LMFDB - Embedded newform 63.4.o.a.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(20,63)]

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([1, 3]))

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

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

chi := DirichletCharacter("63.20");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.o (of order $6$, 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:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	63.41
Dual form			63.4.o.a.20.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.67796 + 2.70082i) q^{2} +(-2.75680 + 4.40455i) q^{3} +(10.5889 - 18.3405i) q^{4} +(3.43953 - 5.95744i) q^{5} +(1.00030 - 28.0499i) q^{6} +(14.2961 - 11.7738i) q^{7} +71.1815i q^{8} +(-11.8001 - 24.2849i) q^{9} +O(q^{10})$	\(q+(-4.67796 + 2.70082i) q^{2} +(-2.75680 + 4.40455i) q^{3} +(10.5889 - 18.3405i) q^{4} +(3.43953 - 5.95744i) q^{5} +(1.00030 - 28.0499i) q^{6} +(14.2961 - 11.7738i) q^{7} +71.1815i q^{8} +(-11.8001 - 24.2849i) q^{9} +37.1582i q^{10} +(-10.9244 + 6.30723i) q^{11} +(51.5901 + 97.2002i) q^{12} +(22.5632 + 13.0269i) q^{13} +(-35.0774 + 93.6886i) q^{14} +(16.7577 + 31.5731i) q^{15} +(-107.537 - 186.260i) q^{16} +124.623 q^{17} +(120.790 + 81.7339i) q^{18} -41.3246i q^{19} +(-72.8415 - 126.165i) q^{20} +(12.4470 + 95.4257i) q^{21} +(34.0694 - 59.0099i) q^{22} +(-97.6910 - 56.4019i) q^{23} +(-313.522 - 196.233i) q^{24} +(38.8392 + 67.2715i) q^{25} -140.733 q^{26} +(139.495 + 14.9746i) q^{27} +(-64.5583 - 386.868i) q^{28} +(114.888 - 66.3304i) q^{29} +(-163.665 - 102.438i) q^{30} +(155.062 + 89.5251i) q^{31} +(512.952 + 296.153i) q^{32} +(2.33600 - 65.5050i) q^{33} +(-582.982 + 336.585i) q^{34} +(-20.9702 - 125.664i) q^{35} +(-570.347 - 40.7306i) q^{36} +148.290 q^{37} +(111.610 + 193.315i) q^{38} +(-119.580 + 63.4683i) q^{39} +(424.060 + 244.831i) q^{40} +(93.6165 - 162.149i) q^{41} +(-315.955 - 412.781i) q^{42} +(99.1611 + 171.752i) q^{43} +267.146i q^{44} +(-185.263 - 13.2303i) q^{45} +609.326 q^{46} +(-92.1405 - 159.592i) q^{47} +(1116.85 + 39.8286i) q^{48} +(65.7542 - 336.638i) q^{49} +(-363.377 - 209.796i) q^{50} +(-343.561 + 548.909i) q^{51} +(477.838 - 275.880i) q^{52} -359.147i q^{53} +(-692.994 + 306.700i) q^{54} +86.7756i q^{55} +(838.078 + 1017.61i) q^{56} +(182.016 + 113.924i) q^{57} +(-358.293 + 620.582i) q^{58} +(-182.287 + 315.730i) q^{59} +(756.510 + 26.9783i) q^{60} +(-300.892 + 173.720i) q^{61} -967.165 q^{62} +(-454.621 - 208.246i) q^{63} -1478.83 q^{64} +(155.214 - 89.6127i) q^{65} +(165.990 + 312.739i) q^{66} +(-182.332 + 315.809i) q^{67} +(1319.62 - 2285.65i) q^{68} +(517.739 - 274.796i) q^{69} +(437.494 + 531.216i) q^{70} -565.793i q^{71} +(1728.64 - 839.949i) q^{72} -737.140i q^{73} +(-693.694 + 400.504i) q^{74} +(-403.373 - 14.3849i) q^{75} +(-757.912 - 437.580i) q^{76} +(-81.9162 + 218.791i) q^{77} +(387.973 - 619.865i) q^{78} +(-451.543 - 782.096i) q^{79} -1479.51 q^{80} +(-450.515 + 573.129i) q^{81} +1011.37i q^{82} +(382.494 + 662.499i) q^{83} +(1881.95 + 782.167i) q^{84} +(428.645 - 742.436i) q^{85} +(-927.743 - 535.633i) q^{86} +(-24.5667 + 688.887i) q^{87} +(-448.958 - 777.618i) q^{88} +395.916 q^{89} +(902.385 - 438.471i) q^{90} +(475.941 - 79.4223i) q^{91} +(-2068.87 + 1194.47i) q^{92} +(-821.793 + 436.175i) q^{93} +(862.059 + 497.710i) q^{94} +(-246.189 - 142.137i) q^{95} +(-2718.53 + 1442.89i) q^{96} +(-243.773 + 140.742i) q^{97} +(601.604 + 1752.37i) q^{98} +(282.080 + 190.873i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) $ 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7	$ 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7} - 18 q^{11} + 204 q^{14} + 66 q^{15} - 242 q^{16} - 210 q^{18} - 57 q^{21} - 34 q^{22} - 102 q^{23} - 352 q^{25} + 300 q^{28} + 246 q^{29} - 144 q^{30} + 1068 q^{32} - 1818 q^{36} + 328 q^{37} - 798 q^{39} - 1158 q^{42} - 170 q^{43} + 968 q^{46} - 79 q^{49} + 288 q^{50} - 204 q^{51} + 1212 q^{56} + 324 q^{57} - 538 q^{58} + 5316 q^{60} + 783 q^{63} - 808 q^{64} + 4350 q^{65} - 590 q^{67} + 384 q^{70} + 4284 q^{72} - 5304 q^{74} - 2787 q^{77} + 612 q^{78} - 302 q^{79} - 3720 q^{81} + 7050 q^{84} - 612 q^{85} - 13692 q^{86} + 1294 q^{88} + 210 q^{91} - 10194 q^{92} - 4266 q^{93} + 6336 q^{95} + 1014 q^{99}+O(q^{100}) $ 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7 - 18 * q^11 + 204 * q^14 + 66 * q^15 - 242 * q^16 - 210 * q^18 - 57 * q^21 - 34 * q^22 - 102 * q^23 - 352 * q^25 + 300 * q^28 + 246 * q^29 - 144 * q^30 + 1068 * q^32 - 1818 * q^36 + 328 * q^37 - 798 * q^39 - 1158 * q^42 - 170 * q^43 + 968 * q^46 - 79 * q^49 + 288 * q^50 - 204 * q^51 + 1212 * q^56 + 324 * q^57 - 538 * q^58 + 5316 * q^60 + 783 * q^63 - 808 * q^64 + 4350 * q^65 - 590 * q^67 + 384 * q^70 + 4284 * q^72 - 5304 * q^74 - 2787 * q^77 + 612 * q^78 - 302 * q^79 - 3720 * q^81 + 7050 * q^84 - 612 * q^85 - 13692 * q^86 + 1294 * q^88 + 210 * q^91 - 10194 * q^92 - 4266 * q^93 + 6336 * q^95 + 1014 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−4.67796	+	2.70082i	−1.65391	+	0.954885i	−0.678466	+	0.734632i	$0.737355\pi$
$2$	−4.67796	+	2.70082i	−1.65391	+	0.954885i	−0.975443	+	0.220252i	$0.929312\pi$
$3$	−2.75680	+	4.40455i	−0.530546	+	0.847656i
$3$	−2.75680	+	4.40455i	−0.530546	+	0.847656i
$4$	10.5889	−	18.3405i	1.32361	−	2.29256i
$5$	3.43953	−	5.95744i	0.307641	−	0.532850i	−0.670205	−	0.742176i	$-0.733794\pi$
$5$	3.43953	−	5.95744i	0.307641	−	0.532850i	0.977846	+	0.209326i	$0.0671271\pi$
$6$	1.00030	−	28.0499i	0.0680619	−	1.90856i
$7$	14.2961	−	11.7738i	0.771914	−	0.635727i
$7$	14.2961	−	11.7738i	0.771914	−	0.635727i
$8$			71.1815i			3.14581i
$9$	−11.8001	−	24.2849i	−0.437041	−	0.899442i
$10$			37.1582i			1.17505i
$11$	−10.9244	+	6.30723i	−0.299440	+	0.172882i	−0.642191	−	0.766544i	$-0.721975\pi$
$11$	−10.9244	+	6.30723i	−0.299440	+	0.172882i	0.342751	+	0.939426i	$0.388641\pi$
$12$	51.5901	+	97.2002i	1.24106	+	2.33827i
$13$	22.5632	+	13.0269i	0.481377	+	0.277923i	0.720990	−	0.692945i	$-0.243687\pi$
$13$	22.5632	+	13.0269i	0.481377	+	0.277923i	−0.239613	+	0.970869i	$0.577021\pi$
$14$	−35.0774	+	93.6886i	−0.669630	+	1.78852i
$15$	16.7577	+	31.5731i	0.288455	+	0.543475i
$16$	−107.537	−	186.260i	−1.68027	−	2.91032i
$17$	124.623			1.77797			0.888987	−	0.457932i	$-0.151410\pi$
$17$	124.623			1.77797			0.888987	+	0.457932i	$0.151410\pi$
$18$	120.790	+	81.7339i	1.58169	+	1.07027i
$19$		−	41.3246i		−	0.498974i	−0.968378	−	0.249487i	$-0.919738\pi$
$19$		−	41.3246i		−	0.498974i	0.968378	−	0.249487i	$-0.0802620\pi$
$20$	−72.8415	−	126.165i	−0.814393	−	1.41057i
$21$	12.4470	+	95.4257i	0.129341	+	0.991600i
$22$	34.0694	−	59.0099i	0.330164	−	0.571862i
$23$	−97.6910	−	56.4019i	−0.885651	−	0.511331i	−0.0131335	−	0.999914i	$-0.504181\pi$
$23$	−97.6910	−	56.4019i	−0.885651	−	0.511331i	−0.872517	+	0.488583i	$0.837514\pi$
$24$	−313.522	−	196.233i	−2.66656	−	1.66900i
$25$	38.8392	+	67.2715i	0.310714	+	0.538172i
$26$	−140.733			−1.06154
$27$	139.495	+	14.9746i	0.994287	+	0.106735i
$28$	−64.5583	−	386.868i	−0.435727	−	2.61111i
$29$	114.888	−	66.3304i	0.735658	−	0.424732i	−0.0848304	−	0.996395i	$-0.527035\pi$
$29$	114.888	−	66.3304i	0.735658	−	0.424732i	0.820489	+	0.571663i	$0.193702\pi$
$30$	−163.665	−	102.438i	−0.996035	−	0.623417i
$31$	155.062	+	89.5251i	0.898386	+	0.518683i	0.876676	−	0.481081i	$-0.159756\pi$
$31$	155.062	+	89.5251i	0.898386	+	0.518683i	0.0217097	+	0.999764i	$0.493089\pi$
$32$	512.952	+	296.153i	2.83369	+	1.63603i
$33$	2.33600	−	65.5050i	0.0123226	−	0.345544i
$34$	−582.982	+	336.585i	−2.94061	+	1.69776i
$35$	−20.9702	−	125.664i	−0.101274	−	0.606890i
$36$	−570.347	−	40.7306i	−2.64049	−	0.188567i
$37$	148.290			0.658884			0.329442	−	0.944176i	$-0.393139\pi$
$37$	148.290			0.658884			0.329442	+	0.944176i	$0.393139\pi$
$38$	111.610	+	193.315i	0.476462	+	0.825257i
$39$	−119.580	+	63.4683i	−0.490977	+	0.260591i
$40$	424.060	+	244.831i	1.67624	+	0.967779i
$41$	93.6165	−	162.149i	0.356596	−	0.617643i	−0.630794	−	0.775951i	$-0.717271\pi$
$41$	93.6165	−	162.149i	0.356596	−	0.617643i	0.987390	+	0.158308i	$0.0506039\pi$
$42$	−315.955	−	412.781i	−1.16078	−	1.51651i
$43$	99.1611	+	171.752i	0.351673	+	0.609115i	0.986543	−	0.163504i	$-0.0522796\pi$
$43$	99.1611	+	171.752i	0.351673	+	0.609115i	−0.634870	+	0.772619i	$0.718946\pi$
$44$			267.146i			0.915312i
$45$	−185.263	−	13.2303i	−0.613719	−	0.0438280i
$46$	609.326			1.95305
$47$	−92.1405	−	159.592i	−0.285959	−	0.495295i	0.686882	−	0.726769i	$-0.258979\pi$
$47$	−92.1405	−	159.592i	−0.285959	−	0.495295i	−0.972841	+	0.231473i	$0.925645\pi$
$48$	1116.85	+	39.8286i	3.35841	+	0.119766i
