) q^{30} +(-87.5631 - 151.664i) q^{31} +(53.9774 + 93.4916i) q^{32} +(-90.3407 + 356.247i) q^{33} +(182.169 - 315.526i) q^{34} +69.3155 q^{35} +(-58.5261 - 31.7234i) q^{36} +16.2458 q^{37} +(141.639 - 245.326i) q^{38} +(-90.8027 - 88.3933i) q^{39} +(88.6453 + 153.538i) q^{40} +(108.031 + 187.115i) q^{41} +(84.3156 + 82.0784i) q^{42} +(31.7145 - 54.9311i) q^{43} -174.391 q^{44} +(-235.051 - 127.406i) q^{45} +431.099 q^{46} +(138.702 - 240.239i) q^{47} +(-99.1739 + 391.079i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(43.5861 + 75.4934i) q^{50} +(563.173 - 159.047i) q^{51} +(30.0650 - 52.0741i) q^{52} -101.268 q^{53} +(-135.051 - 433.308i) q^{54} -700.382 q^{55} +(62.6645 - 108.538i) q^{56} +(437.875 - 123.661i) q^{57} +(-318.383 - 551.456i) q^{58} +(-0.975290 - 1.68925i) q^{59} +(31.1841 - 122.971i) q^{60} +(-16.8446 + 29.1757i) q^{61} +566.543 q^{62} +(5.08141 + 188.932i) q^{63} +271.925 q^{64} +(120.746 - 209.138i) q^{65} +(-851.947 - 829.341i) q^{66} +(171.846 + 297.646i) q^{67} +(138.840 + 240.477i) q^{68} +(496.161 + 482.996i) q^{69} +(-112.120 + 194.197i) q^{70} -908.888 q^{71} +(-411.997 + 252.874i) q^{72} -405.936 q^{73} +(-26.2780 + 45.5148i) q^{74} +(-34.4173 + 135.720i) q^{75} +(107.950 + 186.974i) q^{76} +(247.554 + 428.777i) q^{77} +(394.522 - 111.418i) q^{78} +(-228.979 + 396.603i) q^{79} -768.863 q^{80} +(330.038 - 650.012i) q^{81} -698.972 q^{82} +(-44.7656 + 77.5363i) q^{83} +(-86.3053 + 24.3737i) q^{84} +(557.603 + 965.797i) q^{85} +(102.598 + 177.705i) q^{86} +(251.408 - 991.394i) q^{87} +(-633.178 + 1096.70i) q^{88} +1089.23 q^{89} +(737.148 - 452.444i) q^{90} -170.714 q^{91} +(-164.280 + 284.542i) q^{92} +(652.047 + 634.746i) q^{93} +(448.709 + 777.187i) q^{94} +(433.544 + 750.920i) q^{95} +(-401.948 - 391.283i) q^{96} +(150.691 - 261.004i) q^{97} +158.518 q^{98} +(-51.3439 - 1909.02i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9}+O(q^{10}) $ 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9} + 111 q^{11} - 18 q^{13} + 42 q^{14} - 36 q^{15} - 144 q^{16} - 546 q^{17} - 45 q^{18} + 90 q^{19} + 402 q^{20} - 63 q^{21} + 162 q^{22} + 312 q^{23} - 36 q^{24} - 279 q^{25} + 102 q^{26} + 432 q^{27} + 504 q^{28} + 378 q^{29} - 864 q^{30} - 18 q^{31} + 891 q^{32} + 513 q^{33} + 324 q^{34} - 336 q^{35} + 414 q^{36} - 72 q^{37} + 147 q^{38} - 810 q^{39} - 405 q^{40} + 477 q^{41} + 315 q^{42} + 171 q^{43} - 1896 q^{44} - 720 q^{45} - 756 q^{46} + 654 q^{47} - 2709 q^{48} - 441 q^{49} + 429 q^{50} + 1341 q^{51} - 747 q^{52} - 1896 q^{53} - 108 q^{54} - 432 q^{55} + 525 q^{56} - 1143 q^{57} - 297 q^{58} + 957 q^{59} + 5400 q^{60} + 198 q^{61} - 600 q^{62} - 504 q^{63} + 4770 q^{64} + 2478 q^{65} - 2646 q^{66} + 333 q^{67} + 1443 q^{68} + 3366 q^{69} - 5652 q^{71} - 3681 q^{72} + 306 q^{73} + 2100 q^{74} - 4113 q^{75} + 144 q^{76} + 777 q^{77} + 6336 q^{78} - 1152 q^{79} - 8418 q^{80} - 1917 q^{81} - 6048 q^{82} + 1890 q^{83} + 1008 q^{84} + 648 q^{85} + 3837 q^{86} + 4212 q^{87} + 2268 q^{88} - 2604 q^{89} - 135 q^{90} + 252 q^{91} + 987 q^{92} + 378 q^{93} - 324 q^{94} + 3144 q^{95} + 5643 q^{96} + 1737 q^{97} - 588 q^{98} + 720 q^{99}+O(q^{100}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9 + 111 * q^11 - 18 * q^13 + 42 * q^14 - 36 * q^15 - 144 * q^16 - 546 * q^17 - 45 * q^18 + 90 * q^19 + 402 * q^20 - 63 * q^21 + 162 * q^22 + 312 * q^23 - 36 * q^24 - 279 * q^25 + 102 * q^26 + 432 * q^27 + 504 * q^28 + 378 * q^29 - 864 * q^30 - 18 * q^31 + 891 * q^32 + 513 * q^33 + 324 * q^34 - 336 * q^35 + 414 * q^36 - 72 * q^37 + 147 * q^38 - 810 * q^39 - 405 * q^40 + 477 * q^41 + 315 * q^42 + 171 * q^43 - 1896 * q^44 - 720 * q^45 - 756 * q^46 + 654 * q^47 - 2709 * q^48 - 441 * q^49 + 429 * q^50 + 1341 * q^51 - 747 * q^52 - 1896 * q^53 - 108 * q^54 - 432 * q^55 + 525 * q^56 - 1143 * q^57 - 297 * q^58 + 957 * q^59 + 5400 * q^60 + 198 * q^61 - 600 * q^62 - 504 * q^63 + 4770 * q^64 + 2478 * q^65 - 2646 * q^66 + 333 * q^67 + 1443 * q^68 + 3366 * q^69 - 5652 * q^71 - 3681 * q^72 + 306 * q^73 + 2100 * q^74 - 4113 * q^75 + 144 * q^76 + 777 * q^77 + 6336 * q^78 - 1152 * q^79 - 8418 * q^80 - 1917 * q^81 - 6048 * q^82 + 1890 * q^83 + 1008 * q^84 + 648 * q^85 + 3837 * q^86 + 4212 * q^87 + 2268 * q^88 - 2604 * q^89 - 135 * q^90 + 252 * q^91 + 987 * q^92 + 378 * q^93 - 324 * q^94 + 3144 * q^95 + 5643 * q^96 + 1737 * q^97 - 588 * q^98 + 720 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.61753	+	2.80164i	−0.571883	+	0.990530i	0.424490	+	0.905433i	$0.360453\pi$
$2$	−1.61753	+	2.80164i	−0.571883	+	0.990530i	−0.996373	+	0.0850970i	$0.972880\pi$
$3$	−5.00056	+	1.41222i	−0.962359	+	0.271782i
$3$	−5.00056	+	1.41222i	−0.962359	+	0.271782i
$4$	−1.23279	−	2.13526i	−0.154099	−	0.266908i
$5$	−4.95111	−	8.57557i	−0.442841	−	0.767022i	0.555058	−	0.831811i	$-0.312696\pi$
$5$	−4.95111	−	8.57557i	−0.442841	−	0.767022i	−0.997899	+	0.0647890i	$0.979363\pi$
$6$	4.13202	−	16.2941i	0.281148	−	1.10867i
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$8$	−17.9041			−0.791258
$9$	23.0113	−	14.1238i	0.852269	−	0.523103i
$10$	32.0342			1.01301
$11$	35.3649	−	61.2538i	0.969357	−	1.67897i	0.271932	−	0.962316i	$-0.412337\pi$
$11$	35.3649	−	61.2538i	0.969357	−	1.67897i	0.697424	−	0.716659i	$-0.254329\pi$
$12$	9.18012	+	8.93654i	0.220839	+	0.214980i
$13$	12.1938	+	21.1204i	0.260151	+	0.450595i	0.966282	−	0.257486i	$-0.0828943\pi$
$13$	12.1938	+	21.1204i	0.260151	+	0.450595i	−0.706131	+	0.708081i	$0.749561\pi$
$14$	−11.3227	−	19.6115i	−0.216151	−	0.374385i
$15$	36.8689	+	35.8906i	0.634634	+	0.617795i
$16$	38.8228	−	67.2430i	0.606606	−	1.05067i
$17$	−112.622			−1.60675			−0.803377	−	0.595471i	$-0.796966\pi$
$17$	−112.622			−1.60675			−0.803377	+	0.595471i	$0.796966\pi$
$18$	2.34838	+	87.3149i	0.0307510	+	1.14335i
$19$	−87.5650			−1.05731			−0.528653	−	0.848838i	$-0.677303\pi$
$19$	−87.5650			−1.05731			−0.528653	+	0.848838i	$0.677303\pi$
$20$	−12.2074	+	21.1438i	−0.136483	+	0.236395i
$21$	8.94085	−	35.2571i	0.0929073	−	0.366368i
$22$	114.407	+	198.160i	1.10872	+	1.92035i
$23$	−66.6293	−	115.405i	−0.604050	−	1.04625i	−0.992201	−	0.124650i	$-0.960219\pi$
$23$	−66.6293	−	115.405i	−0.604050	−	1.04625i	0.388150	−	0.921596i	$-0.373114\pi$
$24$	89.5308	−	25.2846i	0.761475	−	0.215050i
$25$	13.4731	−	23.3360i	0.107785	−	0.186688i
$26$	−78.8956			−0.595104
$27$	−95.1235	+	103.124i	−0.678019	+	0.735044i
$28$	17.2591			0.116488
$29$	−98.4166	+	170.462i	−0.630189	+	1.09152i	0.357323	+	0.933981i	$0.383689\pi$
$29$	−98.4166	+	170.462i	−0.630189	+	1.09152i	−0.987513	+	0.157539i	$0.949644\pi$
$30$	−160.189	+	45.2393i	−0.974880	+	0.275318i
$31$	−87.5631	−	151.664i	−0.507316	−	0.878697i	−0.999964	−	0.00846847i	$-0.997304\pi$
$31$	−87.5631	−	151.664i	−0.507316	−	0.878697i	0.492648	−	0.870229i	$-0.336029\pi$
$32$	53.9774	+	93.4916i	0.298186	+	0.516473i
$33$	−90.3407	+	356.247i	−0.476554	+	1.87923i
$34$	182.169	−	315.526i	0.918875	−	1.59154i
$35$	69.3155			0.334756
$36$	−58.5261	−	31.7234i	−0.270954	−	0.146868i
$37$	16.2458			0.0721834			0.0360917	−	0.999348i	$-0.488509\pi$
$37$	16.2458			0.0721834			0.0360917	+	0.999348i	$0.488509\pi$
$38$	141.639	−	245.326i	0.604654	−	1.04729i
$39$	−90.8027	−	88.3933i	−0.372822	−	0.362930i
$40$	88.6453	+	153.538i	0.350401	+	0.606913i
$41$	108.031	+	187.115i	0.411502	+	0.712742i	0.995054	−	0.0993333i	$-0.0316710\pi$
$41$	108.031	+	187.115i	0.411502	+	0.712742i	−0.583552	+	0.812076i	$0.698338\pi$
$42$	84.3156	+	82.0784i	0.309766	+	0.301547i
$43$	31.7145	−	54.9311i	0.112475	−	0.194812i	−0.804293	−	0.594233i	$-0.797456\pi$
$43$	31.7145	−	54.9311i	0.112475	−	0.194812i	0.916767	+	0.399421i	$0.130789\pi$
$44$	−174.391			−0.597509
$45$	−235.051	−	127.406i	−0.778651	−	0.422058i
$46$	431.099			1.38178
$47$	138.702	−	240.239i	0.430464	−	0.745585i	−0.566450	−	0.824096i	$-0.691683\pi$
$47$	138.702	−	240.239i	0.430464	−	0.745585i	0.996913	+	0.0785115i	$0.0250167\pi$
$48$	−99.1739	+	391.079i	−0.298219	+	1.17599i
$49$	−24.5000	−	42.4352i	−0.0714286	−	0.123718i
$50$	43.5861	+	75.4934i	0.123280	+	0.213527i
$51$	563.173	−	159.047i	1.54627	−	0.436686i
$52$	30.0650	−	52.0741i	0.0801782	−	0.138873i
$53$	−101.268			−0.262458			−0.131229	−	0.991352i	$-0.541892\pi$
$53$	−101.268			−0.262458			−0.131229	+	0.991352i	$0.541892\pi$
$54$	−135.051	−	433.308i	−0.340336	−	1.09196i
$55$	−700.382			−1.71708
$56$	62.6645	−	108.538i	0.149534	−	0.259000i
$57$	437.875	−	123.661i	1.01751	−	0.287356i
$58$	−318.383	−	551.456i	−0.720789	−	1.24844i
$59$	−0.975290	−	1.68925i	−0.00215207	−	0.00372749i	0.864947	−	0.501863i	$-0.167352\pi$
$59$	−0.975290	−	1.68925i	−0.00215207	−	0.00372749i	−0.867099	+	0.498135i	$0.834018\pi$
$60$	31.1841	−	122.971i	0.0670976	−	0.264591i
$61$	−16.8446	+	29.1757i	−0.0353563	+	0.0612388i	−0.883162	−	0.469068i	$-0.844590\pi$
$61$	−16.8446	+	29.1757i	−0.0353563	+	0.0612388i	0.847806	+	0.530307i	$0.177923\pi$
$62$	566.543			1.16050
$63$	5.08141	+	188.932i	0.0101619	+	0.377828i
$64$	271.925			0.531103
$65$	120.746	−	209.138i	0.230411	−	0.399083i
$66$	−851.947	−	829.341i	−1.58890	−	1.54674i