$49$	65.7542	−	336.638i	0.191703	−	0.981453i
$50$	−363.377	−	209.796i	−1.02779	−	0.593392i
$51$	−343.561	+	548.909i	−0.943298	+	1.50711i
$52$	477.838	−	275.880i	1.27431	−	0.735724i
$53$		−	359.147i		−	0.930804i	−0.885099	−	0.465402i	$-0.845910\pi$
$53$		−	359.147i		−	0.930804i	0.885099	−	0.465402i	$-0.154090\pi$
$54$	−692.994	+	306.700i	−1.74638	+	0.772899i
$55$			86.7756i			0.212742i
$56$	838.078	+	1017.61i	1.99987	+	2.42829i
$57$	182.016	+	113.924i	0.422958	+	0.264729i
$58$	−358.293	+	620.582i	−0.811141	+	1.40494i
$59$	−182.287	+	315.730i	−0.402232	+	0.696687i	−0.993995	−	0.109425i	$-0.965099\pi$
$59$	−182.287	+	315.730i	−0.402232	+	0.696687i	0.591763	+	0.806112i	$0.298432\pi$
$60$	756.510	+	26.9783i	1.62775	+	0.0580480i
$61$	−300.892	+	173.720i	−0.631561	+	0.364632i	−0.781356	−	0.624085i	$-0.785472\pi$
$61$	−300.892	+	173.720i	−0.631561	+	0.364632i	0.149795	+	0.988717i	$0.452139\pi$
$62$	−967.165			−1.98113
$63$	−454.621	−	208.246i	−0.909157	−	0.416453i
$64$	−1478.83			−2.88833
$65$	155.214	−	89.6127i	0.296183	−	0.171001i
$66$	165.990	+	312.739i	0.309574	+	0.583265i
$67$	−182.332	+	315.809i	−0.332469	+	0.575854i	−0.982995	−	0.183630i	$-0.941215\pi$
$67$	−182.332	+	315.809i	−0.332469	+	0.575854i	0.650526	+	0.759484i	$0.274548\pi$
$68$	1319.62	−	2285.65i	2.35334	−	4.07611i
$69$	517.739	−	274.796i	0.903312	−	0.479442i
$70$	437.494	+	531.216i	0.747008	+	0.907035i
$71$		−	565.793i		−	0.945736i	−0.881133	−	0.472868i	$-0.843219\pi$
$71$		−	565.793i		−	0.945736i	0.881133	−	0.472868i	$-0.156781\pi$
$72$	1728.64	−	839.949i	2.82947	−	1.37485i
$73$		−	737.140i		−	1.18186i	−0.806723	−	0.590929i	$-0.798761\pi$
$73$		−	737.140i		−	1.18186i	0.806723	−	0.590929i	$-0.201239\pi$
$74$	−693.694	+	400.504i	−1.08973	+	0.629158i
$75$	−403.373	−	14.3849i	−0.621033	−	0.0221469i
$76$	−757.912	−	437.580i	−1.14393	−	0.660446i
$77$	−81.9162	+	218.791i	−0.121237	+	0.323812i
$78$	387.973	−	619.865i	0.563196	−	0.899820i
$79$	−451.543	−	782.096i	−0.643070	−	1.11383i	−0.984744	−	0.174012i	$-0.944327\pi$
$79$	−451.543	−	782.096i	−0.643070	−	1.11383i	0.341673	−	0.939819i	$-0.389006\pi$
$80$	−1479.51			−2.06768
$81$	−450.515	+	573.129i	−0.617991	+	0.786186i
$82$			1011.37i			1.36203i
$83$	382.494	+	662.499i	0.505833	+	0.876129i	0.999977	+	0.00674855i	$0.00214815\pi$
$83$	382.494	+	662.499i	0.505833	+	0.876129i	−0.494144	+	0.869380i	$0.664519\pi$
$84$	1881.95	+	782.167i	2.44450	+	1.01597i
$85$	428.645	−	742.436i	0.546978	−	0.947393i
$86$	−927.743	−	535.633i	−1.16327	−	0.671614i
$87$	−24.5667	+	688.887i	−0.0302739	+	0.848925i
$88$	−448.958	−	777.618i	−0.543853	−	0.941981i
$89$	395.916			0.471539			0.235770	−	0.971809i	$-0.424239\pi$
$89$	395.916			0.471539			0.235770	+	0.971809i	$0.424239\pi$
$90$	902.385	−	438.471i	1.05689	−	0.513543i
$91$	475.941	−	79.4223i	0.548265	−	0.0914914i
$92$	−2068.87	+	1194.47i	−2.34451	+	1.35360i
$93$	−821.793	+	436.175i	−0.916300	+	0.486336i
$94$	862.059	+	497.710i	0.945900	+	0.546115i
$95$	−246.189	−	142.137i	−0.265878	−	0.153505i
$96$	−2718.53	+	1442.89i	−2.89019	+	1.53400i
$97$	−243.773	+	140.742i	−0.255169	+	0.147322i	−0.622129	−	0.782915i	$-0.713732\pi$
$97$	−243.773	+	140.742i	−0.255169	+	0.147322i	0.366960	+	0.930237i	$0.380399\pi$
$98$	601.604	+	1752.37i	0.620114	+	1.80629i
$99$	282.080	+	190.873i	0.286365	+	0.193773i
$100$	1645.06			1.64506
$101$	−552.396	−	956.777i	−0.544212	−	0.942603i	−0.998656	−	0.0518275i	$-0.983495\pi$
$101$	−552.396	−	956.777i	−0.544212	−	0.942603i	0.454444	−	0.890775i	$-0.349838\pi$
$102$	124.661	−	3495.67i	0.121012	−	3.39336i
$103$	1350.73	+	779.844i	1.29215	+	0.746023i	0.979035	−	0.203693i	$-0.0652944\pi$
$103$	1350.73	+	779.844i	1.29215	+	0.746023i	0.313114	+	0.949715i	$0.398628\pi$
$104$	−927.272	+	1606.08i	−0.874293	+	1.51432i
$105$	611.305	+	254.067i	0.568165	+	0.236138i
$106$	969.991	+	1680.07i	0.888810	+	1.53946i
$107$			741.988i			0.670380i	0.942151	+	0.335190i	$0.108800\pi$
$107$			741.988i			0.670380i	−0.942151	+	0.335190i	$0.891200\pi$
$108$	1751.73	−	2399.83i	1.56074	−	2.13819i
$109$	−694.460			−0.610249			−0.305125	−	0.952312i	$-0.598698\pi$
$109$	−694.460			−0.610249			−0.305125	+	0.952312i	$0.598698\pi$
$110$	−234.365	−	405.933i	−0.203144	−	0.351856i
$111$	−408.806	+	653.150i	−0.349569	+	0.558507i
$112$	−3730.36	−	1396.66i	−3.14719	−	1.17832i
$113$	1407.16	+	812.424i	1.17145	+	0.676340i	0.954022	−	0.299736i	$-0.0968985\pi$
$113$	1407.16	+	812.424i	1.17145	+	0.676340i	0.217432	+	0.976075i	$0.430232\pi$
$114$	−1159.15	−	41.3370i	−0.952319	−	0.0339611i
$115$	−672.022	+	387.992i	−0.544925	+	0.314613i
$116$		−	2809.46i		−	2.24872i
$117$	50.1084	−	701.664i	0.0395943	−	0.554435i
$118$		−	1969.30i		−	1.53634i
$119$	1781.62	−	1467.29i	1.37244	−	1.13031i
$120$	−2247.42	+	1192.84i	−1.70967	+	0.907425i
$121$	−585.938	+	1014.87i	−0.440224	+	0.762490i
$122$	938.373	−	1625.31i	0.696363	−	1.20614i
$123$	456.109	+	859.350i	0.334358	+	0.629959i
$124$	3283.86	−	1895.94i	2.37822	−	1.37307i
$125$	1394.24			0.997636
$126$	2689.14	−	253.683i	1.90133	−	0.179364i
$127$	−1099.84			−0.768466			−0.384233	−	0.923236i	$-0.625534\pi$
$127$	−1099.84			−0.768466			−0.384233	+	0.923236i	$0.625534\pi$
$128$	2814.28	−	1624.82i	1.94335	−	1.12200i
$129$	−1029.86	−	36.7262i	−0.702899	−	0.0250664i
$130$	−484.056	+	838.409i	−0.326573	+	0.565641i
$131$	−597.844	+	1035.50i	−0.398732	+	0.690624i	−0.993570	−	0.113222i	$-0.963883\pi$
$131$	−597.844	+	1035.50i	−0.398732	+	0.690624i	0.594838	+	0.803846i	$0.297216\pi$
$132$	−1176.66	−	736.467i	−0.775870	−	0.485616i
$133$	−486.548	−	590.778i	−0.317211	−	0.385165i
$134$		−	1969.79i		−	1.26988i
$135$	569.006	−	779.526i	0.362758	−	0.496970i
$136$			8870.86i			5.59316i
$137$	−1175.08	+	678.431i	−0.732800	+	0.423082i	−0.819446	−	0.573157i	$-0.805719\pi$
$137$	−1175.08	+	678.431i	−0.732800	+	0.423082i	0.0866457	+	0.996239i	$0.472385\pi$
$138$	−1679.79	+	2683.81i	−1.03618	+	1.65551i
$139$	−828.064	−	478.083i	−0.505291	−	0.291730i	0.225605	−	0.974219i	$-0.427564\pi$
$139$	−828.064	−	478.083i	−0.505291	−	0.291730i	−0.730896	+	0.682489i	$0.760898\pi$
$140$	−2526.79	−	946.041i	−1.52538	−	0.571108i
$141$	956.944	+	34.1260i	0.571554	+	0.0203825i
$142$	1528.10	+	2646.76i	0.903068	+	1.56416i
$143$	−328.654			−0.192192
$144$	−3254.37	+	4809.43i	−1.88331	+	2.78324i
$145$		−	912.582i		−	0.522660i
$146$	1990.88	+	3448.31i	1.12854	+	1.95469i
$147$	1301.47	+	1217.66i	0.730227	+	0.683205i
$148$	1570.22	−	2719.70i	0.872105	−	1.51053i
$149$	−166.537	−	96.1501i	−0.0915653	−	0.0528653i	0.453518	−	0.891247i	$-0.350169\pi$
$149$	−166.537	−	96.1501i	−0.0915653	−	0.0528653i	−0.545083	+	0.838382i	$0.683502\pi$
$150$	1925.81	−	1022.15i	1.04828	−	0.556386i
$151$	−307.926	−	533.343i	−0.165951	−	0.287436i	0.771041	−	0.636785i	$-0.219736\pi$
$151$	−307.926	−	533.343i	−0.165951	−	0.287436i	−0.936993	+	0.349349i	$0.886403\pi$
$152$	2941.54			1.56968
$153$	−1470.57	−	3026.46i	−0.777047	−	1.59918i
$154$	−207.714	−	1244.74i	−0.108689	−	0.651322i
$155$	1066.68	−	615.849i	0.552761	−	0.319137i
$156$	−102.177	+	2865.21i	−0.0524406	+	1.47051i
$157$	722.630	+	417.211i	0.367339	+	0.212083i	0.672295	−	0.740283i	$-0.265309\pi$
$157$	722.630	+	417.211i	0.367339	+	0.212083i	−0.304956	+	0.952366i	$0.598642\pi$
$158$	4224.60	+	2439.07i	2.12716	+	1.22812i
$159$	1581.88	+	990.096i	0.789001	+	0.493835i
$160$	3528.63	−	2037.26i	1.74352	−	1.00662i
$161$	−2060.66	+	343.871i	−1.00871	+	0.168328i
$162$	559.572	−	3897.84i	0.271383	−	1.89039i
$163$	−3304.12			−1.58772			−0.793860	−	0.608100i	$-0.791932\pi$
$163$	−3304.12			−1.58772			−0.793860	+	0.608100i	$0.791932\pi$
$164$	−1982.59	−	3433.94i	−0.943988	−	1.63504i
$165$	−382.207	−	239.223i	−0.180332	−	0.112870i
$166$	−3578.58	−	2066.09i	−1.67320	−	0.966024i
$167$	−956.456	+	1656.63i	−0.443190	+	0.767628i	−0.997924	−	0.0643998i	$-0.979487\pi$
$167$	−956.456	+	1656.63i	−0.443190	+	0.767628i	0.554734	+	0.832028i	$0.312820\pi$
$168$	−6792.54	+	885.997i	−3.11938	+	0.406882i
$169$	−759.101	−	1314.80i	−0.345517	−	0.598453i
$170$			4630.78i			2.08920i
$171$	−1003.56	+	487.634i	−0.448798	+	0.218072i
$172$	4200.02			1.86191
$173$	−313.536	−	543.061i	−0.137790	−	0.238660i	0.788870	−	0.614561i	$-0.210667\pi$
$173$	−313.536	−	543.061i	−0.137790	−	0.238660i	−0.926660	+	0.375901i	$0.877333\pi$
$174$	−1745.64	−	3288.94i	−0.760555	−	1.43295i
$175$	1347.29	+	504.431i	0.581975	+	0.217894i
$176$	2349.57	+	1356.53i	1.00628	+	0.580977i
$177$	−888.120	−	1673.30i	−0.377148	−	0.710579i
$178$	−1852.08	+	1069.30i	−0.779883	+	0.450266i
$179$			1174.10i			0.490259i	0.969490	+	0.245130i	$0.0788305\pi$
$179$			1174.10i			0.490259i	−0.969490	+	0.245130i	$0.921169\pi$
$180$	−2204.38	+	3257.71i	−0.912802	+	1.34898i
$181$		−	1625.05i		−	0.667344i	−0.942689	−	0.333672i	$-0.891712\pi$
$181$		−	1625.05i		−	0.667344i	0.942689	−	0.333672i	$-0.108288\pi$
$182$	−2011.93	+	1656.97i	−0.819417	+	0.674849i
$183$	64.3405	−	1804.20i	0.0259901	−	0.728801i
$184$	4014.77	−	6953.79i	1.60855	−	2.78609i
$185$	510.048	−	883.428i	0.202700	−	0.351086i
$186$	2666.28	−	4259.93i	1.05108	−	1.67932i
$187$	−1361.44	+	786.027i	−0.532397	+	0.307380i
$188$	−3902.65			−1.51399
$189$	2170.53	−	1428.31i	0.835359	−	0.549704i
$190$	1535.55			0.586318
$191$	113.173	−	65.3404i	0.0428739	−	0.0247532i	−0.478410	−	0.878137i	$-0.658787\pi$
$191$	113.173	−	65.3404i	0.0428739	−	0.0247532i	0.521284	+	0.853383i	$0.325453\pi$
$192$	4076.83	−	6513.56i	1.53240	−	2.44831i
$193$	−570.103	+	987.447i	−0.212626	+	0.368280i	−0.952536	−	0.304427i	$-0.901535\pi$
$193$	−570.103	+	987.447i	−0.212626	+	0.368280i	0.739909	+	0.672707i	$0.234868\pi$
$194$	760.240	−	1316.77i	0.281351	−	0.487314i
$195$	−33.1898	+	930.691i	−0.0121886	+	0.341785i
$196$	−5477.84	−	4770.58i	−1.99630	−	1.73855i
$197$			3462.71i			1.25232i	0.779693	+	0.626162i	$0.215375\pi$
$197$			3462.71i			1.25232i	−0.779693	+	0.626162i	$0.784625\pi$
$198$	−1835.07	−	131.049i	−0.658651	−	0.0470368i
$199$		−	2522.77i		−	0.898667i	−0.893364	−	0.449333i	$-0.851662\pi$
$199$		−	2522.77i		−	0.898667i	0.893364	−	0.449333i	$-0.148338\pi$
$200$	−4788.49	+	2764.63i	−1.69299	+	0.977446i
$201$	−888.342	−	1673.71i	−0.311735	−	0.587337i
$202$	5168.17	+	2983.84i	1.80015	+	1.03932i
$203$	861.477	−	2300.93i	0.297851	−	0.795534i
$204$	6429.32	+	12113.4i	2.20658	+	4.15739i
$205$	−643.994	−	1115.43i	−0.219407	−	0.380025i
$206$	−8424.88			−2.84946
$207$	−216.952	+	3037.97i	−0.0728466	+	1.02006i
$208$		−	5603.51i		−	1.86795i
$209$	260.643	+	451.447i	0.0862635	+	0.149413i
$210$	−3545.85	+	462.509i	−1.16518	+	0.151982i
$211$	−1033.33	+	1789.77i	−0.337143	+	0.583948i	−0.983894	−	0.178753i	$-0.942794\pi$
$211$	−1033.33	+	1789.77i	−0.337143	+	0.583948i	0.646751	+	0.762701i	$0.276127\pi$
$212$	−6586.92	−	3802.96i	−2.13392	−	1.23202i
$213$	2492.06	+	1559.78i	0.801658	+	0.501757i
$214$	−2003.98	−	3470.99i	−0.640135	−	1.10875i
$215$	1364.27			0.432756
$216$	−1065.91	+	9929.44i	−0.335769	+	3.12784i
$217$	3270.83	−	545.817i	1.02322	−	0.170749i
$218$	3248.65	−	1875.61i	1.00930	−	0.582718i
$219$	3246.77	+	2032.15i	1.00181	+	0.627031i
$220$	1591.51	+	918.856i	0.487724	+	0.281588i
$221$	2811.90	+	1623.45i	0.855877	+	0.494141i
$222$	148.335	−	4159.52i	0.0448449	−	1.25752i
$223$	−5321.42	+	3072.32i	−1.59797	+	0.922591i	−0.606097	+	0.795390i	$0.707266\pi$
$223$	−5321.42	+	3072.32i	−1.59797	+	0.922591i	−0.991877	+	0.127201i	$0.959401\pi$
$224$	10820.0	−	1805.59i	3.22743	−	0.538575i
$225$	1175.38	−	1737.02i	0.348260	−	0.514672i
$226$	−8776.84			−2.58331
$227$	455.878	+	789.603i	0.133294	+	0.230871i	0.924944	−	0.380103i	$-0.124111\pi$
$227$	455.878	+	789.603i	0.133294	+	0.230871i	−0.791651	+	0.610974i	$0.790778\pi$
$228$	4016.76	−	2131.94i	1.16674	−	0.619259i
$229$	2305.74	+	1331.22i	0.665360	+	0.384146i	0.794316	−	0.607504i	$-0.207829\pi$
$229$	2305.74	+	1331.22i	0.665360	+	0.384146i	−0.128956	+	0.991650i	$0.541163\pi$
$230$	2095.80	−	3630.02i	0.600838	−	1.04068i
$231$	−737.848	−	963.966i	−0.210160	−	0.274564i
$232$	4721.49	+	8177.87i	1.33613	+	2.31424i
$233$		−	1984.29i		−	0.557918i	−0.960303	−	0.278959i	$-0.910011\pi$
$233$		−	1984.29i		−	0.557918i	0.960303	−	0.278959i	$-0.0899894\pi$
$234$	1660.66	+	3417.69i	0.463936	+	0.954792i
$235$	−1267.68			−0.351891
$236$	3860.42	+	6686.45i	1.06480	+	1.84428i
$237$	4689.59	+	167.238i	1.28532	+	0.0458365i
$238$	−4371.45	+	11675.8i	−1.19059	+	3.17995i
$239$	−1544.98	−	891.996i	−0.418145	−	0.241416i	0.276138	−	0.961118i	$-0.410945\pi$
$239$	−1544.98	−	891.996i	−0.418145	−	0.241416i	−0.694283	+	0.719702i	$0.744278\pi$
$240$	4078.72	−	6516.59i	1.09700	−	1.75268i
$241$	5182.09	−	2991.88i	1.38510	−	0.799685i	0.392338	−	0.919821i	$-0.371666\pi$
$241$	5182.09	−	2991.88i	1.38510	−	0.799685i	0.992757	+	0.120136i	$0.0383331\pi$
$242$		−	6330.05i		−	1.68145i
$243$	−1282.40	−	3564.32i	−0.338542	−	0.940951i
$244$			7357.99i			1.93052i
$245$	−1779.34	−	1549.61i	−0.463991	−	0.404084i
$246$	−4454.61	−	2788.13i	−1.15454	−	0.722622i
$247$	538.330	−	932.414i	0.138677	−	0.240195i
$248$	−6372.53	+	11037.5i	−1.63168	+	2.82615i
$249$	−3972.47	−	141.664i	−1.01102	−	0.0360546i
$250$	−6522.19	+	3765.59i	−1.65000	+	0.952627i
$251$	6093.37			1.53231			0.766155	−	0.642656i	$-0.222167\pi$
$251$	6093.37			1.53231			0.766155	+	0.642656i	$0.222167\pi$
$252$	−8633.26	+	6132.87i	−2.15811	+	1.53307i
$253$	1422.96			0.353599
$254$	5145.02	−	2970.48i	1.27097	−	0.733797i
$255$	2088.40	+	3934.74i	0.512866	+	0.966285i
$256$	−2861.40	+	4956.10i	−0.698585	+	1.20998i
$257$	−2276.03	+	3942.19i	−0.552431	+	0.956838i	0.445668	+	0.895198i	$0.352966\pi$
$257$	−2276.03	+	3942.19i	−0.552431	+	0.956838i	−0.998098	+	0.0616394i	$0.980367\pi$
$258$	4916.83	−	2609.66i	1.18647	−	0.629730i
$259$	2119.96	−	1745.94i	0.508602	−	0.418870i
$260$		−	3795.59i		−	0.905355i
$261$	−2966.51	−	2007.33i	−0.703535	−	0.476056i
$262$		−	6458.68i		−	1.52297i
$263$	−773.268	+	446.447i	−0.181300	+	0.104673i	−0.587903	−	0.808931i	$-0.700046\pi$
$263$	−773.268	+	446.447i	−0.181300	+	0.104673i	0.406604	+	0.913605i	$0.366713\pi$
$264$	4662.74	+	166.280i	1.08701	+	0.0387645i
$265$	−2139.60	−	1235.30i	−0.495979	−	0.286353i
$266$	3871.64	+	1449.56i	0.892426	+	0.334128i
$267$	−1091.46	+	1743.83i	−0.250174	+	0.399703i
$268$	3861.39	+	6688.12i	0.880119	+	1.52441i
$269$	1159.42			0.262792			0.131396	−	0.991330i	$-0.458054\pi$
$269$	1159.42			0.262792			0.131396	+	0.991330i	$0.458054\pi$
$270$	−556.428	+	5183.38i	−0.125419	+	1.16833i
$271$		−	2122.71i		−	0.475813i	−0.971288	−	0.237907i	$-0.923539\pi$
$271$		−	2122.71i		−	0.475813i	0.971288	−	0.237907i	$-0.0764612\pi$
$272$	−13401.7	−	23212.4i	−2.98748	−	5.17447i
$273$	−962.254	+	2315.26i	−0.213327	+	0.513281i
$274$	3664.64	−	6347.35i	0.807989	−	1.39948i
$275$	−848.594	−	489.936i	−0.186080	−	0.107434i
$276$	442.393	−	12405.4i	0.0964817	−	2.70549i
$277$	1721.64	+	2981.97i	0.373442	+	0.646821i	0.990093	−	0.140416i	$-0.0448440\pi$
$277$	1721.64	+	2981.97i	0.373442	+	0.646821i	−0.616650	+	0.787237i	$0.711511\pi$
$278$	5164.87			1.11427
$279$	344.362	−	4822.08i	0.0738940	−	1.03473i
$280$	8944.97	−	1492.69i	1.90916	−	0.318590i
$281$	−3015.50	+	1741.00i	−0.640178	+	0.369607i	−0.784683	−	0.619897i	$-0.787174\pi$
$281$	−3015.50	+	1741.00i	−0.640178	+	0.369607i	0.144505	+	0.989504i	$0.453841\pi$
$282$	−4568.71	+	2424.89i	−0.964762	+	0.512058i
$283$	3071.99	+	1773.61i	0.645268	+	0.372546i	0.786641	−	0.617411i	$-0.211818\pi$
$283$	3071.99	+	1773.61i	0.645268	+	0.372546i	−0.141373	+	0.989956i	$0.545152\pi$
$284$	−10376.9	−	5991.11i	−2.16815	−	1.25178i
$285$	1304.74	−	692.507i	0.271180	−	0.143932i
$286$	1537.43	−	887.635i	0.317867	−	0.183521i
$287$	−570.762	−	3420.31i	−0.117390	−	0.703465i
$288$	1139.17	−	15951.6i	0.233076	−	3.26375i
$289$	10617.9			2.16119
$290$	2464.72	+	4269.02i	0.499080	+	0.864433i
$291$	52.1267	−	1461.71i	0.0105008	−	0.294457i
$292$	−13519.5	−	7805.48i	−2.70948	−	1.56432i
$293$	1203.25	−	2084.09i	0.239914	−	0.415542i	−0.720776	−	0.693168i	$-0.756214\pi$
$293$	1203.25	−	2084.09i	0.239914	−	0.415542i	0.960689	+	0.277626i	$0.0895476\pi$
$294$	−9376.91	−	2181.14i	−1.86011	−	0.432676i
$295$	1253.96	+	2171.93i	0.247486	+	0.428659i
$296$			10555.5i			2.07272i
$297$	−1618.35	+	716.236i	−0.316182	+	0.139933i
$298$	1038.74			0.201921
$299$	−1469.48	−	2545.22i	−0.284222	−	0.492286i
$300$	−4535.09	+	7245.73i	−0.872778	+	1.39444i
$301$	3439.79	+	1287.87i	0.658692	+	0.246617i
$302$	2880.93	+	1663.30i	0.548936	+	0.316929i
$303$	5737.02	+	204.590i	1.08773	+	0.0387901i
$304$	−7697.13	+	4443.94i	−1.45217	+	0.838412i
$305$			2390.06i			0.448703i
$306$	15053.2	+	10185.9i	2.81220	+	1.90291i
$307$			7862.81i			1.46174i	0.682517	+	0.730870i	$0.260886\pi$
$307$			7862.81i			1.46174i	−0.682517	+	0.730870i	$0.739114\pi$
$308$	3145.33	+	3819.13i	0.581888	+	0.706542i
$309$	−7158.55	+	3799.48i	−1.31792	+	0.699498i
$310$	−3326.60	+	5761.83i	−0.609477	+	1.05565i
$311$	−1367.04	+	2367.77i	−0.249252	+	0.431718i	−0.963319	−	0.268360i	$-0.913518\pi$
$311$	−1367.04	+	2367.77i	−0.249252	+	0.431718i	0.714066	+	0.700078i	$0.246852\pi$
$312$	−4517.76	−	8511.86i	−0.819769	−	1.54452i
$313$	−3509.53	+	2026.23i	−0.633771	+	0.365908i	−0.782211	−	0.623014i	$-0.785908\pi$
$313$	−3509.53	+	2026.23i	−0.633771	+	0.365908i	0.148440	+	0.988921i	$0.452575\pi$