$67$	171.846	+	297.646i	0.313348	+	0.542735i	0.979085	−	0.203452i	$-0.0652160\pi$
$67$	171.846	+	297.646i	0.313348	+	0.542735i	−0.665737	+	0.746187i	$0.731883\pi$
$68$	138.840	+	240.477i	0.247600	+	0.428855i
$69$	496.161	+	482.996i	0.865664	+	0.842694i
$70$	−112.120	+	194.197i	−0.191441	+	0.331586i
$71$	−908.888			−1.51923			−0.759613	−	0.650375i	$-0.774612\pi$
$71$	−908.888			−1.51923			−0.759613	+	0.650375i	$0.774612\pi$
$72$	−411.997	+	252.874i	−0.674365	+	0.413910i
$73$	−405.936			−0.650838			−0.325419	−	0.945570i	$-0.605505\pi$
$73$	−405.936			−0.650838			−0.325419	+	0.945570i	$0.605505\pi$
$74$	−26.2780	+	45.5148i	−0.0412805	+	0.0714998i
$75$	−34.4173	+	135.720i	−0.0529889	+	0.208955i
$76$	107.950	+	186.974i	0.162930	+	0.282203i
$77$	247.554	+	428.777i	0.366382	+	0.634593i
$78$	394.522	−	111.418i	0.572703	−	0.161738i
$79$	−228.979	+	396.603i	−0.326103	+	0.564827i	−0.981735	−	0.190254i	$-0.939069\pi$
$79$	−228.979	+	396.603i	−0.326103	+	0.564827i	0.655632	+	0.755080i	$0.272402\pi$
$80$	−768.863			−1.07452
$81$	330.038	−	650.012i	0.452726	−	0.891649i
$82$	−698.972			−0.941323
$83$	−44.7656	+	77.5363i	−0.0592007	+	0.102539i	−0.894107	−	0.447854i	$-0.852189\pi$
$83$	−44.7656	+	77.5363i	−0.0592007	+	0.102539i	0.834906	+	0.550392i	$0.185522\pi$
$84$	−86.3053	+	24.3737i	−0.112103	+	0.0316593i
$85$	557.603	+	965.797i	0.711536	+	1.23242i
$86$	102.598	+	177.705i	0.128645	+	0.222819i
$87$	251.408	−	991.394i	0.309813	−	1.22171i
$88$	−633.178	+	1096.70i	−0.767012	+	1.32850i
$89$	1089.23			1.29728			0.648641	−	0.761094i	$-0.275338\pi$
$89$	1089.23			1.29728			0.648641	+	0.761094i	$0.275338\pi$
$90$	737.148	−	452.444i	0.863358	−	0.529909i
$91$	−170.714			−0.196656
$92$	−164.280	+	284.542i	−0.186167	+	0.322452i
$93$	652.047	+	634.746i	0.727034	+	0.707743i
$94$	448.709	+	777.187i	0.492349	+	0.852774i
$95$	433.544	+	750.920i	0.468218	+	0.810977i
$96$	−401.948	−	391.283i	−0.427330	−	0.415991i
$97$	150.691	−	261.004i	0.157735	−	0.273206i	−0.776316	−	0.630344i	$-0.782914\pi$
$97$	150.691	−	261.004i	0.157735	−	0.273206i	0.934052	+	0.357138i	$0.116247\pi$
$98$	158.518			0.163395
$99$	−51.3439	−	1909.02i	−0.0521238	−	1.93801i
$100$	−66.4381			−0.0664381
$101$	−37.8185	+	65.5035i	−0.0372582	+	0.0645331i	−0.884053	−	0.467386i	$-0.845196\pi$
$101$	−37.8185	+	65.5035i	−0.0372582	+	0.0645331i	0.846795	+	0.531919i	$0.178529\pi$
$102$	−465.356	+	1835.07i	−0.451736	+	1.78136i
$103$	−802.599	−	1390.14i	−0.767791	−	1.32985i	−0.938758	−	0.344576i	$-0.888023\pi$
$103$	−802.599	−	1390.14i	−0.767791	−	1.32985i	0.170968	−	0.985277i	$-0.445311\pi$
$104$	−218.320	−	378.142i	−0.205847	−	0.356537i
$105$	−346.617	+	97.8887i	−0.322155	+	0.0909805i
$106$	163.804	−	283.718i	0.150095	−	0.259973i
$107$	−773.956			−0.699263			−0.349632	−	0.936887i	$-0.613693\pi$
$107$	−773.956			−0.699263			−0.349632	+	0.936887i	$0.613693\pi$
$108$	337.464	+	75.9831i	0.300671	+	0.0676989i
$109$	−316.406			−0.278039			−0.139019	−	0.990290i	$-0.544395\pi$
$109$	−316.406			−0.278039			−0.139019	+	0.990290i	$0.544395\pi$
$110$	1132.89	−	1962.22i	0.981969	−	1.70082i
$111$	−81.2380	+	22.9426i	−0.0694664	+	0.0196181i
$112$	271.760	+	470.701i	0.229276	+	0.397117i
$113$	808.248	+	1399.93i	0.672864	+	1.16543i	0.977088	+	0.212834i	$0.0682694\pi$
$113$	808.248	+	1399.93i	0.672864	+	1.16543i	−0.304224	+	0.952600i	$0.598397\pi$
$114$	−361.821	+	1426.79i	−0.297260	+	1.17220i
$115$	−659.777	+	1142.77i	−0.534996	+	0.926640i
$116$	485.309			0.388447
$117$	578.895	+	313.783i	0.457426	+	0.247943i
$118$	6.31024			0.00492292
$119$	394.177	−	682.734i	0.303648	−	0.525934i
$120$	−660.106	−	642.591i	−0.502160	−	0.488835i
$121$	−1835.85	−	3179.79i	−1.37930	−	2.38903i
$122$	−54.4933	−	94.3851i	−0.0404393	−	0.0700428i
$123$	−804.462	−	783.117i	−0.589723	−	0.574075i
$124$	−215.895	+	373.940i	−0.156354	+	0.270813i
$125$	−1504.60			−1.07661
$126$	−537.538	−	291.366i	−0.380061	−	0.206008i
$127$	1607.28			1.12302			0.561508	−	0.827471i	$-0.310221\pi$
$127$	1607.28			1.12302			0.561508	+	0.827471i	$0.310221\pi$
$128$	−871.665	+	1509.77i	−0.601914	+	1.04255i
$129$	−81.0156	+	319.474i	−0.0552947	+	0.218048i
$130$	390.620	+	676.574i	0.263536	+	0.456458i
$131$	−185.916	−	322.016i	−0.123997	−	0.214768i	0.797344	−	0.603525i	$-0.206238\pi$
$131$	−185.916	−	322.016i	−0.123997	−	0.214768i	−0.921340	+	0.388757i	$0.872905\pi$
$132$	872.052	−	246.278i	0.575018	−	0.162392i
$133$	306.478	−	530.835i	0.199812	−	0.346084i
$134$	−1111.86			−0.716793
$135$	1355.31	+	305.161i	0.864050	+	0.194549i
$136$	2016.40			1.27136
$137$	391.771	−	678.568i	0.244316	−	0.423167i	−0.717623	−	0.696432i	$-0.754770\pi$
$137$	391.771	−	678.568i	0.244316	−	0.423167i	0.961939	+	0.273264i	$0.0881033\pi$
$138$	−2155.74	+	608.806i	−1.32977	+	0.375543i
$139$	−718.761	−	1244.93i	−0.438593	−	0.759666i	0.558988	−	0.829176i	$-0.311190\pi$
$139$	−718.761	−	1244.93i	−0.438593	−	0.759666i	−0.997581	+	0.0695097i	$0.977857\pi$
$140$	−85.4518	−	148.007i	−0.0515857	−	0.0893490i
$141$	−354.319	+	1397.21i	−0.211624	+	0.834512i
$142$	1470.15	−	2546.38i	0.868819	−	1.50484i
$143$	1724.94			1.00872
$144$	−56.3642	−	2095.67i	−0.0326182	−	1.21277i
$145$	1949.08			1.11629
$146$	656.612	−	1137.29i	0.372203	−	0.644674i
$147$	182.442	+	177.601i	0.102364	+	0.0996481i
$148$	−20.0277	−	34.6890i	−0.0111234	−	0.0192663i
$149$	722.401	+	1251.23i	0.397190	+	0.687954i	0.993378	−	0.114891i	$-0.0366519\pi$
$149$	722.401	+	1251.23i	0.397190	+	0.687954i	−0.596188	+	0.802845i	$0.703319\pi$
$150$	−324.568	−	315.956i	−0.176673	−	0.171985i
$151$	324.828	−	562.619i	0.175061	−	0.303214i	−0.765122	−	0.643886i	$-0.777321\pi$
$151$	324.828	−	562.619i	0.175061	−	0.303214i	0.940182	+	0.340672i	$0.110654\pi$
$152$	1567.78			0.836601
$153$	−2591.57	+	1590.65i	−1.36939	+	0.840498i
$154$	−1601.70			−0.838111
$155$	−867.069	+	1501.81i	−0.449320	+	0.778245i
$156$	−76.8019	+	302.858i	−0.0394172	+	0.155436i
$157$	349.646	+	605.605i	0.177738	+	0.307851i	0.941105	−	0.338114i	$-0.109789\pi$
$157$	349.646	+	605.605i	0.177738	+	0.307851i	−0.763368	+	0.645964i	$0.776455\pi$
$158$	−740.759	−	1283.03i	−0.372985	−	0.646029i
$159$	506.399	−	143.013i	0.252579	−	0.0713313i
$160$	534.496	−	925.774i	0.264097	−	0.457430i
$161$	932.810			0.456619
$162$	1287.26	+	1976.06i	0.624299	+	0.958358i
$163$	2915.70			1.40107			0.700537	−	0.713616i	$-0.252944\pi$
$163$	2915.70			1.40107			0.700537	+	0.713616i	$0.252944\pi$
$164$	266.360	−	461.348i	0.126824	−	0.219666i
$165$	3502.30	−	989.093i	1.65245	−	0.466671i
$166$	−144.819	−	250.834i	−0.0677117	−	0.117280i
$167$	−119.408	−	206.820i	−0.0553295	−	0.0958335i	0.837034	−	0.547151i	$-0.184288\pi$
$167$	−119.408	−	206.820i	−0.0553295	−	0.0958335i	−0.892364	+	0.451317i	$0.850954\pi$
$168$	−160.078	+	631.247i	−0.0735137	+	0.289892i
$169$	801.120	−	1387.58i	0.364643	−	0.631580i
$170$	−3607.75			−1.62766
$171$	−2014.98	+	1236.75i	−0.901109	+	0.553080i
$172$	−156.390			−0.0693291
$173$	−1137.51	+	1970.23i	−0.499905	+	0.865861i	−1.00000		0.000109416i	$-0.999965\pi$
$173$	−1137.51	+	1970.23i	−0.499905	+	0.865861i	0.500095	+	0.865971i	$0.333299\pi$
$174$	2370.87	+	2307.96i	1.03296	+	1.00555i
$175$	94.3114	+	163.352i	0.0407387	+	0.0705615i
$176$	−2745.93	−	4756.09i	−1.17604	−	2.03695i
$177$	7.26259	+	7.06989i	0.00308412	+	0.00300229i
$178$	−1761.86	+	3051.63i	−0.741893	+	1.28500i
$179$	−2649.14			−1.10618			−0.553090	−	0.833121i	$-0.686552\pi$
$179$	−2649.14			−1.10618			−0.553090	+	0.833121i	$0.686552\pi$
$180$	17.7231	+	658.961i	0.00733890	+	0.272867i
$181$	−878.174			−0.360631			−0.180315	−	0.983609i	$-0.557712\pi$
$181$	−878.174			−0.360631			−0.180315	+	0.983609i	$0.557712\pi$
$182$	276.134	−	478.279i	0.112464	−	0.194793i
$183$	43.0301	−	169.683i	0.0173818	−	0.0685429i
$184$	1192.94	+	2066.23i	0.477960	+	0.827851i
$185$	−80.4345	−	139.317i	−0.0319658	−	0.0553663i
$186$	−2833.03	+	800.083i	−1.11682	+	0.315403i
$187$	−3982.86	+	6898.52i	−1.55752	+	2.69770i
$188$	−683.965			−0.265337
$189$	−292.223	−	937.589i	−0.112466	−	0.360844i
$190$	−2805.08			−1.07106
$191$	748.166	−	1295.86i	0.283431	−	0.490917i	−0.688796	−	0.724955i	$-0.741861\pi$
$191$	748.166	−	1295.86i	0.283431	−	0.490917i	0.972228	+	0.234038i	$0.0751939\pi$
$192$	−1359.78	+	384.018i	−0.511112	+	0.144344i
$193$	274.978	+	476.276i	0.102556	+	0.177632i	0.912737	−	0.408547i	$-0.133965\pi$
$193$	274.978	+	476.276i	0.102556	+	0.177632i	−0.810181	+	0.586180i	$0.800631\pi$
$194$	487.493	+	844.363i	0.180412	+	0.312483i
$195$	−308.449	+	1216.33i	−0.113274	+	0.446683i
$196$	−60.4069	+	104.628i	−0.0220142	+	0.0381297i
$197$	−756.525			−0.273605			−0.136802	−	0.990598i	$-0.543683\pi$
$197$	−756.525			−0.273605			−0.136802	+	0.990598i	$0.543683\pi$
$198$	5431.42	+	2944.04i	1.94947	+	1.05669i
$199$	2099.11			0.747748			0.373874	−	0.927480i	$-0.378029\pi$
$199$	2099.11			0.747748			0.373874	+	0.927480i	$0.378029\pi$
$200$	−241.224	+	417.811i	−0.0852854	+	0.147719i
$201$	−1279.67	−	1245.71i	−0.449059	−	0.437143i
$202$	−122.345	−	211.908i	−0.0426146	−	0.0738107i