$314$	−4507.25			−0.810060
$315$	−2804.30	+	1992.11i	−0.501601	+	0.356326i
$316$	−19125.3			−3.40470
$317$	−968.686	+	559.271i	−0.171630	+	0.0990909i	−0.583354	−	0.812218i	$-0.698260\pi$
$317$	−968.686	+	559.271i	−0.171630	+	0.0990909i	0.411724	+	0.911309i	$0.364927\pi$
$318$	−10074.0	−	359.255i	−1.77649	−	0.0633523i
$319$	−836.721	+	1449.24i	−0.146857	+	0.254364i
$320$	−5086.47	+	8810.03i	−0.888570	+	1.53905i
$321$	−3268.12	−	2045.51i	−0.568251	−	0.355668i
$322$	8710.95	−	7174.09i	1.50759	−	1.24160i
$323$		−	5150.00i		−	0.887163i
$324$	5741.01	+	14331.4i	0.984398	+	2.45738i
$325$			2023.82i			0.345419i
$326$	15456.5	−	8923.83i	2.62594	−	1.51609i
$327$	1914.49	−	3058.78i	0.323766	−	0.517281i
$328$	11542.0	+	6663.76i	1.94298	+	1.12178i
$329$	−3196.25	−	1196.69i	−0.535608	−	0.200534i
$330$	2434.05	+	86.8018i	0.406030	+	0.0144796i
$331$	3521.44	+	6099.32i	0.584761	+	1.01284i	0.994905	+	0.100815i	$0.0321452\pi$
$331$	3521.44	+	6099.32i	0.584761	+	1.01284i	−0.410144	+	0.912021i	$0.634521\pi$
$332$	16200.7			2.67810
$333$	−1749.84	−	3601.21i	−0.287959	−	0.592628i
$334$		−	10332.9i		−	1.69278i
$335$	1254.28	+	2172.47i	0.204562	+	0.354313i
$336$	16435.5	−	12580.2i	2.66854	−	2.04258i
$337$	1296.20	−	2245.08i	0.209520	−	0.362900i	−0.742043	−	0.670352i	$-0.766143\pi$
$337$	1296.20	−	2245.08i	0.209520	−	0.362900i	0.951564	+	0.307452i	$0.0994764\pi$
$338$	7102.09	+	4100.39i	1.14291	+	0.659858i
$339$	−7457.62	+	3958.21i	−1.19481	+	0.634161i
$340$	−9077.74	−	15723.1i	−1.44797	−	2.50796i
$341$	−2258.62			−0.358684
$342$	3377.62	−	4991.58i	0.534037	−	0.789221i
$343$	−3023.49	−	5586.78i	−0.475957	−	0.879468i
$344$	−12225.6	+	7058.43i	−1.91616	+	1.10629i
$345$	143.700	−	4029.57i	0.0224248	−	0.628826i
$346$	2933.42	+	1693.61i	0.455785	+	0.263148i
$347$	−7226.45	−	4172.19i	−1.11797	−	0.645462i	−0.177090	−	0.984195i	$-0.556668\pi$
$347$	−7226.45	−	4172.19i	−1.11797	−	0.645462i	−0.940882	+	0.338733i	$0.890002\pi$
$348$	12374.4	+	7745.11i	1.90614	+	1.19305i
$349$	−9981.26	+	5762.68i	−1.53090	+	0.883866i	−0.531581	+	0.847008i	$0.678402\pi$
$349$	−9981.26	+	5762.68i	−1.53090	+	0.883866i	−0.999320	+	0.0368588i	$0.988265\pi$
$350$	−7664.95	+	1279.08i	−1.17060	+	0.195343i
$351$	2952.38	+	2155.05i	0.448963	+	0.327716i
$352$	−7471.62			−1.13136
$353$	−5107.82	−	8847.00i	−0.770146	−	1.33393i	−0.937482	−	0.348033i	$-0.886850\pi$
$353$	−5107.82	−	8847.00i	−0.770146	−	1.33393i	0.167336	−	0.985900i	$-0.446484\pi$
$354$	8673.86	+	5428.95i	1.30229	+	0.815101i
$355$	−3370.68	−	1946.06i	−0.503935	−	0.290947i
$356$	4192.30	−	7261.28i	0.624134	−	1.08103i
$357$	1551.19	+	11892.3i	0.229965	+	1.76304i
$358$	−3171.04	−	5492.40i	−0.468141	−	0.810844i
$359$		−	6593.91i		−	0.969396i	−0.874682	−	0.484698i	$-0.838930\pi$
$359$		−	6593.91i		−	0.969396i	0.874682	−	0.484698i	$-0.161070\pi$
$360$	941.753	−	13187.3i	0.137874	−	1.93064i
$361$	5151.28			0.751025
$362$	4388.98	+	7601.93i	0.637236	+	1.10373i
$363$	−2854.75	−	5378.60i	−0.412770	−	0.777695i
$364$	3583.03	−	9569.97i	0.515940	−	1.37803i
$365$	−4391.47	−	2535.41i	−0.629753	−	0.363588i
$366$	4571.85	+	8613.76i	0.652935	+	1.23019i
$367$	4531.96	−	2616.53i	0.644595	−	0.372157i	−0.141787	−	0.989897i	$-0.545285\pi$
$367$	4531.96	−	2616.53i	0.644595	−	0.372157i	0.786382	+	0.617740i	$0.211952\pi$
$368$			24261.3i			3.43670i
$369$	−5042.45	−	360.100i	−0.711381	−	0.0508023i
$370$			5510.19i			0.774219i
$371$	−4228.53	−	5134.38i	−0.591737	−	0.718501i
$372$	−702.198	+	19690.7i	−0.0978690	+	2.74439i
$373$	4889.02	−	8468.04i	0.678670	−	1.17549i	−0.296711	−	0.954967i	$-0.595890\pi$
$373$	4889.02	−	8468.04i	0.678670	−	1.17549i	0.975381	−	0.220524i	$-0.0707768\pi$
$374$	4245.84	−	7354.00i	0.587024	−	1.01676i
$375$	−3843.64	+	6140.99i	−0.529292	+	0.845652i
$376$	11360.0	−	6558.69i	1.55810	−	0.899571i
$377$	3456.31			0.472172
$378$	−6296.05	+	12543.8i	−0.856703	+	1.70683i
$379$	−3637.54			−0.493002			−0.246501	−	0.969143i	$-0.579281\pi$
$379$	−3637.54			−0.493002			−0.246501	+	0.969143i	$0.579281\pi$
$380$	−5213.72	+	3010.14i	−0.703837	+	0.406361i
$381$	3032.05	−	4844.31i	0.407707	−	0.651395i
$382$	−352.946	+	611.320i	−0.0472730	+	0.0818792i
$383$	−4495.26	+	7786.02i	−0.599731	+	1.03876i	0.393129	+	0.919483i	$0.371392\pi$
$383$	−4495.26	+	7786.02i	−0.599731	+	1.03876i	−0.992860	+	0.119281i	$0.961941\pi$
$384$	−601.784	+	16874.9i	−0.0799731	+	2.24256i
$385$	1021.68	+	1240.55i	0.135246	+	0.164219i
$386$		−	6158.98i		−	0.812134i
$387$	3000.88	−	4434.81i	0.394168	−	0.582517i
$388$			5961.21i			0.779987i
$389$	−4843.12	+	2796.17i	−0.631249	+	0.364452i	−0.781236	−	0.624236i	$-0.785410\pi$
$389$	−4843.12	+	2796.17i	−0.631249	+	0.364452i	0.149987	+	0.988688i	$0.452077\pi$
$390$	−2358.37	−	4443.37i	−0.306207	−	0.576920i
$391$	−12174.6	−	7028.99i	−1.57466	−	0.909133i
$392$	23962.4	+	4680.48i	3.08746	+	0.603062i
$393$	−2912.76	−	5487.89i	−0.373865	−	0.704395i
$394$	−9352.16	−	16198.4i	−1.19583	−	2.07123i
$395$	−6212.39			−0.791339
$396$	6487.61	−	3152.35i	0.823270	−	0.400029i
$397$			11561.7i			1.46163i	0.682575	+	0.730815i	$0.260860\pi$
$397$			11561.7i			1.46163i	−0.682575	+	0.730815i	$0.739140\pi$
$398$	6813.56	+	11801.4i	0.858123	+	1.48631i
$399$	3943.43	−	514.367i	0.494783	−	0.0645378i
$400$	8353.35	−	14468.4i	1.04417	−	1.80855i
$401$	3685.19	+	2127.65i	0.458927	+	0.264962i	0.711593	−	0.702592i	$-0.247974\pi$
$401$	3685.19	+	2127.65i	0.458927	+	0.264962i	−0.252666	+	0.967554i	$0.581307\pi$
$402$	8676.03	+	5430.32i	1.07642	+	0.673730i
$403$	2332.46	+	4039.95i	0.288308	+	0.499365i
$404$	−23397.0			−2.88130
$405$	1864.82	+	4655.21i	0.228800	+	0.571159i
$406$	2184.44	+	13090.3i	0.267025	+	1.60015i
$407$	−1619.98	+	935.298i	−0.197296	+	0.113909i
$408$	−39072.1	−	24455.2i	−4.74108	−	2.96743i
$409$	−4853.21	−	2802.00i	−0.586738	−	0.338753i	0.177068	−	0.984199i	$-0.443339\pi$
$409$	−4853.21	−	2802.00i	−0.586738	−	0.338753i	−0.763807	+	0.645445i	$0.776672\pi$
$410$	6025.16	+	3478.63i	0.725759	+	0.419017i
$411$	251.270	−	7045.98i	0.0301563	−	0.845627i
$412$	28605.4	−	16515.3i	3.42060	−	1.97488i
$413$	1111.37	+	6659.90i	0.132413	+	0.793492i
$414$	−7190.11	−	14797.4i	−0.853562	−	1.75665i
$415$	5262.40			0.622460
$416$	7715.90	+	13364.3i	0.909382	+	1.57510i
$417$	4388.55	−	2329.27i	0.515367	−	0.273537i
$418$	−2438.56	−	1407.90i	−0.285344	−	0.164743i
$419$	2039.72	−	3532.89i	0.237820	−	0.411917i	−0.722268	−	0.691613i	$-0.756900\pi$
$419$	2039.72	−	3532.89i	0.237820	−	0.411917i	0.960089	+	0.279696i	$0.0902338\pi$
$420$	11132.7	−	8521.34i	1.29339	−	0.989997i
$421$	8228.54	+	14252.3i	0.952576	+	1.64991i	0.739820	+	0.672805i	$0.234911\pi$
$421$	8228.54	+	14252.3i	0.952576	+	1.64991i	0.212756	+	0.977105i	$0.431756\pi$
$422$		−	11163.3i		−	1.28773i
$423$	−2788.41	+	4120.83i	−0.320514	+	0.473668i
$424$	25564.6			2.92813
$425$	4840.27	+	8383.60i	0.552441	+	0.956857i
$426$	−15870.4	−	565.963i	−1.80499	−	0.0643685i
$427$	−2256.22	+	6026.15i	−0.255705	+	0.682965i
$428$	13608.4	+	7856.81i	1.53688	+	0.887321i
$429$	906.033	−	1447.57i	0.101967	−	0.162912i
$430$	−6382.01	+	3684.65i	−0.715739	+	0.413232i
$431$		−	354.675i		−	0.0396382i	−0.999804	−	0.0198191i	$-0.993691\pi$
$431$		−	354.675i		−	0.0396382i	0.999804	−	0.0198191i	$-0.00630903\pi$
$432$	−12211.7	−	27592.7i	−1.36004	−	3.07304i
$433$		−	3100.88i		−	0.344155i	−0.985083	−	0.172077i	$-0.944952\pi$
$433$		−	3100.88i		−	0.344155i	0.985083	−	0.172077i	$-0.0550479\pi$
$434$	−13826.6	+	11387.2i	−1.52926	+	1.25946i
$435$	4019.51	+	2515.81i	0.443036	+	0.277296i
$436$	−7353.55	+	12736.7i	−0.807732	+	1.39903i
$437$	−2330.78	+	4037.04i	−0.255141	+	0.441917i
$438$	−20676.7	−	737.362i	−2.25564	−	0.0804395i
$439$	13194.9	−	7618.07i	1.43453	−	0.828224i	0.437065	−	0.899430i	$-0.356018\pi$
$439$	13194.9	−	7618.07i	1.43453	−	0.828224i	0.997462	+	0.0712055i	$0.0226846\pi$
$440$	−6176.82			−0.669246
$441$	−8951.14	+	2375.53i	−0.966542	+	0.256509i
$442$	−17538.6			−1.88739
$443$	9086.84	−	5246.29i	0.974557	−	0.562661i	0.0739349	−	0.997263i	$-0.476444\pi$
$443$	9086.84	−	5246.29i	0.974557	−	0.562661i	0.900623	+	0.434602i	$0.143111\pi$
$444$	7650.28	+	14413.8i	0.817717	+	1.54065i
$445$	1361.77	−	2358.65i	0.145065	−	0.251260i
$446$	16595.6	−	28744.4i	1.76194	−	3.05176i
$447$	882.607	−	468.453i	0.0933912	−	0.0495684i
$448$	−21141.4	+	17411.4i	−2.22955	+	1.83619i
$449$			13387.2i			1.40708i	0.710656	+	0.703540i	$0.248398\pi$
$449$			13387.2i			1.40708i	−0.710656	+	0.703540i	$0.751602\pi$
$450$	−806.989	+	11300.2i	−0.0845374	+	1.18377i
$451$			2361.84i			0.246596i
$452$	29800.5	−	17205.3i	3.10110	−	1.79042i
$453$	3198.02	+	114.046i	0.331692	+	0.0118286i
$454$	−4265.16	−	2462.49i	−0.440911	−	0.254560i
$455$	1163.86	−	3108.57i	0.119918	−	0.320290i
$456$	−8109.25	+	12956.2i	−0.832786	+	1.33054i
$457$	−8043.99	−	13932.6i	−0.823374	−	1.42613i	−0.903156	−	0.429313i	$-0.858756\pi$
$457$	−8043.99	−	13932.6i	−0.823374	−	1.42613i	0.0797820	−	0.996812i	$-0.474578\pi$
$458$	−14381.5			−1.46726
$459$	17384.3	+	1866.18i	1.76782	+	0.189773i
$460$			16433.6i			1.66570i
$461$	9398.54	+	16278.7i	0.949530	+	1.64463i	0.746416	+	0.665480i	$0.231773\pi$
$461$	9398.54	+	16278.7i	0.949530	+	1.64463i	0.203115	+	0.979155i	$0.434894\pi$
$462$	6055.13	+	2516.60i	0.609762	+	0.253426i
$463$	−108.245	+	187.487i	−0.0108652	+	0.0188191i	−0.871407	−	0.490561i	$-0.836792\pi$
$463$	−108.245	+	187.487i	−0.0108652	+	0.0188191i	0.860542	+	0.509380i	$0.170125\pi$
$464$	−24709.4	−	14266.0i	−2.47221	−	1.42733i
$465$	−228.091	+	6396.02i	−0.0227473	+	0.637868i
$466$	5359.20	+	9282.42i	0.532748	+	0.922746i
$467$	15356.4			1.52165			0.760826	−	0.648956i	$-0.224794\pi$
$467$	15356.4			1.52165			0.760826	+	0.648956i	$0.224794\pi$
$468$	−12338.3	−	8348.84i	−1.21867	−	0.824627i
$469$	1111.65	+	6661.57i	0.109448	+	0.655869i
$470$	5930.16	−	3423.78i	0.581995	−	0.336015i
$471$	−3829.77	+	2032.69i	−0.374664	+	0.198857i
$472$	−22474.1	−	12975.4i	−2.19164	−	1.26535i
$473$	−2166.56	−	1250.86i	−0.210610	−	0.121596i
$474$	−22389.4	+	11883.4i	−2.16958	+	1.15153i
$475$	2779.97	−	1605.01i	0.268534	−	0.155038i
$476$	−8045.46	−	48212.7i	−0.774712	−	4.64249i
$477$	−8721.85	+	4237.97i	−0.837204	+	0.406799i
$478$	9636.49			0.922098
$479$	−8696.60	−	15063.0i	−0.829557	−	1.43683i	−0.898386	−	0.439206i	$-0.855260\pi$
$479$	−8696.60	−	15063.0i	−0.829557	−	1.43683i	0.0688295	−	0.997628i	$-0.478074\pi$
$480$	−754.537	+	21158.3i	−0.0717494	+	2.01196i
$481$	3345.89	+	1931.75i	0.317172	+	0.183119i
$482$	−16161.1	+	27991.8i	−1.52721	+	2.64521i
$483$	4166.23	−	10024.3i	0.392485	−	0.944348i
$484$	12408.8	+	21492.7i	1.16537	+	2.01848i
$485$			1936.35i			0.181289i
$486$	15625.6	+	13210.2i	1.45842	+	1.23298i
$487$	−14133.8			−1.31512			−0.657560	−	0.753402i	$-0.728412\pi$
$487$	−14133.8			−1.31512			−0.657560	+	0.753402i	$0.728412\pi$
$488$	−12365.6	−	21417.9i	−1.14706	−	1.98677i
$489$	9108.79	−	14553.1i	0.842359	−	1.34584i
$490$	12508.9	+	2443.31i	1.15325	+	0.225260i
$491$	−7929.45	−	4578.07i	−0.728821	−	0.420785i	0.0891699	−	0.996016i	$-0.471579\pi$
$491$	−7929.45	−	4578.07i	−0.728821	−	0.420785i	−0.817991	+	0.575232i	$0.804912\pi$
$492$	20590.6	+	734.289i	1.88678	+	0.0672852i
$493$	14317.7	−	8266.30i	1.30798	−	0.755163i
$494$			5815.73i			0.529680i
$495$	2107.34	−	1023.96i	0.191349	−	0.0929770i
$496$		−	38509.2i		−	3.48612i
$497$	−6661.54	−	8088.60i	−0.601229	−	0.730027i
$498$	18965.6	−	10066.2i	1.70657	−	0.905780i
$499$	−7528.00	+	13038.9i	−0.675349	+	1.16974i	0.301017	+	0.953619i	$0.402674\pi$
$499$	−7528.00	+	13038.9i	−0.675349	+	1.16974i	−0.976367	+	0.216121i	$0.930659\pi$
$500$	14763.4	−	25571.0i	1.32048	−	2.28714i
$501$	−4659.95	−	8779.75i	−0.415551	−	0.782935i
$502$	−28504.5	+	16457.1i	−2.53430	+	1.46318i
$503$	13644.2			1.20948			0.604739	−	0.796424i	$-0.293278\pi$
$503$	13644.2			1.20948			0.604739	+	0.796424i	$0.293278\pi$
$504$	14823.3	−	32360.6i	1.31008	−	2.86003i
$505$	−7599.93			−0.669688
$506$	−6656.54	+	3843.16i	−0.584821	+	0.337647i
$507$	7883.80	+	281.148i	0.690595	+	0.0246276i
$508$	−11646.1	+	20171.6i	−1.01715	+	1.76175i
$509$	−442.839	+	767.020i	−0.0385629	+	0.0667929i	−0.884663	−	0.466232i	$-0.845611\pi$
$509$	−442.839	+	767.020i	−0.0385629	+	0.0667929i	0.846100	+	0.533025i	$0.178945\pi$
$510$	−20396.5	−	12766.1i	−1.77093	−	1.10842i
$511$	−8678.95	−	10538.2i	−0.751339	−	0.912293i
$512$		−	4915.40i		−	0.424281i
$513$	618.817	−	5764.55i	0.0532581	−	0.496123i
$514$		−	24588.6i		−	2.11003i
$515$	9291.75	−	5364.60i	0.795036	−	0.459014i
$516$	−11578.6	+	18499.2i	−0.987829	+	1.57826i
$517$	2013.17	+	1162.30i	0.171255	+	0.0988742i
$518$	−5201.62	+	13893.1i	−0.441208	+	1.17843i
$519$	3256.30	+	116.124i	0.275406	+	0.00982137i
$520$	6378.76	+	11048.3i	0.537937	+	0.931734i
$521$	−8268.31			−0.695281			−0.347641	−	0.937628i	$-0.613017\pi$
$521$	−8268.31			−0.695281			−0.347641	+	0.937628i	$0.613017\pi$
$522$	19298.7	+	1378.19i	1.61816	+	0.115559i
$523$		−	1489.91i		−	0.124568i	−0.998058	−	0.0622841i	$-0.980162\pi$
$523$		−	1489.91i		−	0.124568i	0.998058	−	0.0622841i	$-0.0198385\pi$
$524$	12661.0	+	21929.5i	1.05553	+	1.82823i
$525$	−5936.00	+	4543.59i	−0.493464	+	0.377712i
$526$	2411.55	−	4176.92i	0.199902	−	0.346240i
$527$	19324.3	+	11156.9i	1.59731	+	0.922206i
$528$	−12452.2	+	6609.14i	−1.02635	+	0.544746i
$529$	278.849	+	482.981i	0.0229185	+	0.0396960i
$530$	13345.3			1.09374
$531$	9818.48	+	701.174i	0.802421	+	0.0573039i
$532$	−15987.1	+	2667.84i	−1.30288	+	0.217417i
$533$	4224.58	−	2439.06i	0.343315	−	0.198213i
$534$	396.035	−	11105.4i	0.0320939	−	0.899959i
$535$	4420.35	+	2552.09i	0.357212	+	0.206236i
$536$	−22479.7	−	12978.7i	−1.81152	−	1.04588i
$537$	−5171.39	−	3236.76i	−0.415571	−	0.260105i
$538$	−5423.72	+	3131.39i	−0.434634	+	0.250936i
$539$	1404.93	+	4092.31i	0.112272	+	0.327028i
$540$	−8271.74	−	18690.1i	−0.659183	−	1.48944i
$541$	668.496			0.0531255			0.0265628	−	0.999647i	$-0.491544\pi$
$541$	668.496			0.0531255			0.0265628	+	0.999647i	$0.491544\pi$
$542$	5733.06	+	9929.95i	0.454347	+	0.786952i
$543$	7157.62	+	4479.95i	0.565678	+	0.354057i
$544$	63925.7	+	36907.5i	5.03822	+	2.90882i
$545$	−2388.62	+	4137.20i	−0.187738	+	0.325171i
$546$	−1751.71	−	13429.6i	−0.137301	−	1.05262i
$547$	−10234.9	−	17727.3i	−0.800022	−	1.38568i	−0.919601	−	0.392855i	$-0.871488\pi$
$547$	−10234.9	−	17727.3i	−0.800022	−	1.38568i	0.119578	−	0.992825i	$-0.461846\pi$
$548$			28735.3i			2.23998i
$549$	7769.33	+	5257.22i	0.603983	+	0.408693i
$550$	5292.92			0.410347
$551$	−2741.07	−	4747.68i	−0.211930	−	0.367074i
$552$	19560.4	+	36853.5i	1.50823	+	2.84164i
$553$	−15663.5	−	5864.49i	−1.20449	−	0.450965i
$554$	−16107.6	−	9299.70i	−1.23528	−	0.713189i
$555$	2485.00	+	4681.97i	0.190059	+	0.358087i
$556$	−17536.5	+	10124.7i	−1.33762	+	0.772273i
$557$			18144.3i			1.38025i	0.723692	+	0.690123i	$0.242444\pi$
$557$			18144.3i			1.38025i	−0.723692	+	0.690123i	$0.757556\pi$
$558$	11412.7	+	23487.5i	0.865835	+	1.78191i
$559$			5167.04i			0.390952i
$560$	−21151.2	+	17419.5i	−1.59607	+	1.31448i
$561$	291.120	−	8163.44i	0.0219093	−	0.614368i
$562$	9404.27	−	16288.7i	0.705864	−	1.22259i
$563$	−2055.50	+	3560.22i	−0.153870	+	0.266511i	−0.932647	−	0.360790i	$-0.882507\pi$
$563$	−2055.50	+	3560.22i	−0.153870	+	0.266511i	0.778777	+	0.627301i	$0.215840\pi$
$564$	10758.8	−	17189.4i	0.803243	−	1.28334i
$565$	9679.93	−	5588.71i	0.720775	−	0.416140i
$566$	−19160.9			−1.42295
$567$	307.334	+	13497.8i	0.0227634	+	0.999741i
$568$	40274.0			2.97510
$569$	−16501.7	+	9527.28i	−1.21580	+	0.701941i	−0.964016	−	0.265843i	$-0.914350\pi$
$569$	−16501.7	+	9527.28i	−1.21580	+	0.701941i	−0.251781	+	0.967784i	$0.581016\pi$
$570$	−4233.20	+	6763.40i	−0.311069	+	0.496996i
$571$	4482.05	−	7763.14i	0.328491	−	0.568962i	−0.653722	−	0.756735i	$-0.726793\pi$
$571$	4482.05	−	7763.14i	0.328491	−	0.568962i	0.982213	+	0.187772i	$0.0601268\pi$
$572$	−3480.07	+	6027.66i	−0.254387	+	0.440611i
$573$	−24.2001	+	678.606i	−0.00176435	+	0.0494750i
$574$	11907.6	+	14458.5i	0.865881	+	1.05137i
$575$		−	8762.43i		−	0.635511i
$576$	17450.3	+	35913.2i	1.26232	+	2.59789i
$577$			13608.3i			0.981840i	0.871205	+	0.490920i	$0.163339\pi$
$577$			13608.3i			0.981840i	−0.871205	+	0.490920i	$0.836661\pi$
$578$	−49670.3	+	28677.2i	−3.57442	+	2.06369i
$579$	−2777.60	−	5233.24i	−0.199366	−	0.375623i
$580$	−16737.2	−	9663.21i	−1.19823	−	0.691798i
$581$	13268.3	+	4967.70i	0.947438	+	0.354725i
$582$	3703.97	+	6978.60i	0.263805	+	0.497032i
$583$	2265.22	+	3923.48i	0.160919	+	0.278720i
$584$	52470.7			3.71790
$585$	−4007.77	−	2711.91i	−0.283250	−	0.191665i
$586$			12999.1i			0.916359i
$587$	−4471.37	−	7744.64i	−0.314401	−	0.544558i	0.664909	−	0.746924i	$-0.268470\pi$
$587$	−4471.37	−	7744.64i	−0.314401	−	0.544558i	−0.979310	+	0.202366i	$0.935137\pi$
$588$	36113.6	−	10975.9i	2.53282	−	0.769791i
$589$	3699.59	−	6407.87i	0.258809	−	0.448271i
$590$	−11732.0	−	6773.45i	−0.818640	−	0.472642i
$591$	−15251.7	−	9546.00i	−1.06154	−	0.664416i
$592$	−15946.7	−	27620.5i	−1.10710	−	1.91756i
$593$	−19338.8			−1.33921			−0.669604	−	0.742719i	$-0.733536\pi$
$593$	−19338.8			−1.33921			−0.669604	+	0.742719i	$0.733536\pi$
$594$	5636.14	−	7721.39i	0.389316	−	0.533355i
$595$	−2613.37	−	15660.7i	−0.180063	−	1.07903i
$596$	−3526.88	+	2036.24i	−0.242393	+	0.139946i