$203$	−688.916	−	1193.24i	−0.238189	−	0.412556i
$204$	−1033.88	−	1006.45i	−0.354835	−	0.345420i
$205$	1069.74	−	1852.85i	0.364460	−	0.631262i
$206$	5192.91			1.75634
$207$	−3163.18	−	1714.57i	−1.06211	−	0.575703i
$208$	1893.60			0.631237
$209$	−3096.73	+	5363.69i	−1.02491	+	1.77519i
$210$	286.413	−	1129.43i	0.0941161	−	0.371135i
$211$	−950.469	−	1646.26i	−0.310109	−	0.537124i	0.668277	−	0.743913i	$-0.267032\pi$
$211$	−950.469	−	1646.26i	−0.310109	−	0.537124i	−0.978386	+	0.206788i	$0.933699\pi$
$212$	124.843	+	216.235i	0.0404446	+	0.0700521i
$213$	4544.95	−	1283.55i	1.46204	−	0.412898i
$214$	1251.90	−	2168.35i	0.399897	−	0.692641i
$215$	−628.087			−0.199233
$216$	1703.10	−	1846.34i	0.536488	−	0.581610i
$217$	1225.88			0.383495
$218$	511.796	−	886.456i	0.159005	−	0.275406i
$219$	2029.91	−	573.270i	0.626340	−	0.176886i
$220$	863.427	+	1495.50i	0.264601	+	0.458302i
$221$	−1373.29	−	2378.62i	−0.417999	−	0.723995i
$222$	67.1279	−	264.710i	0.0202943	−	0.0800278i
$223$	2732.81	−	4733.36i	0.820638	−	1.42139i	−0.0845704	−	0.996418i	$-0.526952\pi$
$223$	2732.81	−	4733.36i	0.820638	−	1.42139i	0.905208	−	0.424969i	$-0.139715\pi$
$224$	−755.683			−0.225407
$225$	−19.5606	−	727.282i	−0.00579574	−	0.215491i
$226$	−5229.46			−1.53920
$227$	1503.06	−	2603.38i	0.439480	−	0.761201i	−0.558170	−	0.829727i	$-0.688496\pi$
$227$	1503.06	−	2603.38i	0.439480	−	0.761201i	0.997649	+	0.0685257i	$0.0218295\pi$
$228$	−803.858	−	782.528i	−0.233495	−	0.227299i
$229$	3159.82	+	5472.96i	0.911819	+	1.57932i	0.811493	+	0.584362i	$0.198655\pi$
$229$	3159.82	+	5472.96i	0.911819	+	1.57932i	0.100326	+	0.994955i	$0.468012\pi$
$230$	−2134.42	−	3696.92i	−0.611910	−	1.05986i
$231$	−1843.44	−	1794.52i	−0.525062	−	0.511130i
$232$	1762.06	−	3051.98i	0.498643	−	0.863674i
$233$	−4373.16			−1.22959			−0.614796	−	0.788686i	$-0.710762\pi$
$233$	−4373.16			−1.22959			−0.614796	+	0.788686i	$0.710762\pi$
$234$	−1815.49	+	1114.30i	−0.507189	+	0.311301i
$235$	−2746.92			−0.762507
$236$	−2.40466	+	4.16500i	−0.000663264	+	0.00114881i
$237$	584.933	−	2306.61i	0.160318	−	0.632195i
$238$	1275.18	+	2208.68i	0.347302	+	0.601545i
$239$	2256.37	+	3908.15i	0.610680	+	1.05773i	0.991126	+	0.132925i	$0.0424371\pi$
$239$	2256.37	+	3908.15i	0.610680	+	1.05773i	−0.380446	+	0.924803i	$0.624230\pi$
$240$	3844.75	−	1085.80i	1.03407	−	0.292035i
$241$	−1095.60	+	1897.64i	−0.292838	+	0.507211i	−0.974480	−	0.224476i	$-0.927933\pi$
$241$	−1095.60	+	1897.64i	−0.292838	+	0.507211i	0.681641	+	0.731686i	$0.261266\pi$
$242$	11878.2			3.15520
$243$	−732.414	+	3716.51i	−0.193351	+	0.981130i
$244$	83.0638			0.0217935
$245$	−242.604	+	420.203i	−0.0632629	+	0.109575i
$246$	3495.25	−	987.101i	0.905891	−	0.255834i
$247$	−1067.75	−	1849.41i	−0.275059	−	0.476416i
$248$	1567.74	+	2715.41i	0.401418	+	0.695276i
$249$	114.355	−	450.944i	0.0291042	−	0.114769i
$250$	2433.74	−	4215.36i	0.615692	−	1.06641i
$251$	6001.50			1.50921			0.754605	−	0.656180i	$-0.227829\pi$
$251$	6001.50			1.50921			0.754605	+	0.656180i	$0.227829\pi$
$252$	397.154	−	243.764i	0.0992792	−	0.0609353i
$253$	−9425.35			−2.34216
$254$	−2599.82	+	4503.02i	−0.642233	+	1.11238i
$255$	−4152.25	−	4042.07i	−1.01970	−	0.992644i
$256$	−1732.19	−	3000.23i	−0.422897	−	0.732479i
$257$	63.3400	+	109.708i	0.0153737	+	0.0266280i	0.873610	−	0.486627i	$-0.161773\pi$
$257$	63.3400	+	109.708i	0.0153737	+	0.0266280i	−0.858236	+	0.513255i	$0.828440\pi$
$258$	−764.007	−	743.735i	−0.184360	−	0.179469i
$259$	−56.8602	+	98.4847i	−0.0136414	+	0.0236276i
$260$	−595.420			−0.142025
$261$	142.884	+	5312.57i	0.0338863	+	1.25992i
$262$	1202.90			0.283646
$263$	1500.83	−	2599.51i	0.351882	−	0.609477i	−0.634698	−	0.772761i	$-0.718875\pi$
$263$	1500.83	−	2599.51i	0.351882	−	0.609477i	0.986579	+	0.163284i	$0.0522086\pi$
$264$	1617.47	−	6378.29i	0.377078	−	1.48696i
$265$	501.391	+	868.434i	0.116227	+	0.201311i
$266$	991.472	+	1717.28i	0.228538	+	0.395839i
$267$	−5446.76	+	1538.23i	−1.24845	+	0.352578i
$268$	423.701	−	733.872i	0.0965734	−	0.167270i
$269$	1834.75			0.415861			0.207931	−	0.978144i	$-0.433327\pi$
$269$	1834.75			0.415861			0.207931	+	0.978144i	$0.433327\pi$
$270$	−3047.21	+	3303.49i	−0.686841	+	0.744608i
$271$	−4187.75			−0.938701			−0.469350	−	0.883012i	$-0.655512\pi$
$271$	−4187.75			−0.938701			−0.469350	+	0.883012i	$0.655512\pi$
$272$	−4372.30	+	7573.04i	−0.974667	+	1.68817i
$273$	853.666	−	241.085i	0.189253	−	0.0534474i
$274$	1267.40	+	2195.20i	0.279440	+	0.484004i
$275$	−952.947	−	1650.55i	−0.208963	−	0.361935i
$276$	419.659	−	1654.87i	0.0915235	−	0.360911i
$277$	−1672.53	+	2896.91i	−0.362789	+	0.628369i	−0.988419	−	0.151751i	$-0.951509\pi$
$277$	−1672.53	+	2896.91i	−0.362789	+	0.628369i	0.625630	+	0.780120i	$0.284842\pi$
$278$	4650.46			1.00330
$279$	−4157.00	−	2253.25i	−0.892019	−	0.483508i
$280$	−1241.03			−0.264878
$281$	3996.54	−	6922.21i	0.848447	−	1.46955i	−0.0341468	−	0.999417i	$-0.510871\pi$
$281$	3996.54	−	6922.21i	0.848447	−	1.46955i	0.882594	−	0.470136i	$-0.155795\pi$
$282$	−3341.36	−	3252.70i	−0.705585	−	0.686863i
$283$	−4046.09	−	7008.03i	−0.849876	−	1.47203i	−0.881318	−	0.472523i	$-0.843343\pi$
$283$	−4046.09	−	7008.03i	−0.849876	−	1.47203i	0.0314421	−	0.999506i	$-0.489990\pi$
$284$	1120.47	+	1940.71i	0.234112	+	0.405493i
$285$	−3228.43	−	3142.76i	−0.671002	−	0.653198i
$286$	−2790.13	+	4832.66i	−0.576868	+	0.999164i
$287$	−1512.43			−0.311066
$288$	2562.54	+	1389.00i	0.524303	+	0.284192i
$289$	7770.69			1.58166
$290$	−3152.70	+	5460.63i	−0.638389	+	1.10572i
$291$	−384.944	+	1517.98i	−0.0775457	+	0.305791i
$292$	500.435	+	866.779i	0.100294	+	0.173714i
$293$	−1048.47	−	1816.01i	−0.209053	−	0.362090i	0.742364	−	0.669997i	$-0.233705\pi$
$293$	−1048.47	−	1816.01i	−0.209053	−	0.362090i	−0.951416	+	0.307907i	$0.900371\pi$
$294$	−792.678	+	223.862i	−0.157245	+	0.0444078i
$295$	−9.65753	+	16.7273i	−0.00190604	+	0.00330137i
$296$	−290.866			−0.0571158
$297$	2952.70	+	9473.64i	0.576878	+	1.85090i
$298$	−4674.01			−0.908585
$299$	1624.93	−	2814.47i	0.314289	−	0.544364i
$300$	332.228	−	93.8251i	0.0639373	−	0.0180566i
$301$	222.001	+	384.518i	0.0425115	+	0.0736320i
$302$	1050.84	+	1820.11i	0.200228	+	0.346806i
$303$	96.6084	−	380.963i	0.0183169	−	0.0722301i
$304$	−3399.52	+	5888.14i	−0.641368	+	1.11088i
$305$	333.598			0.0626287
$306$	−264.479	−	9833.57i	−0.0494093	−	1.83708i
$307$	2843.40			0.528604			0.264302	−	0.964440i	$-0.414858\pi$
$307$	2843.40			0.528604			0.264302	+	0.964440i	$0.414858\pi$
$308$	610.367	−	1057.19i	0.112919	−	0.195581i
$309$	5976.63	+	5818.05i	1.10032	+	1.07112i
$310$	−2805.02	−	4858.43i	−0.513917	−	0.890130i
$311$	1675.49	+	2902.04i	0.305494	+	0.529130i	0.977371	−	0.211532i	$-0.0678452\pi$
$311$	1675.49	+	2902.04i	0.305494	+	0.529130i	−0.671878	+	0.740662i	$0.734512\pi$
$312$	1625.74	+	1582.61i	0.294999	+	0.287171i
$313$	2818.46	−	4881.72i	0.508974	−	0.881569i	−0.490972	−	0.871175i	$-0.663358\pi$
$313$	2818.46	−	4881.72i	0.508974	−	0.881569i	0.999946	−	0.0103933i	$-0.00330834\pi$
$314$	−2262.25			−0.406580
$315$	1595.04	−	978.997i	0.285302	−	0.175112i
$316$	1129.13			0.201009
$317$	−2314.20	+	4008.30i	−0.410026	+	0.710185i	−0.994892	−	0.100944i	$-0.967814\pi$
$317$	−2314.20	+	4008.30i	−0.410026	+	0.710185i	0.584866	+	0.811130i	$0.301147\pi$
$318$	−418.443	+	1650.08i	−0.0737897	+	0.290980i
$319$	6960.99	+	12056.8i	1.22176	+	2.11614i
$320$	−1346.33	−	2331.91i	−0.235194	−	0.407368i
$321$	3870.22	−	1093.00i	0.672942	−	0.190047i
$322$	−1508.85	+	2613.40i	−0.261133	+	0.452295i
$323$	9861.74			1.69883
$324$	−1794.82	+	96.6149i	−0.307753	+	0.0165663i
$325$	657.154			0.112161
$326$	−4716.22	+	8168.74i	−0.801250	+	1.38781i
$327$	1582.21	−	446.835i	0.267573	−	0.0755658i
$328$	−1934.20	−	3350.13i	−0.325604	−	0.563963i
$329$	970.915	+	1681.67i	0.162700	+	0.281805i
$330$	−2893.99	+	11412.1i	−0.482755	+	1.90368i
$331$	−3864.43	+	6693.38i	−0.641716	+	1.11148i	0.343333	+	0.939214i	$0.388444\pi$
$331$	−3864.43	+	6693.38i	−0.641716	+	1.11148i	−0.985050	+	0.172271i	$0.944889\pi$
$332$	220.747			0.0364912
$333$	373.836	−	229.452i	0.0615197	−	0.0377594i
$334$	772.580			0.126568
$335$	1701.66	−	2947.35i	0.277526	−	0.480690i
$336$	−2023.68	−	1969.99i	−0.328574	−	0.319856i
$337$	−2138.41	−	3703.83i	−0.345657	−	0.598696i	0.639816	−	0.768528i	$-0.279011\pi$
$337$	−2138.41	−	3703.83i	−0.345657	−	0.598696i	−0.985473	+	0.169833i	$0.945677\pi$
$338$	2591.67	+	4488.90i	0.417066	+	0.722379i
$339$	−6018.70	−	5859.00i	−0.964280	−	0.938694i
$340$	1374.82	−	2381.26i	0.219294	−	0.379829i
$341$	−12386.6			−1.96708
$342$	−205.636	−	7645.74i	−0.0325132	−	1.20887i
$343$	343.000			0.0539949
$344$	−567.820	+	983.494i	−0.0889966	+	0.154147i
$345$	1685.42	−	6646.23i	0.263014	−	1.03716i
$346$	−3679.92	−	6373.81i	−0.571774	−	0.990342i
$347$	−2924.12	−	5064.72i	−0.452377	−	0.783540i	0.546156	−	0.837683i	$-0.316091\pi$
$347$	−2924.12	−	5064.72i	−0.452377	−	0.783540i	−0.998533	+	0.0541434i	$0.982757\pi$
$348$	−2426.82	+	685.363i	−0.373825	+	0.105573i
$349$	2494.35	−	4320.34i	0.382577	−	0.662643i	−0.608853	−	0.793283i	$-0.708370\pi$