$597$	11111.7	+	6954.78i	0.761760	+	0.476784i
$598$	13748.3	+	7937.61i	0.940153	+	0.542798i
$599$	7181.37	+	4146.16i	0.489854	+	0.282817i	0.724514	−	0.689260i	$-0.242064\pi$
$599$	7181.37	+	4146.16i	0.489854	+	0.282817i	−0.234660	+	0.972078i	$0.575398\pi$
$600$	1023.94	−	28712.7i	0.0696700	−	1.95365i
$601$	−16063.4	+	9274.20i	−1.09025	+	0.629455i	−0.933643	−	0.358206i	$-0.883389\pi$
$601$	−16063.4	+	9274.20i	−1.09025	+	0.629455i	−0.156606	+	0.987661i	$0.550055\pi$
$602$	−19569.5	+	3265.65i	−1.32491	+	0.221093i
$603$	9820.94	+	701.350i	0.663250	+	0.0473651i
$604$	−13042.3			−0.878618
$605$	4030.70	+	6981.38i	0.270862	+	0.469146i
$606$	−27390.1	+	14537.6i	−1.83605	+	0.974504i
$607$	4155.60	+	2399.24i	0.277876	+	0.160432i	0.632461	−	0.774592i	$-0.282045\pi$
$607$	4155.60	+	2399.24i	0.277876	+	0.160432i	−0.354586	+	0.935024i	$0.615378\pi$
$608$	12238.4	−	21197.5i	0.816336	−	1.41394i
$609$	7759.63	+	10137.6i	0.516315	+	0.674543i
$610$	−6455.12	−	11180.6i	−0.428460	−	0.742114i
$611$		−	4801.21i		−	0.317899i
$612$	−71078.4	−	5075.97i	−4.69473	−	0.335268i
$613$	−19326.3			−1.27338			−0.636690	−	0.771120i	$-0.719697\pi$
$613$	−19326.3			−1.27338			−0.636690	+	0.771120i	$0.719697\pi$
$614$	−21236.0	−	36781.9i	−1.39579	−	2.41758i
$615$	6688.33	+	238.516i	0.438536	+	0.0156388i
$616$	−15573.9	−	5830.91i	−1.01865	−	0.381387i
$617$	18359.9	+	10600.1i	1.19796	+	0.691642i	0.960100	−	0.279658i	$-0.0902211\pi$
$617$	18359.9	+	10600.1i	1.19796	+	0.691642i	0.237859	+	0.971300i	$0.423554\pi$
$618$	23225.7	−	37107.8i	1.51177	−	2.41536i
$619$	3393.65	−	1959.33i	0.220359	−	0.127224i	−0.385757	−	0.922600i	$-0.626060\pi$
$619$	3393.65	−	1959.33i	0.220359	−	0.127224i	0.606117	+	0.795376i	$0.292726\pi$
$620$		−	26084.6i		−	1.68965i
$621$	−12782.8	−	9330.64i	−0.826015	−	0.602940i
$622$		−	14768.5i		−	0.952029i
$623$	5660.04	−	4661.44i	0.363988	−	0.299770i
$624$	24680.9	+	15447.7i	1.58338	+	0.991034i
$625$	−59.3801	+	102.849i	−0.00380033	+	0.00658236i
$626$	10945.0	−	18957.2i	0.698799	−	1.21036i
$627$	−2706.96	−	96.5343i	−0.172417	−	0.00614866i
$628$	15303.7	−	8835.58i	0.972426	−	0.561430i
$629$	18480.4			1.17148
$630$	7738.06	−	16892.9i	0.489352	−	1.06830i
$631$	−5823.13			−0.367378			−0.183689	−	0.982984i	$-0.558804\pi$
$631$	−5823.13			−0.367378			−0.183689	+	0.982984i	$0.558804\pi$
$632$	55670.7	−	32141.5i	3.50390	−	2.02297i
$633$	−5034.47	−	9485.39i	−0.316117	−	0.595593i
$634$	3020.98	−	5232.50i	0.189241	−	0.327774i
$635$	−3782.94	+	6552.25i	−0.236412	+	0.409477i
$636$	34909.1	−	18528.4i	2.17647	−	1.15519i
$637$	5868.97	−	6739.07i	0.365050	−	0.419170i
$638$		−	9039.34i		−	0.560926i
$639$	−13740.2	+	6676.41i	−0.850634	+	0.413325i
$640$		−	22354.5i		−	1.38069i
$641$	18914.5	−	10920.3i	1.16549	−	0.672894i	0.212874	−	0.977080i	$-0.431718\pi$
$641$	18914.5	−	10920.3i	1.16549	−	0.672894i	0.952613	+	0.304186i	$0.0983844\pi$
$642$	20812.7	+	742.211i	1.27946	+	0.0456273i
$643$	−21222.1	−	12252.6i	−1.30158	−	0.751470i	−0.320909	−	0.947110i	$-0.603988\pi$
$643$	−21222.1	−	12252.6i	−1.30158	−	0.751470i	−0.980676	+	0.195640i	$0.937322\pi$
$644$	−15513.3	+	41434.7i	−0.949240	+	2.53533i
$645$	−3761.02	+	6009.00i	−0.229597	+	0.366828i
$646$	13909.2	+	24091.5i	0.847138	+	1.46729i
$647$	1181.15			0.0717709			0.0358855	−	0.999356i	$-0.488575\pi$
$647$	1181.15			0.0717709			0.0358855	+	0.999356i	$0.488575\pi$
$648$	−40796.2	−	32068.3i	−2.47319	−	1.94408i
$649$		−	4598.89i		−	0.278155i
$650$	−5465.96	−	9467.33i	−0.329835	−	0.571291i
$651$	−6612.94	+	15911.2i	−0.398128	+	0.957927i
$652$	−34986.9	+	60599.0i	−2.10152	+	3.63994i
$653$	−19828.3	−	11447.9i	−1.18827	−	0.686050i	−0.230360	−	0.973106i	$-0.573990\pi$
$653$	−19828.3	−	11447.9i	−1.18827	−	0.686050i	−0.957914	+	0.287056i	$0.907324\pi$
$654$	−694.669	+	19479.5i	−0.0415347	+	1.16470i
$655$	4112.60	+	7123.24i	0.245332	+	0.424928i
$656$	−40269.1			−2.39672
$657$	−17901.4	+	8698.32i	−1.06301	+	0.516520i
$658$	18184.0	−	3034.44i	1.07733	−	0.179779i
$659$	−27.2112	+	15.7104i	−0.00160849	+	0.000928663i	−0.500804	−	0.865561i	$-0.666962\pi$
$659$	−27.2112	+	15.7104i	−0.00160849	+	0.000928663i	0.499196	+	0.866489i	$0.333629\pi$
$660$	−8434.61	+	4476.76i	−0.497450	+	0.264027i
$661$	9789.93	+	5652.22i	0.576073	+	0.332596i	0.759571	−	0.650424i	$-0.225409\pi$
$661$	9789.93	+	5652.22i	0.576073	+	0.332596i	−0.183498	+	0.983020i	$0.558742\pi$
$662$	−32946.3	−	19021.6i	−1.93428	−	1.11676i
$663$	−14902.4	+	7909.62i	−0.872944	+	0.463324i
$664$	−47157.6	+	27226.5i	−2.75613	+	1.59125i
$665$	−5193.02	+	866.582i	−0.302822	+	0.0505333i
$666$	17911.9	+	12120.3i	1.04215	+	0.705184i
$667$	−14964.6			−0.868715
$668$	20255.6	+	35083.7i	1.17322	+	2.03208i
$669$	1137.89	−	31908.2i	0.0657601	−	1.84401i
$670$	−11734.9	−	6775.15i	−0.676655	−	0.390667i
$671$	2191.38	−	3795.58i	0.126076	−	0.218371i
$672$	−21875.9	+	52635.1i	−1.25578	+	3.02149i
$673$	4328.66	+	7497.46i	0.247931	+	0.429429i	0.962952	−	0.269674i	$-0.0869161\pi$
$673$	4328.66	+	7497.46i	0.247931	+	0.429429i	−0.715021	+	0.699103i	$0.753583\pi$
$674$			14003.2i			0.800271i
$675$	4410.51	+	9965.62i	0.251497	+	0.568262i
$676$	−32152.1			−1.82932
$677$	10348.5	+	17924.2i	0.587483	+	1.01755i	0.994561	+	0.104156i	$0.0332143\pi$
$677$	10348.5	+	17924.2i	0.587483	+	1.01755i	−0.407078	+	0.913393i	$0.633452\pi$
$678$	24196.0	−	38658.0i	1.37056	−	2.18975i
$679$	−1827.92	+	4882.20i	−0.103312	+	0.275938i
$680$	52847.7	+	30511.6i	2.98032	+	1.72069i
$681$	−4734.61	−	168.843i	−0.266418	−	0.00950085i
$682$	10565.7	−	6100.13i	0.593230	−	0.342502i
$683$		−	20058.0i		−	1.12372i	−0.827233	−	0.561859i	$-0.810086\pi$
$683$		−	20058.0i		−	1.12372i	0.827233	−	0.561859i	$-0.189914\pi$
$684$	−1683.17	+	23569.3i	−0.0940902	+	1.31754i
$685$			9333.94i			0.520630i
$686$	29232.7	+	17968.8i	1.62698	+	1.00008i
$687$	−12219.9	+	6485.83i	−0.678628	+	0.360189i
$688$	21327.1	−	36939.6i	1.18181	−	2.04696i
$689$	4678.56	−	8103.50i	0.258692	−	0.448068i
$690$	10210.9	+	19238.3i	0.563367	+	1.06143i
$691$	−4672.42	+	2697.62i	−0.257232	+	0.148513i	−0.623071	−	0.782165i	$-0.714115\pi$
$691$	−4672.42	+	2697.62i	−0.257232	+	0.148513i	0.365839	+	0.930678i	$0.380782\pi$
$692$	−13280.0			−0.729522
$693$	6279.94	−	592.427i	0.344235	−	0.0324739i
$694$	45073.4			2.46537
$695$	−5696.30	+	3288.76i	−0.310897	+	0.179496i
$696$	−49036.0	−	1748.70i	−2.67055	−	0.0952358i
$697$	11666.8	−	20207.5i	0.634019	−	1.09815i
$698$	31128.0	−	53915.2i	1.68798	−	2.92367i
$699$	8739.89	+	5470.28i	0.472923	+	0.296002i
$700$	23517.8	−	19368.6i	1.26984	−	1.04581i
$701$		−	18702.4i		−	1.00767i	−0.863799	−	0.503837i	$-0.831921\pi$
$701$		−	18702.4i		−	1.00767i	0.863799	−	0.503837i	$-0.168079\pi$
$702$	−19631.5	−	2107.41i	−1.05547	−	0.113304i
$703$		−	6128.01i		−	0.328766i
$704$	16155.4	−	9327.30i	0.864883	−	0.499340i
$705$	3494.74	−	5583.56i	0.186694	−	0.298282i
$706$	47788.3	+	27590.6i	2.54750	+	1.47080i
$707$	−19162.0	−	7174.33i	−1.01932	−	0.381639i
$708$	−40093.2	−	1429.78i	−2.12824	−	0.0758962i
$709$	−9346.71	−	16189.0i	−0.495096	−	0.857531i	0.504888	−	0.863185i	$-0.331534\pi$
$709$	−9346.71	−	16189.0i	−0.495096	−	0.857531i	−0.999984	+	0.00565368i	$0.998200\pi$
$710$	21023.9			1.11128
$711$	−13664.9	+	20194.5i	−0.720778	+	1.06519i
$712$			28181.9i			1.48337i
$713$	−10098.8	−	17491.6i	−0.530438	−	0.918745i
$714$	−39375.3	−	51442.0i	−2.06384	−	2.69632i
$715$	−1130.41	+	1957.94i	−0.0591260	+	0.102409i
$716$	21533.6	+	12432.4i	1.12395	+	0.648912i
$717$	8188.05	−	4345.90i	0.426483	−	0.226360i
$718$	17809.0	+	30846.0i	0.925661	+	1.60329i
$719$	−18386.7			−0.953697			−0.476848	−	0.878986i	$-0.658221\pi$
$719$	−18386.7			−0.953697			−0.476848	+	0.878986i	$0.658221\pi$
$720$	17458.4	+	35929.9i	0.903662	+	1.85976i
$721$	28491.8	−	4754.56i	1.47169	−	0.245588i
$722$	−24097.5	+	13912.7i	−1.24213	+	0.717142i
$723$	−1108.10	+	31072.8i	−0.0569996	+	1.59835i
$724$	−29804.2	−	17207.5i	−1.52992	−	0.883302i
$725$	8924.29	+	5152.44i	0.457159	+	0.263941i
$726$	27881.0	+	17450.7i	1.42529	+	0.892088i
$727$	−1268.25	+	732.227i	−0.0647000	+	0.0373546i	−0.532001	−	0.846744i	$-0.678560\pi$
$727$	−1268.25	+	732.227i	−0.0647000	+	0.0373546i	0.467301	+	0.884098i	$0.345226\pi$
$728$	5653.40	+	33878.2i	0.287814	+	1.72474i
$729$	19234.5	+	4177.74i	0.977215	+	0.212251i
$730$	27390.8			1.38874
$731$	12357.8	+	21404.3i	0.625265	+	1.08299i
$732$	−32408.6	−	20284.5i	−1.63642	−	1.02423i
$733$	5272.89	+	3044.31i	0.265701	+	0.153402i	0.626932	−	0.779074i	$-0.284310\pi$
$733$	5272.89	+	3044.31i	0.265701	+	0.153402i	−0.361231	+	0.932476i	$0.617644\pi$
$734$	−14133.5	+	24480.0i	−0.710734	+	1.23103i
$735$	11730.6	−	3565.24i	0.588693	−	0.178919i
$736$	−33407.2	−	57863.0i	−1.67311	−	2.89790i
$737$		−	4600.05i		−	0.229912i
$738$	24560.9	−	11934.2i	1.22507	−	0.595264i
$739$	239.229			0.0119082			0.00595412	−	0.999982i	$-0.498105\pi$
$739$	239.229			0.0119082			0.00595412	+	0.999982i	$0.498105\pi$
$740$	−10801.7	−	18709.0i	−0.536590	−	0.929402i
$741$	2622.80	+	4941.58i	0.130028	+	0.244984i
$742$	33647.9	+	12597.9i	1.66476	+	0.623294i
$743$	5720.45	+	3302.70i	0.282454	+	0.163075i	0.634534	−	0.772895i	$-0.281192\pi$
$743$	5720.45	+	3302.70i	0.282454	+	0.163075i	−0.352080	+	0.935970i	$0.614526\pi$
$744$	−31047.6	−	58496.4i	−1.52992	−	2.88250i
$745$	−1145.62	+	661.423i	−0.0563385	+	0.0325271i
$746$			52817.5i			2.59221i
$747$	11575.3	−	17106.4i	0.566957	−	0.837871i
$748$			33292.5i			1.62740i
$749$	8736.03	+	10607.5i	0.426178	+	0.517476i
$750$	1394.66	−	39108.3i	0.0679009	−	1.90404i
$751$	−16064.2	+	27824.1i	−0.780549	+	1.35195i	0.151073	+	0.988523i	$0.451727\pi$
$751$	−16064.2	+	27824.1i	−0.780549	+	1.35195i	−0.931622	+	0.363428i	$0.881606\pi$
$752$	−19817.1	+	34324.2i	−0.960978	+	1.66446i
$753$	−16798.2	+	26838.5i	−0.812962	+	1.29887i
$754$	−16168.5	+	9334.87i	−0.780930	+	0.450870i
$755$	−4236.48			−0.204214
$756$	−3212.37	−	54932.7i	−0.154540	−	2.64270i
$757$	37994.5			1.82422			0.912109	−	0.409948i	$-0.134453\pi$
$757$	37994.5			1.82422			0.912109	+	0.409948i	$0.134453\pi$
$758$	17016.3	−	9824.34i	0.815380	−	0.470760i
$759$	−3922.81	+	6267.49i	−0.187601	+	0.299731i
$760$	10117.5	−	17524.1i	0.482896	−	0.836401i
$761$	2352.30	−	4074.31i	0.112051	−	0.194078i	−0.804546	−	0.593890i	$-0.797591\pi$
$761$	2352.30	−	4074.31i	0.112051	−	0.194078i	0.916597	+	0.399812i	$0.130925\pi$
$762$	−1100.17	+	30850.5i	−0.0523033	+	1.46666i
$763$	−9928.03	+	8176.45i	−0.471060	+	0.387952i
$764$		−	2767.53i		−	0.131054i
$765$	−23088.1	−	1648.80i	−1.09118	−	0.0779250i
$766$		−	48563.6i		−	2.29070i
$767$	−8225.95	+	4749.25i	−0.387251	+	0.223580i
$768$	−13941.1	−	26266.2i	−0.655019	−	1.23411i
$769$	−9940.18	−	5738.97i	−0.466128	−	0.269119i	0.248490	−	0.968635i	$-0.420066\pi$
$769$	−9940.18	−	5738.97i	−0.466128	−	0.269119i	−0.714617	+	0.699516i	$0.753399\pi$
$770$	−8129.88	−	3043.86i	−0.380494	−	0.142459i
$771$	−11089.0	−	20892.7i	−0.517979	−	0.975918i
$772$	12073.5	+	20911.9i	0.562868	+	0.974916i
$773$	−22568.8			−1.05012			−0.525059	−	0.851066i	$-0.675957\pi$
$773$	−22568.8			−1.05012			−0.525059	+	0.851066i	$0.675957\pi$
$774$	−2060.34	+	28850.7i	−0.0956812	+	1.33982i
$775$			13908.4i			0.644649i
$776$	−10018.3	−	17352.1i	−0.463446	−	0.802713i
$777$	1845.77	+	14150.7i	0.0852207	+	0.653349i
$778$	15103.9	−	26160.8i	0.696018	−	1.20554i
$779$	−6700.72	−	3868.66i	−0.308188	−	0.177932i
$780$	16717.9	+	10463.7i	0.767430	+	0.480333i
$781$	3568.58	+	6180.97i	0.163501	+	0.283191i
$782$	75936.1			3.47247
$783$	17019.5	−	7532.34i	0.776790	−	0.343785i
$784$	−69773.4	+	23953.8i	−3.17845	+	1.09119i
$785$	4971.02	−	2870.02i	0.226017	−	0.130491i
$786$	28447.6	+	17805.3i	1.29096	+	0.808007i
$787$	−1440.47	−	831.659i	−0.0652445	−	0.0376689i	0.467023	−	0.884245i	$-0.345327\pi$
$787$	−1440.47	−	831.659i	−0.0652445	−	0.0376689i	−0.532267	+	0.846576i	$0.678660\pi$
$788$	63507.7	+	36666.2i	2.87103	+	1.65759i
$789$	165.350	−	4636.66i	0.00746086	−	0.209214i
$790$	29061.3	−	16778.5i	1.30880	−	0.755638i
$791$	29682.1	−	4953.19i	1.33423	−	0.222649i
$792$	−13586.6	+	20078.9i	−0.609571	+	0.900848i
$793$	−9052.11			−0.405359
$794$	−31226.2	−	54085.4i	−1.39569	−	2.41740i
$795$	11339.4	−	6018.49i	0.505869	−	0.268495i
$796$	−46268.8	−	26713.3i	−2.06025	−	1.18948i
$797$	5493.37	−	9514.80i	0.244147	−	0.422875i	−0.717744	−	0.696307i	$-0.754825\pi$
$797$	5493.37	−	9514.80i	0.244147	−	0.422875i	0.961891	+	0.273432i	$0.0881587\pi$
$798$	−17058.0	+	13056.7i	−0.756699	+	0.579200i
$799$	−11482.8	−	19888.9i	−0.508428	−	0.880622i
$800$			46009.4i			2.03335i
$801$	−4671.85	−	9614.79i	−0.206082	−	0.424122i
$802$	−22985.6			−1.01203
$803$	4649.31	+	8052.84i	0.204322	+	0.353896i
$804$	−40103.2	−	1430.14i	−1.75912	−	0.0627328i
$805$	−5039.11	+	13459.0i	−0.220628	+	0.589278i
$806$	−21822.3	−	12599.1i	−0.953672	−	0.550603i
$807$	−3196.29	+	5106.72i	−0.139423	+	0.222757i
$808$	68104.8	−	39320.3i	2.96525	−	1.71199i
$809$		−	29805.7i		−	1.29532i	−0.761930	−	0.647659i	$-0.775748\pi$
$809$		−	29805.7i		−	1.29532i	0.761930	−	0.647659i	$-0.224252\pi$
$810$	−21296.5	−	16740.3i	−0.923805	−	0.726168i
$811$			12409.9i			0.537323i	0.963235	+	0.268662i	$0.0865813\pi$
$811$			12409.9i			0.537323i	−0.963235	+	0.268662i	$0.913419\pi$
$812$	−33078.0	−	40164.1i	−1.42957	−	1.73582i
$813$	9349.58	+	5851.88i	0.403326	+	0.252441i
$814$	5052.14	−	8750.57i	0.217540	−	0.376790i
$815$	−11364.6	+	19684.1i	−0.488448	+	0.846017i
$816$	139186.	+	4963.56i	5.97117	+	0.212941i
$817$	7097.58	−	4097.79i	0.303932	−	0.175476i
$818$	30270.8			1.29388
$819$	−7544.92	−	10621.0i	−0.321906	−	0.453147i
$820$	−27276.7			−1.16164
$821$	−3158.37	+	1823.49i	−0.134261	+	0.0775154i	−0.565626	−	0.824662i	$-0.691365\pi$
$821$	−3158.37	+	1823.49i	−0.134261	+	0.0775154i	0.431365	+	0.902177i	$0.358032\pi$
$822$	17854.5	+	33639.5i	0.757600	+	1.42739i
$823$	20305.8	−	35170.6i	0.860042	−	1.48964i	−0.0118459	−	0.999930i	$-0.503771\pi$
$823$	20305.8	−	35170.6i	0.860042	−	1.48964i	0.871888	−	0.489706i	$-0.162896\pi$
$824$	−55510.5	+	96146.9i	−2.34684	+	4.06485i
$825$	4497.35	−	2387.02i	0.189791	−	0.100734i
$826$	−23186.1	−	28153.2i	−0.976693	−	1.18592i
$827$		−	15836.6i		−	0.665891i	−0.942946	−	0.332945i	$-0.891958\pi$
$827$		−	15836.6i		−	0.665891i	0.942946	−	0.332945i	$-0.108042\pi$
$828$	53420.4	+	36147.6i	2.24214	+	1.51717i
$829$		−	8427.35i		−	0.353069i	−0.984294	−	0.176534i	$-0.943511\pi$
$829$		−	8427.35i		−	0.353069i	0.984294	−	0.176534i	$-0.0564886\pi$
$830$	−24617.3	+	14212.8i	−1.02949	+	0.594377i
$831$	−17880.5	−	637.644i	−0.746410	−	0.0266181i
$832$	−33367.1	−	19264.5i	−1.39038	−	0.802735i
$833$	8194.50	−	41952.9i	0.340844	−	1.74500i
$834$	−14238.5	+	22748.9i	−0.591174	+	0.944521i
$835$	6579.52	+	11396.1i	0.272687	+	0.472308i
$836$	11039.7			0.456717
$837$	20289.7	+	14810.3i	0.837892	+	0.611610i
$838$			22035.6i			0.908363i
$839$	−1249.78	−	2164.69i	−0.0514270	−	0.0890742i	0.839166	−	0.543875i	$-0.183044\pi$
$839$	−1249.78	−	2164.69i	−0.0514270	−	0.0890742i	−0.890593	+	0.454801i	$0.849710\pi$
$840$	−18084.9	+	43513.6i	−0.742843	+	1.78734i
$841$	−3395.06	+	5880.42i	−0.139205	+	0.241110i
$842$	−76985.6	−	44447.6i	−3.15095	−	1.81920i
$843$	644.814	−	18081.5i	0.0263447	−	0.738744i
$844$	21883.5	+	37903.4i	0.892491	+	1.54584i
$845$	−10443.8			−0.425181
$846$	1914.46	−	26808.1i	0.0778021	−	1.08946i
$847$	3572.35	+	21407.4i	0.144920	+	0.868439i
$848$	−66894.8	+	38621.7i	−2.70894	+	1.56400i
$849$	−16280.8	+	8641.23i	−0.658135	+	0.349312i
$850$	−45285.2	−	26145.4i	−1.82738	−	1.05504i
$851$	−14486.6	−	8363.83i	−0.583541	−	0.336908i
$852$	54995.2	−	29189.3i	2.21139	−	1.17372i
$853$	14523.6	−	8385.18i	0.582974	−	0.336580i	−0.179340	−	0.983787i	$-0.557396\pi$
$853$	14523.6	−	8385.18i	0.582974	−	0.336580i	0.762314	+	0.647207i	$0.224063\pi$
$854$	−5721.07	−	34283.7i	−0.229240	−	1.37373i
$855$	−546.737	+	7655.91i	−0.0218690	+	0.306230i
$856$	−52815.8			−2.10889
$857$	−5953.98	−	10312.6i	−0.237321	−	0.411052i	0.722624	−	0.691242i	$-0.242936\pi$
$857$	−5953.98	−	10312.6i	−0.237321	−	0.411052i	−0.959945	+	0.280190i	$0.909603\pi$
$858$	−328.753	+	9218.71i	−0.0130809	+	0.366809i
$859$	40304.1	+	23269.6i	1.60088	+	0.924270i	0.991311	+	0.131538i	$0.0419915\pi$
$859$	40304.1	+	23269.6i	1.60088	+	0.924270i	0.609571	+	0.792732i	$0.291342\pi$
$860$	14446.1	−	25021.4i	0.572800	−	0.992118i
$861$	16638.4	+	6915.16i	0.658577	+	0.273714i
$862$	957.913	+	1659.15i	0.0378499	+	0.0655580i
$863$			33359.8i			1.31585i	0.753083	+	0.657926i	$0.228566\pi$
$863$			33359.8i			1.31585i	−0.753083	+	0.657926i	$0.771434\pi$
$864$	67119.3	+	48993.0i	2.64288	+	1.92914i
$865$	−4313.67			−0.169560
$866$	8374.93	+	14505.8i	0.328628	+	0.569200i
$867$	−29271.5	+	46767.2i	−1.14661	+	1.83195i
$868$	24623.8	−	65768.1i	0.962889	−	2.57179i
$869$	9865.71	+	5695.97i	0.385122	+	0.222350i
$870$	−25597.8	−	912.856i	−0.997527	−	0.0355733i
$871$	−8228.01	+	4750.44i	−0.320087	+	0.184802i
$872$		−	49432.7i		−	1.91973i
$873$	6294.47	+	4259.23i	0.244027	+	0.165124i
$874$		−	25180.1i		−	0.974520i
$875$	19932.1	−	16415.5i	0.770089	−	0.634223i
$876$	71650.1	−	38029.1i	2.76351	−	1.46676i
$877$	−2221.72	+	3848.13i	−0.0855441	+	0.148167i	−0.905623	−	0.424084i	$-0.860596\pi$
$877$	−2221.72	+	3848.13i	−0.0855441	+	0.148167i	0.820079	+	0.572251i	$0.193930\pi$