$349$	2494.35	−	4320.34i	0.382577	−	0.662643i	0.991430	+	0.130640i	$0.0417032\pi$
$350$	−610.206			−0.0931910
$351$	−3337.93	−	751.566i	−0.507595	−	0.114290i
$352$	7635.62			1.15619
$353$	5868.39	−	10164.4i	0.884824	−	1.53256i	0.0389094	−	0.999243i	$-0.487612\pi$
$353$	5868.39	−	10164.4i	0.884824	−	1.53256i	0.845915	−	0.533318i	$-0.179055\pi$
$354$	−31.5547	+	8.91143i	−0.00473761	+	0.00133796i
$355$	4500.00	+	7794.23i	0.672775	+	1.16528i
$356$	−1342.80	−	2325.79i	−0.199910	−	0.346255i
$357$	−1006.94	+	3970.72i	−0.149279	+	0.588663i
$358$	4285.06	−	7421.95i	0.632605	−	1.09570i
$359$	−4291.93			−0.630974			−0.315487	−	0.948930i	$-0.602168\pi$
$359$	−4291.93			−0.630974			−0.315487	+	0.948930i	$0.602168\pi$
$360$	4208.38	+	2281.10i	0.616114	+	0.333957i
$361$	808.635			0.117894
$362$	1420.47	−	2460.33i	0.206238	−	0.357215i
$363$	13670.9	+	13308.1i	1.97668	+	1.92423i
$364$	210.455	+	364.519i	0.0303045	+	0.0524890i
$365$	2009.83	+	3481.13i	0.288218	+	0.499207i
$366$	405.790	+	395.022i	0.0579534	+	0.0564157i
$367$	−3230.95	+	5596.17i	−0.459548	+	0.795960i	−0.998937	−	0.0460963i	$-0.985322\pi$
$367$	−3230.95	+	5596.17i	−0.459548	+	0.795960i	0.539389	+	0.842057i	$0.318655\pi$
$368$	−10346.9			−1.46568
$369$	5128.70	+	2779.95i	0.723548	+	0.392191i
$370$	520.420			0.0731226
$371$	354.439	−	613.907i	0.0495999	−	0.0859096i
$372$	551.509	−	2174.80i	0.0768667	−	0.303114i
$373$	−2066.93	−	3580.03i	−0.286921	−	0.496962i	0.686152	−	0.727458i	$-0.259298\pi$
$373$	−2066.93	−	3580.03i	−0.286921	−	0.496962i	−0.973073	+	0.230496i	$0.925965\pi$
$374$	−12884.8	−	22317.1i	−1.78143	−	3.08553i
$375$	7523.86	−	2124.83i	1.03608	−	0.292602i
$376$	−2483.34	+	4301.28i	−0.340608	+	0.589950i
$377$	−4800.31			−0.655778
$378$	3099.47	+	697.873i	0.421744	+	0.0949595i
$379$	−1623.62			−0.220053			−0.110026	−	0.993929i	$-0.535094\pi$
$379$	−1623.62			−0.220053			−0.110026	+	0.993929i	$0.535094\pi$
$380$	1068.94	−	1851.46i	0.144304	−	0.249942i
$381$	−8037.30	+	2269.83i	−1.08074	+	0.305215i
$382$	2420.36	+	4192.18i	0.324179	+	0.561494i
$383$	−334.741	−	579.788i	−0.0446592	−	0.0773519i	0.842832	−	0.538177i	$-0.180887\pi$
$383$	−334.741	−	579.788i	−0.0446592	−	0.0773519i	−0.887491	+	0.460825i	$0.847554\pi$
$384$	2226.69	−	8780.68i	0.295913	−	1.16689i
$385$	2451.34	−	4245.84i	0.324498	−	0.562047i
$386$	−1779.14			−0.234600
$387$	−46.0441	−	1711.96i	−0.00604794	−	0.224868i
$388$	−743.083			−0.0972276
$389$	2438.29	−	4223.23i	0.317805	−	0.550454i	−0.662225	−	0.749305i	$-0.730388\pi$
$389$	2438.29	−	4223.23i	0.317805	−	0.550454i	0.980030	+	0.198851i	$0.0637211\pi$
$390$	−2908.79	−	2831.61i	−0.377673	−	0.367652i
$391$	7503.91	+	12997.2i	0.970560	+	1.68106i
$392$	438.651	+	759.766i	0.0565185	+	0.0978928i
$393$	1384.44	+	1347.71i	0.177699	+	0.172984i
$394$	1223.70	−	2119.51i	0.156470	−	0.271014i
$395$	4534.79			0.577646
$396$	−4012.95	+	2463.06i	−0.509238	+	0.312559i
$397$	5451.74			0.689207			0.344604	−	0.938748i	$-0.388013\pi$
$397$	5451.74			0.689207			0.344604	+	0.938748i	$0.388013\pi$
$398$	−3395.37	+	5880.95i	−0.427624	+	0.740666i
$399$	−782.906	+	3087.29i	−0.0982314	+	0.387363i
$400$	−1046.12	−	1811.94i	−0.130765	−	0.226492i
$401$	−6197.98	−	10735.2i	−0.771851	−	1.33689i	−0.936547	−	0.350541i	$-0.885998\pi$
$401$	−6197.98	−	10735.2i	−0.771851	−	1.33689i	0.164696	−	0.986344i	$-0.447336\pi$
$402$	5559.94	−	1570.19i	0.689812	−	0.194811i
$403$	2135.46	−	3698.73i	0.263958	−	0.457188i
$404$	186.490			0.0229659
$405$	−7208.28	+	388.021i	−0.884401	+	0.0476073i
$406$	4457.36			0.544865
$407$	574.530	−	995.115i	0.0699715	−	0.121194i
$408$	−10083.1	+	2847.59i	−1.22350	+	0.345532i
$409$	−5834.92	−	10106.4i	−0.705424	−	1.22183i	−0.966538	−	0.256522i	$-0.917423\pi$
$409$	−5834.92	−	10106.4i	−0.705424	−	1.22183i	0.261114	−	0.965308i	$-0.415910\pi$
$410$	3460.68	+	5994.08i	0.416856	+	0.722016i
$411$	−1000.79	+	3946.49i	−0.120110	+	0.473640i
$412$	−1978.88	+	3427.52i	−0.236632	+	0.409859i
$413$	13.6541			0.00162681
$414$	9920.13	−	6088.75i	1.17765	−	0.722815i
$415$	886.557			0.104866
$416$	−1316.38	+	2280.04i	−0.155147	+	0.268722i
$417$	5352.32	+	5210.31i	0.628548	+	0.611870i
$418$	−10018.1	−	17351.9i	−1.17225	−	2.03040i
$419$	−1948.44	−	3374.79i	−0.227177	−	0.393483i	0.729793	−	0.683668i	$-0.239616\pi$
$419$	−1948.44	−	3374.79i	−0.227177	−	0.393483i	−0.956970	+	0.290185i	$0.906283\pi$
$420$	636.325	+	619.441i	0.0739273	+	0.0719657i
$421$	−3823.60	+	6622.68i	−0.442639	+	0.766674i	−0.997884	−	0.0650131i	$-0.979291\pi$
$421$	−3823.60	+	6622.68i	−0.442639	+	0.766674i	0.555245	+	0.831687i	$0.312624\pi$
$422$	6149.64			0.709383
$423$	−201.372	−	7487.21i	−0.0231467	−	0.860616i
$424$	1813.12			0.207672
$425$	−1517.36	+	2628.15i	−0.173183	+	0.299962i
$426$	−3755.54	+	14809.5i	−0.427128	+	1.68432i
$427$	−117.912	−	204.230i	−0.0133634	−	0.0231461i
$428$	954.129	+	1652.60i	0.107756	+	0.186639i
$429$	−8625.66	+	2435.99i	−0.970748	+	0.274151i
$430$	1015.95	−	1759.68i	0.113938	−	0.197347i
$431$	9785.23			1.09359			0.546796	−	0.837266i	$-0.315847\pi$
$431$	9785.23			1.09359			0.546796	+	0.837266i	$0.315847\pi$
$432$	3241.40	+	10399.9i	0.361000	+	1.15826i
$433$	2714.44			0.301265			0.150632	−	0.988590i	$-0.451869\pi$
$433$	2714.44			0.301265			0.150632	+	0.988590i	$0.451869\pi$
$434$	−1982.90	+	3434.48i	−0.219314	+	0.379863i
$435$	−9746.52	+	2752.53i	−1.07428	+	0.303388i
$436$	390.064	+	675.610i	0.0428456	+	0.0742107i
$437$	5834.39	+	10105.5i	0.638666	+	1.10620i
$438$	−1677.34	+	6614.35i	−0.182982	+	0.721566i
$439$	2344.74	−	4061.21i	0.254916	−	0.441528i	−0.709957	−	0.704246i	$-0.751285\pi$
$439$	2344.74	−	4061.21i	0.254916	−	0.441528i	0.964873	+	0.262718i	$0.0846188\pi$
$440$	12539.7			1.35866
$441$	−1163.12	−	630.456i	−0.125594	−	0.0680765i
$442$	8885.37			0.956185
$443$	6201.10	−	10740.6i	0.665063	−	1.15192i	−0.314205	−	0.949355i	$-0.601738\pi$
$443$	6201.10	−	10740.6i	0.665063	−	1.15192i	0.979268	−	0.202568i	$-0.0649289\pi$
$444$	149.138	+	145.181i	0.0159410	+	0.0155180i
$445$	−5392.89	−	9340.77i	−0.574489	−	0.995045i
$446$	8840.78	+	15312.7i	0.938617	+	1.62573i
$447$	−5379.43	−	5236.69i	−0.569213	−	0.554110i
$448$	−951.737	+	1648.46i	−0.100369	+	0.173844i
$449$	−15666.5			−1.64665			−0.823327	−	0.567567i	$-0.807885\pi$
$449$	−15666.5			−1.64665			−0.823327	+	0.567567i	$0.807885\pi$
$450$	2069.22	+	1121.60i	0.216765	+	0.117495i
$451$	15282.0			1.59557
$452$	1992.81	−	3451.64i	0.207376	−	0.359185i
$453$	−829.784	+	3272.14i	−0.0860632	+	0.339379i
$454$	4862.50	+	8422.09i	0.502661	+	0.870635i
$455$	845.223	+	1463.97i	0.0870872	+	0.150839i
$456$	−7839.76	+	2214.04i	−0.805111	+	0.227373i
$457$	−1854.38	+	3211.88i	−0.189812	+	0.328764i	−0.945188	−	0.326528i	$-0.894121\pi$
$457$	−1854.38	+	3211.88i	−0.189812	+	0.328764i	0.755375	+	0.655292i	$0.227455\pi$
$458$	−20444.4			−2.08581
$459$	10713.0	−	11614.0i	1.08941	−	1.18104i
$460$	3253.48			0.329770
$461$	−1393.09	+	2412.91i	−0.140744	+	0.243775i	−0.927777	−	0.373135i	$-0.878283\pi$
$461$	−1393.09	+	2412.91i	−0.140744	+	0.243775i	0.787033	+	0.616911i	$0.211616\pi$
$462$	8009.43	−	2261.96i	0.806563	−	0.227783i
$463$	4788.05	+	8293.14i	0.480604	+	0.832430i	0.999752	−	0.0222541i	$-0.00708427\pi$
$463$	4788.05	+	8293.14i	0.480604	+	0.832430i	−0.519149	+	0.854684i	$0.673751\pi$
$464$	7641.61	+	13235.7i	0.764554	+	1.32425i
$465$	2214.95	−	8734.37i	0.220894	−	0.871068i
$466$	7073.70	−	12252.0i	0.703182	−	1.21795i
$467$	−10292.2			−1.01984			−0.509922	−	0.860221i	$-0.670326\pi$
$467$	−10292.2			−1.01984			−0.509922	+	0.860221i	$0.670326\pi$
$468$	−43.6494	−	1622.92i	−0.00431131	−	0.160298i
$469$	−2405.84			−0.236869
$470$	4443.22	−	7695.88i	0.436064	−	0.755286i
$471$	−2603.68	−	2534.59i	−0.254716	−	0.247957i
$472$	17.4617	+	30.2446i	0.00170284	+	0.00294941i
$473$	−2243.16	−	3885.27i	−0.218056	−	0.377685i
$474$	5516.14	+	5369.77i	0.534524	+	0.520341i
$475$	−1179.77	+	2043.42i	−0.113961	+	0.197386i
$476$	−1943.75			−0.187168
$477$	−2330.31	+	1430.29i	−0.223685	+	0.137293i
$478$	−14599.0			−1.39695
$479$	−9648.64	+	16711.9i	−0.920371	+	1.59413i	−0.121530	+	0.992588i	$0.538780\pi$
$479$	−9648.64	+	16711.9i	−0.920371	+	1.59413i	−0.798841	+	0.601542i	$0.794553\pi$
$480$	−1365.38	+	5384.21i	−0.129835	+	0.511989i
$481$	198.098	+	343.116i	0.0187786	+	0.0325255i
$482$	−3544.34	−	6138.98i	−0.334938	−	0.580130i
$483$	−4664.57	+	1317.33i	−0.439432	+	0.124101i
$484$	−4526.46	+	7840.06i	−0.425100	+	0.736294i
$485$	−2984.34			−0.279406
$486$	−9227.64	−	8063.53i	−0.861264	−	0.752611i
$487$	−12934.5			−1.20353			−0.601766	−	0.798672i	$-0.705536\pi$
$487$	−12934.5			−1.20353			−0.601766	+	0.798672i	$0.705536\pi$
$488$	301.588	−	522.366i	0.0279759	−	0.0484557i
$489$	−14580.1	+	4117.60i	−1.34834	+	0.380786i
$490$	−784.838	−	1359.38i	−0.0723579	−	0.125328i
$491$	5914.84	+	10244.8i	0.543651	+	0.941632i	0.998690	+	0.0511605i	$0.0162920\pi$
$491$	5914.84	+	10244.8i	0.543651	+	0.941632i	−0.455039	+	0.890472i	$0.650375\pi$
$492$	−680.423	+	2683.16i	−0.0623493	+	0.245866i
$493$	11083.9	−	19197.8i	1.01256	−	1.75380i
$494$	6908.49			0.629206
$495$	−16116.7	+	9892.04i	−1.46342	+	0.898211i
$496$	−13597.8			−1.23096
$497$	3181.11	−	5509.84i	0.287107	−	0.497284i
$498$	1078.41	+	1049.80i	0.0970376	+	0.0944628i
$499$	3379.74	+	5853.88i	0.303202	+	0.525162i	0.976859	−	0.213882i	$-0.0686109\pi$
$499$	3379.74	+	5853.88i	0.303202	+	0.525162i	−0.673657	+	0.739044i	$0.735278\pi$
$500$	1854.87	+	3212.72i	0.165904	+	0.287355i
$501$	889.180	+	865.586i	0.0792927	+	0.0771887i
$502$	−9707.60	+	16814.1i	−0.863090	+	1.49492i
$503$	16856.9			1.49425			0.747127	−	0.664681i	$-0.231432\pi$
$503$	16856.9			1.49425			0.747127	+	0.664681i	$0.231432\pi$
$504$	−90.9783	−	3382.66i	−0.00804067	−	0.298959i
$505$	748.973			0.0659978
$506$	15245.8	−	26406.5i	1.33944	−	2.31998i
$507$	−2046.48	+	8070.04i	−0.179265	+	0.706910i
$508$	−1981.44	−	3431.96i	−0.173056	−	0.299742i
$509$	3581.29	+	6202.97i	0.311862	+	0.540161i	0.978765	−	0.204983i	$-0.0657140\pi$
$509$	3581.29	+	6202.97i	0.311862	+	0.540161i	−0.666903	+	0.745144i	$0.732381\pi$
$510$	18040.8	−	5094.94i	1.56639	−	0.442368i
$511$	1420.78	−	2460.85i	0.122997	−	0.213037i
$512$	−2739.20			−0.236439
$513$	8329.49	−	9030.04i	0.716873	−	0.777166i
$514$	−409.817			−0.0351678
$515$	−7947.51	+	13765.5i	−0.680018	+	1.17783i
$516$	782.037	−	220.857i	0.0667195	−	0.0188424i
$517$	−9810.38	−	16992.1i	−0.834546	−	1.44548i
$518$	−183.946	−	318.604i	−0.0156025	−	0.0270244i
$519$	2905.81	−	11458.7i	0.245763	−	0.969134i
$520$	−2161.85	+	3744.44i	−0.182315	+	0.315778i
$521$	−2414.92			−0.203070			−0.101535	−	0.994832i	$-0.532375\pi$
$521$	−2414.92			−0.203070			−0.101535	+	0.994832i	$0.532375\pi$
$522$	−15115.0	−	8192.92i	−1.26737	−	0.686963i
$523$	−9967.09			−0.833328			−0.416664	−	0.909061i	$-0.636801\pi$
$523$	−9967.09			−0.833328			−0.416664	+	0.909061i	$0.636801\pi$
$524$	−458.392	+	793.958i	−0.0382156	+	0.0661913i
$525$	−702.299	−	683.665i	−0.0583826	−	0.0568335i
$526$	4855.25	+	8409.55i	0.402470	+	0.697098i
$527$	9861.52	+	17080.7i	0.815132	+	1.41185i
$528$	20447.8	+	19905.3i	1.68537	+	1.64065i
$529$	−2795.42	+	4841.80i	−0.229754	+	0.397945i
$530$	−3244.05			−0.265873
$531$	−46.3013	−	25.0971i	−0.00378400	−	0.00205107i
$532$	−1511.30			−0.123163
$533$	−2634.62	+	4563.30i	−0.214105	+	0.370841i
$534$	4500.72	−	17748.0i	0.364729	−	1.43826i
$535$	3831.94	+	6637.12i	0.309662	+	0.536351i
$536$	−3076.75	−	5329.09i	−0.247939	−	0.429443i
$537$	13247.2	−	3741.17i	1.06454	−	0.300640i
$538$	−2967.76	+	5140.31i	−0.237824	+	0.411923i
$539$	−3465.76			−0.276959
$540$	−1019.22	−	3270.15i	−0.0812229	−	0.260601i
$541$	−11805.7			−0.938197			−0.469099	−	0.883146i	$-0.655421\pi$
$541$	−11805.7			−0.938197			−0.469099	+	0.883146i	$0.655421\pi$
$542$	6773.81	−	11732.6i	0.536826	−	0.929811i
$543$	4391.36	−	1240.17i	0.347056	−	0.0980128i
$544$	−6079.03	−	10529.2i	−0.479111	−	0.829845i
$545$	1566.56	+	2713.36i	0.123127	+	0.213262i
$546$	−705.393	+	2781.63i	−0.0552895	+	0.218027i
$547$	−3631.58	+	6290.08i	−0.283867	+	0.491672i	−0.972334	−	0.233596i	$-0.924951\pi$
$547$	−3631.58	+	6290.08i	−0.283867	+	0.491672i	0.688467	+	0.725268i	$0.258284\pi$
$548$	−1931.89			−0.150596
$549$	24.4556	+	909.280i	0.00190116	+	0.0706870i
$550$	6165.68			0.478010
$551$	8617.85	−	14926.6i	0.666303	−	1.15407i
$552$	−8883.34	−	8647.63i	−0.684964	−	0.666789i
$553$	−1602.85	−	2776.22i	−0.123255	−	0.213484i
$554$	−5410.73	−	9371.66i	−0.414946	−	0.718707i
$555$	598.964	+	583.071i	0.0458101	+	0.0445946i
$556$	−1772.17	+	3069.49i	−0.135174	+	0.234128i
$557$	−11910.0			−0.906005			−0.453003	−	0.891509i	$-0.649647\pi$
$557$	−11910.0			−0.906005			−0.453003	+	0.891509i	$0.649647\pi$
$558$	13036.9	−	8001.73i	0.989059	−	0.607061i
$559$	1546.89			0.117042
$560$	2691.02	−	4660.99i	0.203065	−	0.351719i
$561$	10174.3	−	40121.2i	0.765706	−	3.01946i
$562$	12929.0	+	22393.7i	0.970424	+	1.68082i
$563$	−2324.56	−	4026.25i	−0.174011	−	0.301396i	0.765807	−	0.643070i	$-0.222340\pi$
$563$	−2324.56	−	4026.25i	−0.174011	−	0.301396i	−0.939819	+	0.341674i	$0.889006\pi$
$564$	3420.21	−	965.908i	0.255349	−	0.0721136i
$565$	8003.45	−	13862.4i	0.595943	−	1.03220i
$566$	26178.6			1.94412
$567$	2785.36	+	4275.79i	0.206304	+	0.316695i
$568$	16272.8			1.20210
$569$	6419.17	−	11118.3i	0.472945	−	0.819165i	−0.526575	−	0.850128i	$-0.676524\pi$
$569$	6419.17	−	11118.3i	0.472945	−	0.819165i	0.999521	+	0.0309634i	$0.00985754\pi$
$570$	14027.0	−	3961.38i	1.03075	−	0.291095i
$571$	8254.20	+	14296.7i	0.604952	+	1.04781i	0.992059	+	0.125773i	$0.0401410\pi$
$571$	8254.20	+	14296.7i	0.604952	+	1.04781i	−0.387107	+	0.922035i	$0.626526\pi$
$572$	−2126.49	−	3683.19i	−0.155443	−	0.269234i
$573$	−1911.21	+	7536.61i	−0.139340	+	0.549470i
$574$	2446.40	−	4237.29i	0.177893	−	0.308120i
$575$	−3590.80			−0.260429
$576$	6257.34	−	3840.61i	0.452643	−	0.277822i
$577$	−20917.8			−1.50922			−0.754611	−	0.656172i	$-0.772174\pi$
$577$	−20917.8			−1.50922			−0.754611	+	0.656172i	$0.772174\pi$
$578$	−12569.3	+	21770.7i	−0.904523	+	1.56668i
$579$	−2047.65	−	1993.32i	−0.146973	−	0.143073i
$580$	−2402.82	−	4161.80i	−0.172020	−	0.297947i
$581$	−313.359	−	542.754i	−0.0223758	−	0.0387560i
$582$	−3630.17	−	3533.84i	−0.258548	−	0.251688i
$583$	−3581.35	+	6203.08i	−0.254416	+	0.440661i
$584$	7267.93			0.514981
$585$	−175.303	−	6517.93i	−0.0123896	−	0.460655i
$586$	6783.74			0.478215
$587$	8769.34	−	15188.9i	0.616609	−	1.06800i	−0.373492	−	0.927634i	$-0.621839\pi$
$587$	8769.34	−	15188.9i	0.616609	−	1.06800i	0.990100	−	0.140364i	$-0.0448272\pi$
$588$	154.311	−	608.506i	0.0108226	−	0.0426775i
$589$	7667.47	+	13280.4i	0.536388	+	0.929051i
$590$	−31.2427	−	54.1139i	−0.00218007	−	0.00377599i
$591$	3783.05	−	1068.38i	0.263306	−	0.0743608i
$592$	630.706	−	1092.41i	0.0437869	−	0.0758412i
$593$	−10298.7			−0.713184			−0.356592	−	0.934260i	$-0.616061\pi$
$593$	−10298.7			−0.713184			−0.356592	+	0.934260i	$0.616061\pi$
$594$	−31317.8	−	7051.49i	−2.16328	−	0.487081i
$595$	−7806.44			−0.537871
$596$	1781.14	−	3085.03i	0.122414	−	0.212026i
$597$	−10496.7	+	2964.40i	−0.719602	+	0.203224i
$598$	5256.75	+	9104.96i	0.359473	+	0.622625i
$599$	−690.954	−	1196.77i	−0.0471313	−	0.0816338i	0.841497	−	0.540261i	$-0.181675\pi$
$599$	−690.954	−	1196.77i	−0.0471313	−	0.0816338i	−0.888629	+	0.458627i	$0.848341\pi$
$600$	616.212	−	2429.95i	0.0419279	−	0.165337i
$601$	4644.44	−	8044.41i	0.315226	−	0.545987i	−0.664260	−	0.747502i	$-0.731253\pi$
$601$	4644.44	−	8044.41i	0.315226	−	0.545987i	0.979485	+	0.201515i	$0.0645864\pi$
$602$	−1436.37			−0.0972462
$603$	8158.28	+	4422.10i	0.550963	+	0.298643i
$604$	−1601.79			−0.107907
$605$	−18179.0	+	31487.0i	−1.22162	+	2.11591i
$606$	911.053	+	886.880i	0.0610710	+	0.0594505i
$607$	−10086.7	−	17470.7i	−0.674477	−	1.16823i	−0.976621	−	0.214967i	$-0.931036\pi$
$607$	−10086.7	−	17470.7i	−0.674477	−	1.16823i	0.302144	−	0.953262i	$-0.402298\pi$
$608$	−4726.53	−	8186.59i	−0.315273	−	0.546069i
$609$	5130.08	+	4993.96i	0.341349	+	0.332291i
$610$	−539.604	+	934.622i	−0.0358163	+	0.0620356i
$611$	6765.25			0.447942
$612$	6591.32	+	3572.75i	0.435357	+	0.235980i
$613$	9495.67			0.625655			0.312828	−	0.949810i	$-0.398724\pi$
$613$	9495.67			0.625655			0.312828	+	0.949810i	$0.398724\pi$
$614$	−4599.28	+	7966.19i	−0.302300	+	0.523598i
$615$	−2732.69	+	10776.0i	−0.179175	+	0.706554i
$616$	−4432.25	−	7676.88i	−0.289903	−	0.502127i
$617$	12675.7	+	21955.0i	0.827074	+	1.43253i	0.900324	+	0.435221i	$0.143330\pi$
$617$	12675.7	+	21955.0i	0.827074	+	1.43253i	−0.0732492	+	0.997314i	$0.523337\pi$
$618$	−25967.5	+	7333.52i	−1.69023	+	0.477342i
$619$	−8175.92	+	14161.1i	−0.530885	+	0.919520i	0.468465	+	0.883482i	$0.344807\pi$
$619$	−8175.92	+	14161.1i	−0.530885	+	0.919520i	−0.999350	+	0.0360380i	$0.988526\pi$
$620$	4275.67			0.276960
$621$	18239.0	+	4106.69i	1.17859	+	0.265371i
$622$	−10840.6			−0.698826
$623$	−3812.30	+	6603.11i	−0.245163	+	0.424635i
$624$	−9469.05	+	2674.17i	−0.607477	+	0.171559i
$625$	5765.32	+	9985.83i	0.368980	+	0.639093i
$626$	9117.88	+	15792.6i	0.582146	+	1.00831i
$627$	7910.69	−	31194.8i	0.503863	−	1.98692i
$628$	862.084	−	1493.17i	0.0547785	−	0.0948791i
$629$	−1829.63			−0.115981
$630$	162.779	+	6052.28i	0.0102941	+	0.382744i
$631$	−27863.6			−1.75789			−0.878946	−	0.476920i	$-0.841753\pi$
$631$	−27863.6			−1.75789			−0.878946	+	0.476920i	$0.841753\pi$
$632$	4099.67	−	7100.83i	0.258032	−	0.446924i
$633$	7077.76	+	6889.96i	0.444417	+	0.432624i
$634$	−7486.55	−	12967.1i	−0.468973	−	0.812285i
$635$	−7957.81	−	13783.3i	−0.497317	−	0.861378i
$636$	−929.656	−	904.989i	−0.0579611	−	0.0564232i
$637$	597.499	−	1034.90i	0.0371645	−	0.0643707i
$638$	−45038.4			−2.79481
$639$	−20914.7	+	12836.9i	−1.29479	+	0.794712i
$640$	17262.8			1.06621
$641$	−809.006	+	1401.24i	−0.0498499	+	0.0863426i	−0.889874	−	0.456207i	$-0.849208\pi$
$641$	−809.006	+	1401.24i	−0.0498499	+	0.0863426i	0.840024	+	0.542550i	$0.182541\pi$
$642$	−3198.00	+	12610.9i	−0.196597	+	0.775254i
$643$	−5923.15	−	10259.2i	−0.363276	−	0.629212i	0.625222	−	0.780447i	$-0.285008\pi$
$643$	−5923.15	−	10259.2i	−0.363276	−	0.629212i	−0.988498	+	0.151235i	$0.951675\pi$
$644$	−1149.96	−	1991.79i	−0.0703647	−	0.121875i
$645$	3140.79	−	886.997i	0.191734	−	0.0541480i
$646$	−15951.6	+	27629.0i	−0.971531	+	1.68274i
$647$	12354.4			0.750696			0.375348	−	0.926884i	$-0.377523\pi$
$647$	12354.4			0.750696			0.375348	+	0.926884i	$0.377523\pi$
$648$	−5909.04	+	11637.9i	−0.358224	+	0.705525i
$649$	−137.964			−0.00834448
$650$	−1062.96	+	1841.11i	−0.0641429	+	0.111099i
$651$	−6130.11	+	1731.22i	−0.369060	+	0.104227i
$652$	−3594.46	−	6225.78i	−0.215905	−	0.373958i
$653$	6693.41	+	11593.3i	0.401123	+	0.694766i	0.993862	−	0.110629i	$-0.0352866\pi$
$653$	6693.41	+	11593.3i	0.401123	+	0.694766i	−0.592739	+	0.805395i	$0.701953\pi$
$654$	−1307.40	+	5155.55i	−0.0781701	+	0.308254i
$655$	−1840.98	+	3188.67i	−0.109821	+	0.190216i
$656$	16776.2			0.998478
$657$	−9341.10	+	5733.35i	−0.554690	+	0.340455i
$658$	−6281.93			−0.372181
$659$	6433.85	−	11143.8i	0.380314	−	0.658724i	−0.610793	−	0.791791i	$-0.709149\pi$
$659$	6433.85	−	11143.8i	0.380314	−	0.658724i	0.991107	+	0.133067i	$0.0424824\pi$
$660$	−6429.59	−	6258.99i	−0.379199	−	0.369138i
$661$	11256.4	+	19496.6i	0.662363	+	1.14725i	0.979993	+	0.199032i	$0.0637799\pi$
$661$	11256.4	+	19496.6i	0.662363	+	1.14725i	−0.317629	+	0.948215i	$0.602887\pi$
$662$	−12501.6	−	21653.5i	−0.733973	−	1.27128i
$663$	10226.4	+	9955.02i	0.599034	+	0.583139i
$664$	801.489	−	1388.22i	0.0468431	−	0.0811346i
$665$	−6069.62			−0.353939
$666$	38.1512	+	1418.50i	0.00221972	+	0.0825311i
$667$	26229.7			1.52267
$668$	−294.410	+	509.933i	−0.0170525	+	0.0295358i
$669$	−6981.03	+	27528.8i	−0.403441	+	1.59092i
$670$	5504.95	+	9534.85i	0.317425	+	0.549796i
$671$	1191.42	+	2063.59i	0.0685457	+	0.118725i
$672$	3778.84	−	1067.19i	0.216923	−	0.0612615i
$673$	11281.8	−	19540.6i	0.646181	−	1.11922i	−0.337846	−	0.941201i	$-0.609698\pi$
$673$	11281.8	−	19540.6i	0.646181	−	1.11922i	0.984027	−	0.178018i	$-0.0569684\pi$
$674$	13835.7			0.790701
$675$	1124.90	+	3609.20i	0.0641441	+	0.205805i
$676$	−3950.46			−0.224765
$677$	2677.93	−	4638.32i	0.152026	−	0.263316i	−0.779946	−	0.625846i	$-0.784754\pi$
$677$	2677.93	−	4638.32i	0.152026	−	0.263316i	0.931972	+	0.362530i	$0.118087\pi$
$678$	26150.2	−	7385.14i	1.48126	−	0.418325i
$679$	1054.84	+	1827.03i	0.0596184	+	0.103262i
$680$	−9983.40	−	17291.8i	−0.563009	−	0.975160i
$681$	−3839.62	+	15141.0i	−0.216057	+	0.851991i
$682$	20035.7	−	34702.9i	1.12494	−	1.94845i
$683$	−16933.7			−0.948682			−0.474341	−	0.880341i	$-0.657314\pi$
$683$	−16933.7			−0.948682			−0.474341	+	0.880341i	$0.657314\pi$
$684$	5124.84	+	2777.86i	0.286481	+	0.155284i
$685$	−7758.81			−0.432772
$686$	−554.812	+	960.963i	−0.0308788	+	0.0534836i
$687$	−23529.9	−	22905.5i	−1.30673	−	1.27205i
$688$	−2462.49	−	4265.16i	−0.136456	−	0.236348i
$689$	−1234.85	−	2138.83i	−0.0682788	−	0.118262i
$690$	15894.1	+	15472.4i	0.876927	+	0.853659i
$691$	16215.5	−	28086.0i	0.892715	−	1.54623i	0.0561077	−	0.998425i	$-0.482131\pi$
$691$	16215.5	−	28086.0i	0.892715	−	1.54623i	0.836607	−	0.547803i	$-0.184536\pi$
$692$	5609.28			0.308140
$693$	11752.5	+	6370.30i	0.644214	+	0.349188i
$694$	18919.4			1.03483
$695$	−7117.32	+	12327.6i	−0.388454	+	0.672822i
$696$	−4501.24	+	17750.1i	−0.245142	+	0.966687i
$697$	−12166.6	−	21073.2i	−0.661182	−	1.14520i
$698$	8069.36	+	13976.5i	0.437579	+	0.757908i
$699$	21868.2	−	6175.85i	1.18331	−	0.334181i
$700$	232.533	−	402.759i	0.0125556	−	0.0217470i
$701$	20140.3			1.08515			0.542575	−	0.840008i	$-0.317450\pi$
$701$	20140.3			1.08515			0.542575	+	0.840008i	$0.317450\pi$
$702$	7504.82	−	8136.01i	0.403492	−	0.437427i
$703$	−1422.56			−0.0763199
$704$	9616.60	−	16656.4i	0.514829	−	0.891709i
$705$	13736.1	−	3879.25i	0.733806	−	0.207235i
$706$	18984.6	+	32882.3i	1.01203	+	1.75289i
$707$	−264.729	−	458.525i	−0.0140823	−	0.0243912i
$708$	6.14278	−	24.2233i	0.000326073	−	0.00128583i
$709$	5495.90	−	9519.17i	0.291118	−	0.504231i	−0.682956	−	0.730459i	$-0.739306\pi$
$709$	5495.90	−	9519.17i	0.291118	−	0.504231i	0.974074	+	0.226228i	$0.0726394\pi$
$710$	−29115.5			−1.53899
$711$	332.439	+	12360.4i	0.0175351	+	0.651970i
$712$	−19501.7			−1.02649
$713$	−11668.5	+	20210.5i	−0.612889	+	1.06155i
$714$	−9495.78	−	9243.82i	−0.497718	−	0.484512i
$715$	−8540.35	−	14792.3i	−0.446701	−	0.773708i
$716$	3265.85	+	5656.62i	0.170462	+	0.295248i
$717$	−16802.3	−	16356.5i	−0.875164	−	0.851943i
$718$	6942.32	−	12024.5i	0.360843	−	0.624998i
$719$	27381.0			1.42022			0.710110	−	0.704091i	$-0.248645\pi$
$719$	27381.0			1.42022			0.710110	+	0.704091i	$0.248645\pi$
$720$	−17692.5	+	10859.3i	−0.915780	+	0.562084i
$721$	11236.4			0.580395
$722$	−1307.99	+	2265.51i	−0.0674216	+	0.116778i
$723$	2798.75	−	11036.5i	0.143965	−	0.567707i
$724$	1082.61	+	1875.13i	0.0555729	+	0.0962551i
$725$	2651.94	+	4593.30i	0.135849	+	0.235298i
$726$	−59397.6	+	16774.6i	−3.03644	+	0.857526i
$727$	−5329.82	+	9231.51i	−0.271901	+	0.470946i	−0.969349	−	0.245690i	$-0.920986\pi$
$727$	−5329.82	+	9231.51i	−0.271901	+	0.470946i	0.697448	+	0.716636i	$0.254319\pi$
$728$	3056.48			0.155606
$729$	−1586.05	−	19619.0i	−0.0805796	−	0.996748i
$730$	−13003.8			−0.659306
$731$	−3571.74	+	6186.44i	−0.180719	+	0.313015i
$732$	−415.366	+	117.304i	−0.0209732	+	0.00592307i
$733$	11625.9	+	20136.7i	0.585829	+	1.01469i	0.994771	+	0.102126i	$0.0325644\pi$
$733$	11625.9	+	20136.7i	0.585829	+	1.01469i	−0.408942	+	0.912560i	$0.634102\pi$
$734$	−10452.3	−	18103.9i	−0.525615	−	0.910392i
$735$	619.740	−	2443.86i	0.0311013	−	0.122644i
$736$	7192.95	−	12458.5i	0.360238	−	0.623951i
$737$	24309.3			1.21498
$738$	−16084.2	+	9872.12i	−0.802261	+	0.492409i
$739$	17081.5			0.850276			0.425138	−	0.905128i	$-0.360225\pi$
$739$	17081.5			0.850276			0.425138	+	0.905128i	$0.360225\pi$
$740$	−198.318	+	343.498i	−0.00985180	+	0.0170638i
$741$	7951.14	+	7740.17i	0.394187	+	0.383728i
$742$	1146.63	+	1986.02i	0.0567307	+	0.0982604i
$743$	−7360.54	−	12748.8i	−0.363435	−	0.629487i	0.625089	−	0.780554i	$-0.285063\pi$
$743$	−7360.54	−	12748.8i	−0.363435	−	0.629487i	−0.988524	+	0.151066i	$0.951729\pi$
$744$	−11674.3	−	11364.6i	−0.575272	−	0.560007i
$745$	7153.37	−	12390.0i	0.351784	−	0.609308i
$746$	13373.3			0.656340
$747$	64.9921	+	2416.47i	0.00318332	+	0.118359i
$748$	19640.2			0.960049
$749$	2708.85	−	4691.86i	0.132148	−	0.228888i
$750$	−6217.05	+	24516.1i	−0.302686	+	1.19360i
$751$	−4922.01	−	8525.17i	−0.239157	−	0.414232i	0.721316	−	0.692606i	$-0.243538\pi$
$751$	−4922.01	−	8525.17i	−0.239157	−	0.414232i	−0.960473	+	0.278375i	$0.910204\pi$
$752$	−10769.6	−	18653.5i	−0.522244	−	0.904553i
$753$	−30010.9	+	8475.44i	−1.45240	+	0.410175i
$754$	7764.63	−	13448.7i	0.375028	−	0.649568i
$755$	−6433.04			−0.310096
$756$	−1641.75	+	1779.83i	−0.0789812	+	0.0856239i
$757$	11665.0			0.560066			0.280033	−	0.959990i	$-0.409655\pi$
$757$	11665.0			0.560066			0.280033	+	0.959990i	$0.409655\pi$
$758$	2626.26	−	4548.81i	0.125844	−	0.217969i
$759$	47132.1	−	13310.7i	2.25400	−	0.636557i
$760$	−7762.23	−	13444.6i	−0.370481	−	0.641692i
$761$	−11946.9	−	20692.6i	−0.569086	−	0.985686i	−0.996657	−	0.0817041i	$-0.973964\pi$
$761$	−11946.9	−	20692.6i	−0.569086	−	0.985686i	0.427570	−	0.903982i	$-0.359370\pi$
$762$	6641.31	−	26189.1i	0.315734	−	1.24506i
$763$	1107.42	−	1918.11i	0.0525444	−	0.0910095i
$764$	−3689.34			−0.174706
$765$	26471.9	+	14348.8i	1.25110	+	0.678144i
$766$	2165.81			0.102159
$767$	23.7851	−	41.1970i	0.00111973	−	0.00193942i
$768$	12898.9	+	12556.6i	0.606053	+	0.589972i
$769$	−10516.9	−	18215.7i	−0.493170	−	0.854195i	0.506800	−	0.862064i	$-0.330828\pi$
$769$	−10516.9	−	18215.7i	−0.493170	−	0.854195i	−0.999969	+	0.00786927i	$0.997495\pi$
$770$	7930.21	+	13735.5i	0.371149	+	0.642850i
$771$	−471.668	−	459.152i	−0.0220320	−	0.0214474i
$772$	677.982	−	1174.30i	0.0316077	−	0.0547461i
$773$	−1340.67			−0.0623810			−0.0311905	−	0.999513i	$-0.509930\pi$
$773$	−1340.67			−0.0623810			−0.0311905	+	0.999513i	$0.509930\pi$
$774$	4870.78	+	2640.15i	0.226197	+	0.122607i
$775$	−4718.97			−0.218723
$776$	−2697.99	+	4673.05i	−0.124809	+	0.216176i
$777$	145.251	−	572.778i	0.00670637	−	0.0264457i
$778$	7887.99	+	13662.4i	0.363494	+	0.629590i
$779$	−9459.72	−	16384.7i	−0.435083	−	0.753586i
$780$	2977.44	−	840.864i	0.136679	−	0.0385997i
$781$	−32142.7	+	55672.8i	−1.47267	+	2.55074i
$782$	−48551.2			−2.22019
$783$	−8217.02	−	26364.1i	−0.375035	−	1.20329i
$784$	−3804.63			−0.173316
$785$	3462.27	−	5996.83i	0.157419	−	0.272657i
$786$	−6015.16	+	1698.75i	−0.272969	+	0.0770897i
$787$	−8865.01	−	15354.7i	−0.401529	−	0.695469i	0.592381	−	0.805658i	$-0.298188\pi$
$787$	−8865.01	−	15354.7i	−0.401529	−	0.695469i	−0.993911	+	0.110188i	$0.964855\pi$
$788$	932.639	+	1615.38i	0.0421623	+	0.0730273i
$789$	−3833.90	+	15118.5i	−0.172992	+	0.682170i
$790$	−7335.16	+	12704.9i	−0.330346	+	0.572176i
$791$	−11315.5			−0.508637
$792$	919.269	+	34179.3i	0.0412434	+	1.53347i
$793$	−821.603			−0.0367919
$794$	−8818.35	+	15273.8i	−0.394146	+	0.682680i
$795$	−3733.65	−	3634.59i	−0.166565	−	0.162145i
$796$	−2587.77	−	4482.15i	−0.115227	−	0.199580i
$797$	−20459.7	−	35437.2i	−0.909309	−	1.57497i	−0.815026	−	0.579424i	$-0.803277\pi$
$797$	−20459.7	−	35437.2i	−0.909309	−	1.57497i	−0.0942830	−	0.995545i	$-0.530056\pi$
$798$	−7383.10	−	7187.19i	−0.327517	−	0.318827i
$799$	−15620.9	+	27056.2i	−0.691649	+	1.19797i
$800$	2908.96			0.128559
$801$	25064.6	−	15384.0i	1.10563	−	0.678612i
$802$	40101.6			1.76563
$803$	−14355.9	+	24865.1i	−0.630894	+	1.09274i
$804$	−1082.36	+	4268.13i	−0.0474774	+	0.187221i
$805$	−4618.44	−	7999.37i	−0.202210	−	0.350237i
$806$	6908.34	+	11965.6i	0.301906	+	0.522916i
$807$	−9174.78	+	2591.07i	−0.400208	+	0.113023i
$808$	677.107	−	1172.78i	0.0294809	−	0.0510624i
$809$	−9938.95			−0.431935			−0.215967	−	0.976401i	$-0.569290\pi$
$809$	−9938.95			−0.431935			−0.215967	+	0.976401i	$0.569290\pi$
$810$	10572.5	−	20822.6i	0.458617	−	0.903251i
$811$	36553.0			1.58268			0.791339	−	0.611378i	$-0.209385\pi$
$811$	36553.0			1.58268			0.791339	+	0.611378i	$0.209385\pi$
$812$	−1698.58	+	2942.03i	−0.0734096	+	0.127149i
$813$	20941.1	−	5914.02i	0.903367	−	0.255122i
$814$	1858.64	+	3219.25i	0.0800310	+	0.138618i
$815$	−14435.9	−	25003.8i	−0.620452	−	1.07466i
$816$	11169.2	−	44044.1i	0.479165	−	1.88952i
$817$	−2777.08	+	4810.04i	−0.118920	+	0.205976i
$818$	37752.6			1.61368
$819$	−3928.34	+	2411.13i	−0.167604	+	0.102871i
$820$	−5275.10			−0.224652
$821$	14194.7	−	24586.0i	0.603410	−	1.04514i	−0.388891	−	0.921284i	$-0.627142\pi$
$821$	14194.7	−	24586.0i	0.603410	−	1.04514i	0.992301	−	0.123852i	$-0.0395249\pi$
$822$	−9437.83	−	9187.41i	−0.400465	−	0.389839i
$823$	−17054.5	−	29539.2i	−0.722336	−	1.25112i	−0.960061	−	0.279790i	$-0.909735\pi$
$823$	−17054.5	−	29539.2i	−0.722336	−	1.25112i	0.237726	−	0.971332i	$-0.423598\pi$
$824$	14369.8	+	24889.3i	0.607521	+	1.05226i
$825$	7096.22	+	6907.93i	0.299465	+	0.291519i
$826$	−22.0858	+	38.2538i	−0.000930344	+	0.00161140i
$827$	36501.0			1.53478			0.767391	−	0.641180i	$-0.221555\pi$
$827$	36501.0			1.53478			0.767391	+	0.641180i	$0.221555\pi$
$828$	238.508	+	8867.93i	0.0100105	+	0.372200i
$829$	−43602.7			−1.82676			−0.913380	−	0.407108i	$-0.866537\pi$
$829$	−43602.7			−1.82676			−0.913380	+	0.407108i	$0.866537\pi$
$830$	−1434.03	+	2483.81i	−0.0599710	+	0.103873i
$831$	4272.53	−	16848.2i	0.178354	−	0.703316i
$832$	3315.81	+	5743.15i	0.138167	+	0.239313i
$833$	2759.24	+	4779.14i	0.114768	+	0.198784i
$834$	−23254.9	+	6567.47i	−0.965531	+	0.272677i
$835$	−1182.40	+	2047.97i	−0.0490043	+	0.0848780i
$836$	15270.5			0.631749
$837$	23969.4	+	5396.94i	0.989851	+	0.222874i
$838$	12606.6			0.519675
$839$	−8686.25	+	15045.0i	−0.357429	+	0.619085i	−0.987531	−	0.157428i	$-0.949680\pi$
$839$	−8686.25	+	15045.0i	−0.357429	+	0.619085i	0.630102	+	0.776513i	$0.283013\pi$
$840$	6205.87	−	1752.61i	0.254908	−	0.0719891i
$841$	−7177.14	−	12431.2i	−0.294278	−	0.509704i
$842$	−12369.6	−	21424.7i	−0.506275	−	0.876894i
$843$	−10209.3	+	40258.9i	−0.417113	+	1.64483i
$844$	−2343.46	+	4059.00i	−0.0955751	+	0.165541i
$845$	−15865.7			−0.645914
$846$	21302.2	+	11546.6i	0.865703	+	0.469244i
$847$	25702.0			1.04266
$848$	−3931.52	+	6809.59i	−0.159209	+	0.275758i
$849$	30129.6	+	29330.1i	1.21796	+	1.18564i
$850$	−4908.75	−	8502.20i	−0.198081	−	0.343086i
$851$	−1082.44	−	1874.85i	−0.0436024	−	0.0755216i
$852$	−8343.70	−	8122.31i	−0.335505	−	0.326603i
$853$	−24044.0	+	41645.4i	−0.965122	+	1.67164i	−0.255836	+	0.966720i	$0.582351\pi$
$853$	−24044.0	+	41645.4i	−0.965122	+	1.67164i	−0.709286	+	0.704921i	$0.750982\pi$
$854$	762.906			0.0305692
$855$	20582.2	+	11156.3i	0.823272	+	0.446245i
$856$	13857.0			0.553298
$857$	11483.5	−	19890.0i	0.457723	−	0.792800i	−0.541117	−	0.840947i	$-0.681998\pi$
$857$	11483.5	−	19890.0i	0.457723	−	0.792800i	0.998840	+	0.0481472i	$0.0153317\pi$
$858$	7127.48	−	28106.3i	0.283599	−	1.11834i
$859$	9449.01	+	16366.2i	0.375315	+	0.650065i	0.990374	−	0.138416i	$-0.0442010\pi$
$859$	9449.01	+	16366.2i	0.375315	+	0.650065i	−0.615059	+	0.788481i	$0.710868\pi$
$860$	774.302	+	1341.13i	0.0307017	+	0.0531770i
$861$	7563.01	−	2135.88i	0.299357	−	0.0845421i
$862$	−15827.9	+	27414.7i	−0.625406	+	1.08324i
$863$	−46155.5			−1.82057			−0.910284	−	0.413983i	$-0.864137\pi$
$863$	−46155.5			−1.82057			−0.910284	+	0.413983i	$0.864137\pi$
$864$	−14775.7	−	3326.89i	−0.581806	−	0.130999i
$865$	22527.8			0.885513
$866$	−4390.68	+	7604.89i	−0.172288	+	0.298412i
$867$	−38857.8	+	10973.9i	−1.52212	+	0.429866i
$868$	−1511.26	−	2617.58i	−0.0590963	−	0.102358i
$869$	16195.6	+	28051.7i	0.632220	+	1.09504i
$870$	8053.66	−	31758.5i	0.313844	−	1.23760i
$871$	−4190.93	+	7258.90i	−0.163036	+	0.282386i
$872$	5664.98			0.220000
$873$	−218.778	−	8134.36i	−0.00848168	−	0.315357i
$874$	−37749.2			−1.46097
$875$	5266.11	−	9121.17i	0.203460	−	0.352402i
$876$	−3726.54	−	3627.66i	−0.143731	−	0.139917i
$877$	4542.36	+	7867.60i	0.174897	+	0.302930i	0.940126	−	0.340828i	$-0.110707\pi$
$877$	4542.36	+	7867.60i	0.174897	+	0.302930i	−0.765229	+	0.643759i	$0.777374\pi$
$878$	7585.36	+	13138.2i	0.291564	+	0.505004i
$879$	7807.57	+	7600.40i	0.299593	+	0.291644i
$880$	−27190.8	+	47095.8i	−1.04159	+	1.80409i
$881$	−1877.31			−0.0717914			−0.0358957	−	0.999356i	$-0.511428\pi$
$881$	−1877.31			−0.0717914			−0.0358957	+	0.999356i	$0.511428\pi$
$882$	3647.70	−	2238.87i	0.139257	−	0.0854724i
$883$	−37140.8			−1.41550			−0.707751	−	0.706462i	$-0.750290\pi$
$883$	−37140.8			−1.41550			−0.707751	+	0.706462i	$0.750290\pi$
$884$	−3385.98	+	5864.69i	−0.128827	+	0.223134i
$885$	24.6704	−	97.2847i	0.000937048	−	0.00369513i
$886$	20060.9	+	34746.5i	0.760676	+	1.31753i
$887$	8549.77	+	14808.6i	0.323645	+	0.560570i	0.981237	−	0.192804i	$-0.0617583\pi$
$887$	8549.77	+	14808.6i	0.323645	+	0.560570i	−0.657592	+	0.753374i	$0.728425\pi$
$888$	1454.50	−	410.767i	0.0549659	−	0.0155230i
$889$	−5625.48	+	9743.61i	−0.212230	+	0.367593i
$890$	34892.6			1.31416
$891$	−28144.0	−	43203.7i	−1.05820	−	1.62444i
$892$	−13475.9			−0.505839
$893$	−12145.5	+	21036.6i	−0.455131	+	0.788311i
$894$	23372.7	−	6600.73i	0.874385	−	0.246937i
$895$	13116.2	+	22717.9i	0.489862	+	0.848465i
$896$	−6101.66	−	10568.4i	−0.227502	−	0.394046i
$897$	−4150.94	+	16368.7i	−0.154510	+	0.609292i
$898$	25341.0	−	43891.9i	0.941693	−	1.63106i
$899$	34470.6			1.27882
$900$	−1528.82	+	938.357i	−0.0566231	+	0.0347539i
$901$	11405.0			0.421706
$902$	−24719.1	+	42814.7i	−0.912478	+	1.58046i
$903$	−1653.16	−	1609.29i	−0.0609231	−	0.0593066i
$904$	−14471.0	−	25064.5i	−0.532409	−	0.922160i
$905$	4347.93	+	7530.84i	0.159702	+	0.276612i
$906$	−7825.17	−	7617.54i	−0.286947	−	0.279333i
$907$	1790.41	−	3101.08i	0.0655454	−	0.113528i	−0.831390	−	0.555689i	$-0.812455\pi$
$907$	1790.41	−	3101.08i	0.0655454	−	0.113528i	0.896936	+	0.442161i	$0.145788\pi$
$908$	−7411.88			−0.270894
$909$	54.9061	+	2041.46i	0.00200343	+	0.0744895i
$910$	−5468.69			−0.199214
$911$	−6731.50	+	11659.3i	−0.244813	+	0.424028i	−0.962079	−	0.272771i	$-0.912060\pi$
$911$	−6731.50	+	11659.3i	−0.244813	+	0.424028i	0.717266	+	0.696799i	$0.245393\pi$
$912$	8684.17	−	34244.9i	0.315309	−	1.24338i
$913$	3166.26	+	5484.13i	0.114773	+	0.198793i
$914$	−5999.02	−	10390.6i	−0.217101	−	0.376029i
$915$	−1668.18	+	471.113i	−0.0602713	+	0.0170213i
$916$	7790.80	−	13494.1i	0.281021	−	0.486743i
$917$	2602.82			0.0937326
$918$	15209.7	+	48799.9i	0.546835	+	1.75451i
$919$	−42732.6			−1.53386			−0.766930	−	0.641731i	$-0.778217\pi$
$919$	−42732.6			−1.53386			−0.766930	+	0.641731i	$0.778217\pi$
$920$	11812.7	−	20460.3i	0.423320	−	0.733212i
$921$	−14218.6	+	4015.51i	−0.508707	+	0.143665i
$922$	−4506.74	−	7805.89i	−0.160978	−	0.278822i
$923$	−11082.8	−	19196.0i	−0.395229	−	0.684556i
$924$	−1559.20	+	6148.50i	−0.0555129	+	0.218908i
$925$	218.880	−	379.112i	0.00778026	−	0.0134758i
$926$	−30979.2			−1.09940
$927$	−38102.9	−	20653.2i	−1.35001	−	0.731759i
$928$	−21249.1			−0.751654
$929$	8732.83	−	15125.7i	0.308412	−	0.534186i	−0.669603	−	0.742719i	$-0.733536\pi$
$929$	8732.83	−	15125.7i	0.308412	−	0.534186i	0.978015	+	0.208534i	$0.0668690\pi$
$930$	20887.8	+	20333.6i	0.736493	+	0.716951i
$931$	2145.34	+	3715.84i	0.0755218	+	0.130808i
$932$	5391.20	+	9337.83i	0.189479	+	0.328188i
$933$	−12476.7	−	12145.7i	−0.437802	−	0.426186i
$934$	16648.0	−	28835.1i	0.583231	−	1.01019i
$935$	78878.3			2.75893
$936$	−10364.6	−	5618.02i	−0.361943	−	0.196187i
$937$	9734.10			0.339380			0.169690	−	0.985497i	$-0.445723\pi$
$937$	9734.10			0.339380			0.169690	+	0.985497i	$0.445723\pi$
$938$	3891.52	−	6740.31i	0.135461	−	0.234626i
$939$	−7199.84	+	28391.6i	−0.250221	+	0.986715i
$940$	3386.38	+	5865.39i	0.117502	+	0.203519i
$941$	7233.04	+	12528.0i	0.250574	+	0.434007i	0.963684	−	0.267045i	$-0.0860473\pi$
$941$	7233.04	+	12528.0i	0.250574	+	0.434007i	−0.713110	+	0.701052i	$0.752714\pi$
$942$	11312.5	−	3194.79i	0.391276	−	0.110501i
$943$	14396.0	−	24934.7i	0.497136	−	0.861065i
$944$	−151.454			−0.00522183
$945$	−6593.53	+	7148.08i	−0.226971	+	0.246060i
$946$	14513.5			0.498810
$947$	−20855.4	+	36122.6i	−0.715638	+	1.23952i	0.247075	+	0.968996i	$0.420531\pi$
$947$	−20855.4	+	36122.6i	−0.715638	+	1.23952i	−0.962713	+	0.270525i	$0.912803\pi$
$948$	−5646.31	+	1594.59i	−0.193443	+	0.0546305i
$949$	−4949.92	−	8573.51i	−0.169316	−	0.293264i
$950$	−3816.62	−	6610.58i	−0.130345	−	0.225764i
$951$	5911.68	−	23311.9i	0.201577	−	0.794891i
$952$	−7057.39	+	12223.8i	−0.240264	+	0.416149i
$953$	14166.1			0.481516			0.240758	−	0.970585i	$-0.422604\pi$
$953$	14166.1			0.481516			0.240758	+	0.970585i	$0.422604\pi$
$954$	−237.817	−	8842.24i	−0.00807086	−	0.300082i
$955$	−14817.0			−0.502060
$956$	5563.28	−	9635.88i	0.188211	−	0.325990i
$957$	−51835.7	−	50460.3i	−1.75090	−	1.70444i
$958$	−31213.9	−	54064.1i	−1.05269	−	1.82331i
$959$	2742.40	+	4749.97i	0.0923427	+	0.159942i
$960$	10025.6	+	9759.56i	0.337056	+	0.328113i
$961$	−439.090	+	760.525i	−0.0147390	+	0.0255287i
$962$	−1281.72			−0.0429566
$963$	−17809.7	+	10931.2i	−0.595961	+	0.365787i
$964$	5402.62			0.180505
$965$	2722.89	−	4716.18i	0.0908320	−	0.157326i
$966$	3854.39	−	15199.3i	0.128378	−	0.506241i
$967$	−2863.72	−	4960.11i	−0.0952338	−	0.164950i	0.814472	−	0.580202i	$-0.197027\pi$
$967$	−2863.72	−	4960.11i	−0.0952338	−	0.164950i	−0.909706	+	0.415253i	$0.863693\pi$
$968$	32869.4	+	56931.4i	1.09139	+	1.89034i
$969$	−49314.3	+	13926.9i	−1.63488	+	0.461711i
$970$	4827.26	−	8361.06i	0.159788	−	0.276760i
$971$	−4097.18			−0.135412			−0.0677059	−	0.997705i	$-0.521568\pi$
$971$	−4097.18			−0.135412			−0.0677059	+	0.997705i	$0.521568\pi$
$972$	8838.65	−	3017.80i	0.291666	−	0.0995844i
$973$	10062.7			0.331546
$974$	20922.0	−	36238.0i	0.688279	−	1.19213i
$975$	−3286.14	+	928.045i	−0.107939	+	0.0304833i
$976$	1307.91	+	2265.37i	0.0428946	+	0.0742957i
$977$	20104.2	+	34821.5i	0.658332	+	1.14026i	0.981047	+	0.193769i	$0.0620711\pi$
$977$	20104.2	+	34821.5i	0.658332	+	1.14026i	−0.322715	+	0.946496i	$0.604596\pi$
$978$	12047.7	−	47508.6i	0.393910	−	1.55333i
$979$	38520.5	−	66719.5i	1.25753	−	2.17810i
$980$	1196.32			0.0389951
$981$	−7280.91	+	4468.85i	−0.236964	+	0.145443i
$982$	−38269.7			−1.24362
$983$	20792.0	−	36012.8i	0.674630	−	1.16849i	−0.301947	−	0.953325i	$-0.597637\pi$
$983$	20792.0	−	36012.8i	0.674630	−	1.16849i	0.976577	−	0.215169i	$-0.0690301\pi$
$984$	14403.2	+	14021.0i	0.466623	+	0.454242i
$985$	3745.64	+	6487.63i	0.121163	+	0.209861i
$986$	35856.9	+	62106.0i	1.15813	+	2.00594i
$987$	−7230.02	−	7038.18i	−0.233165	−	0.226978i
$988$	−2632.64	+	4559.87i	−0.0847728	+	0.146831i
$989$	−8452.45			−0.271762
$990$	−1644.76	−	61153.8i	−0.0528020	−	1.96323i
$991$	−39978.9			−1.28150			−0.640752	−	0.767748i	$-0.721377\pi$
$991$	−39978.9			−1.28150			−0.640752	+	0.767748i	$0.721377\pi$
$992$	9452.85	−	16372.8i	0.302549	−	0.524030i
$993$	9871.79	−	38928.1i	0.315480	−	1.24405i
$994$	10291.1	+	17824.6i	0.328383	+	0.568776i
$995$	−10392.9	−	18001.0i	−0.331133	−	0.573539i
$996$	−1103.86	+	311.743i	−0.0351176	+	0.00991763i
$997$	−9012.56	+	15610.2i	−0.286290	+	0.495868i	−0.972921	−	0.231138i	$-0.925755\pi$
$997$	−9012.56	+	15610.2i	−0.286290	+	0.495868i	0.686632	+	0.727006i	$0.259089\pi$
$998$	−21867.3			−0.693584
$999$	−1545.35	+	1675.33i	−0.0489418	+	0.0530580i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.f.c.43.2	yes	18
3.2	odd	2		189.4.f.c.127.8		18
9.2	odd	6		567.4.a.k.1.2		9
9.4	even	3	inner	63.4.f.c.22.2	✓	18
9.5	odd	6		189.4.f.c.64.8		18
9.7	even	3		567.4.a.j.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.f.c.22.2	✓	18	9.4	even	3	inner
63.4.f.c.43.2	yes	18	1.1	even	1	trivial
189.4.f.c.64.8		18	9.5	odd	6
189.4.f.c.127.8		18	3.2	odd	2
567.4.a.j.1.8		9	9.7	even	3
567.4.a.k.1.2		9	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61753 + 2.80164i) q^{2} +(-5.00056 + 1.41222i) q^{3} +(-1.23279 - 2.13526i) q^{4} +(-4.95111 - 8.57557i) q^{5} +(4.13202 - 16.2941i) q^{6} +(-3.50000 + 6.06218i) q^{7} -17.9041 q^{8} +(23.0113 - 14.1238i) q^{9} +O(q^{10})\)	\(q+(-1.61753 + 2.80164i) q^{2} +(-5.00056 + 1.41222i) q^{3} +(-1.23279 - 2.13526i) q^{4} +(-4.95111 - 8.57557i) q^{5} +(4.13202 - 16.2941i) q^{6} +(-3.50000 + 6.06218i) q^{7} -17.9041 q^{8} +(23.0113 - 14.1238i) q^{9} +32.0342 q^{10} +(35.3649 - 61.2538i) q^{11} +(9.18012 + 8.93654i) q^{12} +(12.1938 + 21.1204i) q^{13} +(-11.3227 - 19.6115i) q^{14} +(36.8689 + 35.8906i) q^{15} +(38.8228 - 67.2430i) q^{16} -112.622 q^{17} +(2.34838 + 87.3149i) q^{18} -87.5650 q^{19} +(-12.2074 + 21.1438i) q^{20} +(8.94085 - 35.2571i) q^{21} +(114.407 + 198.160i) q^{22} +(-66.6293 - 115.405i) q^{23} +(89.5308 - 25.2846i) q^{24} +(13.4731 - 23.3360i) q^{25} -78.8956 q^{26} +(-95.1235 + 103.124i) q^{27} +17.2591 q^{28} +(-98.4166 + 170.462i) q^{29} +(-160.189 + 45.2393i) q^{30} +(-87.5631 - 151.664i) q^{31} +(53.9774 + 93.4916i) q^{32} +(-90.3407 + 356.247i) q^{33} +(182.169 - 315.526i) q^{34} +69.3155 q^{35} +(-58.5261 - 31.7234i) q^{36} +16.2458 q^{37} +(141.639 - 245.326i) q^{38} +(-90.8027 - 88.3933i) q^{39} +(88.6453 + 153.538i) q^{40} +(108.031 + 187.115i) q^{41} +(84.3156 + 82.0784i) q^{42} +(31.7145 - 54.9311i) q^{43} -174.391 q^{44} +(-235.051 - 127.406i) q^{45} +431.099 q^{46} +(138.702 - 240.239i) q^{47} +(-99.1739 + 391.079i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(43.5861 + 75.4934i) q^{50} +(563.173 - 159.047i) q^{51} +(30.0650 - 52.0741i) q^{52} -101.268 q^{53} +(-135.051 - 433.308i) q^{54} -700.382 q^{55} +(62.6645 - 108.538i) q^{56} +(437.875 - 123.661i) q^{57} +(-318.383 - 551.456i) q^{58} +(-0.975290 - 1.68925i) q^{59} +(31.1841 - 122.971i) q^{60} +(-16.8446 + 29.1757i) q^{61} +566.543 q^{62} +(5.08141 + 188.932i) q^{63} +271.925 q^{64} +(120.746 - 209.138i) q^{65} +(-851.947 - 829.341i) q^{66} +(171.846 + 297.646i) q^{67} +(138.840 + 240.477i) q^{68} +(496.161 + 482.996i) q^{69} +(-112.120 + 194.197i) q^{70} -908.888 q^{71} +(-411.997 + 252.874i) q^{72} -405.936 q^{73} +(-26.2780 + 45.5148i) q^{74} +(-34.4173 + 135.720i) q^{75} +(107.950 + 186.974i) q^{76} +(247.554 + 428.777i) q^{77} +(394.522 - 111.418i) q^{78} +(-228.979 + 396.603i) q^{79} -768.863 q^{80} +(330.038 - 650.012i) q^{81} -698.972 q^{82} +(-44.7656 + 77.5363i) q^{83} +(-86.3053 + 24.3737i) q^{84} +(557.603 + 965.797i) q^{85} +(102.598 + 177.705i) q^{86} +(251.408 - 991.394i) q^{87} +(-633.178 + 1096.70i) q^{88} +1089.23 q^{89} +(737.148 - 452.444i) q^{90} -170.714 q^{91} +(-164.280 + 284.542i) q^{92} +(652.047 + 634.746i) q^{93} +(448.709 + 777.187i) q^{94} +(433.544 + 750.920i) q^{95} +(-401.948 - 391.283i) q^{96} +(150.691 - 261.004i) q^{97} +158.518 q^{98} +(-51.3439 - 1909.02i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9}+O(q^{10}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9} + 111 q^{11} - 18 q^{13} + 42 q^{14} - 36 q^{15} - 144 q^{16} - 546 q^{17} - 45 q^{18} + 90 q^{19} + 402 q^{20} - 63 q^{21} + 162 q^{22} + 312 q^{23} - 36 q^{24} - 279 q^{25} + 102 q^{26} + 432 q^{27} + 504 q^{28} + 378 q^{29} - 864 q^{30} - 18 q^{31} + 891 q^{32} + 513 q^{33} + 324 q^{34} - 336 q^{35} + 414 q^{36} - 72 q^{37} + 147 q^{38} - 810 q^{39} - 405 q^{40} + 477 q^{41} + 315 q^{42} + 171 q^{43} - 1896 q^{44} - 720 q^{45} - 756 q^{46} + 654 q^{47} - 2709 q^{48} - 441 q^{49} + 429 q^{50} + 1341 q^{51} - 747 q^{52} - 1896 q^{53} - 108 q^{54} - 432 q^{55} + 525 q^{56} - 1143 q^{57} - 297 q^{58} + 957 q^{59} + 5400 q^{60} + 198 q^{61} - 600 q^{62} - 504 q^{63} + 4770 q^{64} + 2478 q^{65} - 2646 q^{66} + 333 q^{67} + 1443 q^{68} + 3366 q^{69} - 5652 q^{71} - 3681 q^{72} + 306 q^{73} + 2100 q^{74} - 4113 q^{75} + 144 q^{76} + 777 q^{77} + 6336 q^{78} - 1152 q^{79} - 8418 q^{80} - 1917 q^{81} - 6048 q^{82} + 1890 q^{83} + 1008 q^{84} + 648 q^{85} + 3837 q^{86} + 4212 q^{87} + 2268 q^{88} - 2604 q^{89} - 135 q^{90} + 252 q^{91} + 987 q^{92} + 378 q^{93} - 324 q^{94} + 3144 q^{95} + 5643 q^{96} + 1737 q^{97} - 588 q^{98} + 720 q^{99}+O(q^{100}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9 + 111 * q^11 - 18 * q^13 + 42 * q^14 - 36 * q^15 - 144 * q^16 - 546 * q^17 - 45 * q^18 + 90 * q^19 + 402 * q^20 - 63 * q^21 + 162 * q^22 + 312 * q^23 - 36 * q^24 - 279 * q^25 + 102 * q^26 + 432 * q^27 + 504 * q^28 + 378 * q^29 - 864 * q^30 - 18 * q^31 + 891 * q^32 + 513 * q^33 + 324 * q^34 - 336 * q^35 + 414 * q^36 - 72 * q^37 + 147 * q^38 - 810 * q^39 - 405 * q^40 + 477 * q^41 + 315 * q^42 + 171 * q^43 - 1896 * q^44 - 720 * q^45 - 756 * q^46 + 654 * q^47 - 2709 * q^48 - 441 * q^49 + 429 * q^50 + 1341 * q^51 - 747 * q^52 - 1896 * q^53 - 108 * q^54 - 432 * q^55 + 525 * q^56 - 1143 * q^57 - 297 * q^58 + 957 * q^59 + 5400 * q^60 + 198 * q^61 - 600 * q^62 - 504 * q^63 + 4770 * q^64 + 2478 * q^65 - 2646 * q^66 + 333 * q^67 + 1443 * q^68 + 3366 * q^69 - 5652 * q^71 - 3681 * q^72 + 306 * q^73 + 2100 * q^74 - 4113 * q^75 + 144 * q^76 + 777 * q^77 + 6336 * q^78 - 1152 * q^79 - 8418 * q^80 - 1917 * q^81 - 6048 * q^82 + 1890 * q^83 + 1008 * q^84 + 648 * q^85 + 3837 * q^86 + 4212 * q^87 + 2268 * q^88 - 2604 * q^89 - 135 * q^90 + 252 * q^91 + 987 * q^92 + 378 * q^93 - 324 * q^94 + 3144 * q^95 + 5643 * q^96 + 1737 * q^97 - 588 * q^98 + 720 * q^99

Introduction

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