$878$	−41150.1	+	71274.0i	−1.58172	+	2.73961i
$879$	5862.36	+	11045.2i	0.224952	+	0.423829i
$880$	16162.9	−	9331.63i	0.619147	−	0.357465i
$881$	−31877.6			−1.21905			−0.609525	−	0.792767i	$-0.708640\pi$
$881$	−31877.6			−1.21905			−0.609525	+	0.792767i	$0.708640\pi$
$882$	35457.2	−	35288.1i	1.35364	−	1.34718i
$883$	7852.54			0.299274			0.149637	−	0.988741i	$-0.452190\pi$
$883$	7852.54			0.299274			0.149637	+	0.988741i	$0.452190\pi$
$884$	59549.7	−	34381.0i	2.26569	−	1.30810i
$885$	−13023.3	−	464.429i	−0.494658	−	0.0176402i
$886$	−28338.6	+	49083.9i	−1.07455	+	1.86118i
$887$	−6816.09	+	11805.8i	−0.258018	+	0.446900i	−0.965711	−	0.259620i	$-0.916403\pi$
$887$	−6816.09	+	11805.8i	−0.258018	+	0.446900i	0.707693	+	0.706520i	$0.249736\pi$
$888$	−46492.2	−	29099.4i	−1.75695	−	1.09967i
$889$	−15723.4	+	12949.3i	−0.593190	+	0.488535i
$890$			14711.5i			0.554081i
$891$	1306.77	−	9102.62i	0.0491340	−	0.342255i
$892$			130130.i			4.88460i
$893$	−6595.07	+	3807.66i	−0.247139	+	0.142686i
$894$	−2863.59	+	4575.17i	−0.107128	+	0.171159i
$895$	6994.64	+	4038.36i	0.261235	+	0.150824i
$896$	21102.7	−	56363.3i	0.786819	−	2.10152i
$897$	15261.6	+	544.250i	0.568082	+	0.0202586i
$898$	−36156.3	−	62624.6i	−1.34360	−	2.32718i
$899$	23752.9			0.881207
$900$	−19411.8	−	39950.0i	−0.718956	−	1.47963i
$901$		−	44758.0i		−	1.65495i
$902$	−6378.91	−	11048.6i	−0.235471	−	0.407847i
$903$	−15155.3	+	11600.3i	−0.558513	+	0.427502i
$904$	−57829.5	+	100164.i	−2.12763	+	3.68517i
$905$	−9681.16	−	5589.42i	−0.355594	−	0.205302i
$906$	−15268.2	+	8103.79i	−0.559883	+	0.297164i
$907$	12109.3	+	20974.0i	0.443312	+	0.767840i	0.997933	−	0.0642638i	$-0.0204699\pi$
$907$	12109.3	+	20974.0i	0.443312	+	0.767840i	−0.554621	+	0.832103i	$0.687137\pi$
$908$	19308.9			0.705715
$909$	−16716.9	+	24705.0i	−0.609973	+	0.901443i
$910$	2951.19	+	17685.1i	0.107507	+	0.644238i
$911$	23767.6	−	13722.2i	0.864385	−	0.499053i	−0.00109314	−	0.999999i	$-0.500348\pi$
$911$	23767.6	−	13722.2i	0.864385	−	0.499053i	0.865478	+	0.500946i	$0.167015\pi$
$912$	1645.90	−	46153.4i	0.0597600	−	1.67576i
$913$	−8357.06	−	4824.95i	−0.302933	−	0.174899i
$914$	75258.9	+	43450.7i	2.72357	+	1.57245i
$915$	−10527.1	−	6588.92i	−0.380346	−	0.238058i
$916$	48830.3	−	28192.2i	1.76135	−	1.01692i
$917$	3644.94	+	21842.4i	0.131261	+	0.786586i
$918$	−86363.1	+	38221.9i	−3.10502	+	1.37420i
$919$	34400.6			1.23479			0.617395	−	0.786653i	$-0.288188\pi$
$919$	34400.6			1.23479			0.617395	+	0.786653i	$0.288188\pi$
$920$	−27617.9	−	47835.5i	−0.989711	−	1.71423i
$921$	−34632.1	−	21676.2i	−1.23905	−	0.775521i
$922$	−87932.0	−	50767.5i	−3.14087	−	1.81338i
$923$	7370.51	−	12766.1i	0.262842	−	0.455256i
$924$	−25492.6	+	3325.17i	−0.907624	+	0.118387i
$925$	5759.47	+	9975.69i	0.204724	+	0.354593i
$926$		−	1169.41i		−	0.0415001i
$927$	2999.71	−	42004.6i	0.106282	−	1.48826i
$928$	78575.8			2.77950
$929$	9180.18	+	15900.5i	0.324211	+	0.561550i	0.981352	−	0.192217i	$-0.0615679\pi$
$929$	9180.18	+	15900.5i	0.324211	+	0.561550i	−0.657141	+	0.753767i	$0.728235\pi$
$930$	−16207.5	−	30536.4i	−0.571468	−	1.07670i
$931$	−13911.4	−	2717.26i	−0.489719	−	0.0956550i
$932$	−36392.7	−	21011.4i	−1.27906	−	0.738466i
$933$	−6660.34	−	12548.7i	−0.233708	−	0.440326i
$934$	−71836.8	+	41475.0i	−2.51667	+	1.45300i
$935$			10814.3i			0.378250i
$936$	49945.5	+	3566.79i	1.74414	+	0.124556i
$937$		−	55153.5i		−	1.92293i	−0.274924	−	0.961466i	$-0.588653\pi$
$937$		−	55153.5i		−	1.92293i	0.274924	−	0.961466i	$-0.411347\pi$
$938$	−23191.9	−	28160.2i	−0.807296	−	0.980238i
$939$	750.452	−	21043.8i	0.0260810	−	0.731351i
$940$	−13423.3	+	23249.8i	−0.465766	+	0.806730i
$941$	20322.4	−	35199.5i	0.704029	−	1.21941i	−0.263011	−	0.964793i	$-0.584716\pi$
$941$	20322.4	−	35199.5i	0.704029	−	1.21941i	0.967041	−	0.254622i	$-0.0819510\pi$
$942$	12425.6	−	19852.4i	0.429774	−	0.686652i
$943$	−18291.0	+	10560.3i	−0.631640	+	0.364677i
$944$	78410.6			2.70344
$945$	−1043.46	−	17843.5i	−0.0359192	−	0.614233i
$946$	13513.4			0.464439
$947$	−30834.2	+	17802.2i	−1.05806	+	0.610868i	−0.924894	−	0.380226i	$-0.875846\pi$
$947$	−30834.2	+	17802.2i	−1.05806	+	0.610868i	−0.133162	+	0.991094i	$0.542513\pi$
$948$	52724.7	−	84238.4i	1.80635	−	2.88601i
$949$	9602.62	−	16632.2i	0.328466	−	0.568920i
$950$	−8669.72	+	15016.4i	−0.296087	+	0.512838i
$951$	207.137	−	5808.43i	0.00706296	−	0.198056i
$952$	104444.	+	126818.i	3.55572	+	4.31744i
$953$			28893.7i			0.982118i	0.871126	+	0.491059i	$0.163390\pi$
$953$			28893.7i			0.982118i	−0.871126	+	0.491059i	$0.836610\pi$
$954$	29354.5	−	43381.2i	0.996212	−	1.47224i
$955$		−	898.962i		−	0.0304604i
$956$	−32719.2	+	18890.5i	−1.10692	+	0.639081i
$957$	−4076.59	−	7680.66i	−0.137699	−	0.259436i
$958$	81364.7	+	46975.9i	2.74402	+	1.58426i
$959$	−8811.24	+	23534.0i	−0.296694	+	0.792444i
$960$	−24781.8	−	46691.1i	−0.833156	−	1.56974i
$961$	1133.99	+	1964.13i	0.0380648	+	0.0659302i
$962$	−20869.3			−0.699431
$963$	18019.1	−	8755.53i	0.602968	−	0.292983i
$964$		−	126723.i		−	4.23388i
$965$	3921.77	+	6792.71i	0.130825	+	0.226596i
$966$	7584.29	+	58145.4i	0.252609	+	1.93664i
$967$	24894.3	−	43118.2i	0.827867	−	1.43391i	−0.0718412	−	0.997416i	$-0.522887\pi$
$967$	24894.3	−	43118.2i	0.827867	−	1.43391i	0.899708	−	0.436492i	$-0.143779\pi$
$968$	−72240.2	−	41707.9i	−2.39865	−	1.38486i
$969$	22683.4	+	14197.5i	0.752009	+	0.470681i
$970$	−5229.74	−	9058.18i	−0.173110	−	0.299836i
$971$	−23098.3			−0.763397			−0.381698	−	0.924287i	$-0.624661\pi$
$971$	−23098.3			−0.763397			−0.381698	+	0.924287i	$0.624661\pi$
$972$	−78950.4	−	14222.4i	−2.60528	−	0.469324i
$973$	−17466.9	+	2914.78i	−0.575502	+	0.0960365i
$974$	66117.4	−	38172.9i	2.17509	−	1.25579i
$975$	−8914.00	−	5579.26i	−0.292796	−	0.183261i
$976$	64714.2	+	37362.8i	2.12239	+	1.22536i
$977$	3023.09	+	1745.38i	0.0989940	+	0.0571542i	0.548680	−	0.836033i	$-0.315131\pi$
$977$	3023.09	+	1745.38i	0.0989940	+	0.0571542i	−0.449686	+	0.893187i	$0.648464\pi$
$978$	−3305.11	+	92680.2i	−0.108063	+	3.03025i
$979$	−4325.16	+	2497.13i	−0.141198	+	0.0815206i
$980$	−47261.7	+	16225.4i	−1.54053	+	0.528877i
$981$	8194.70	+	16864.9i	0.266704	+	0.548884i
$982$	49458.2			1.60720
$983$	7109.05	+	12313.2i	0.230665	+	0.399523i	0.958004	−	0.286755i	$-0.0925766\pi$
$983$	7109.05	+	12313.2i	0.230665	+	0.399523i	−0.727339	+	0.686278i	$0.759243\pi$
$984$	−61169.8	+	32466.5i	−1.98173	+	1.05182i
$985$	20628.9	+	11910.1i	0.667301	+	0.385266i
$986$	−44651.6	+	77338.9i	−1.44219	+	2.49794i
$987$	14082.3	−	10779.0i	0.454149	−	0.347619i
$988$	−11400.6	−	19746.4i	−0.367107	−	0.635848i
$989$		−	22371.5i		−	0.719285i
$990$	−7092.51	+	10481.6i	−0.227692	+	0.336492i
$991$	−263.472			−0.00844549			−0.00422274	−	0.999991i	$-0.501344\pi$
$991$	−263.472			−0.00844549			−0.00422274	+	0.999991i	$0.501344\pi$
$992$	53026.3	+	91844.2i	1.69716	+	2.93957i
$993$	−36572.7	−	1304.23i	−1.16878	−	0.0416804i
$994$	53008.3	+	19846.5i	1.69147	+	0.633293i
$995$	−15029.3	−	8677.16i	−0.478854	−	0.276467i
$996$	−44662.1	+	71356.8i	−1.42086	+	2.27011i
$997$	−41959.3	+	24225.2i	−1.33286	+	0.769528i	−0.985737	−	0.168290i	$-0.946175\pi$
$997$	−41959.3	+	24225.2i	−1.33286	+	0.769528i	−0.347125	+	0.937819i	$0.612842\pi$
$998$		−	81327.1i		−	2.57952i
$999$	20685.6	+	2220.57i	0.655120	+	0.0703262i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.o.a.41.1	yes	44
3.2	odd	2		189.4.o.a.125.21		44
7.6	odd	2	inner	63.4.o.a.41.2	yes	44
9.2	odd	6	inner	63.4.o.a.20.2	yes	44
9.4	even	3		567.4.c.c.566.31		44
9.5	odd	6		567.4.c.c.566.14		44
9.7	even	3		189.4.o.a.62.22		44
21.20	even	2		189.4.o.a.125.22		44
63.13	odd	6		567.4.c.c.566.13		44
63.20	even	6	inner	63.4.o.a.20.1	✓	44
63.34	odd	6		189.4.o.a.62.21		44
63.41	even	6		567.4.c.c.566.32		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.o.a.20.1	✓	44	63.20	even	6	inner
63.4.o.a.20.2	yes	44	9.2	odd	6	inner
63.4.o.a.41.1	yes	44	1.1	even	1	trivial
63.4.o.a.41.2	yes	44	7.6	odd	2	inner
189.4.o.a.62.21		44	63.34	odd	6
189.4.o.a.62.22		44	9.7	even	3
189.4.o.a.125.21		44	3.2	odd	2
189.4.o.a.125.22		44	21.20	even	2
567.4.c.c.566.13		44	63.13	odd	6
567.4.c.c.566.14		44	9.5	odd	6
567.4.c.c.566.31		44	9.4	even	3
567.4.c.c.566.32		44	63.41	even	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.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.67796 + 2.70082i) q^{2} +(-2.75680 + 4.40455i) q^{3} +(10.5889 - 18.3405i) q^{4} +(3.43953 - 5.95744i) q^{5} +(1.00030 - 28.0499i) q^{6} +(14.2961 - 11.7738i) q^{7} +71.1815i q^{8} +(-11.8001 - 24.2849i) q^{9} +O(q^{10})\)	\(q+(-4.67796 + 2.70082i) q^{2} +(-2.75680 + 4.40455i) q^{3} +(10.5889 - 18.3405i) q^{4} +(3.43953 - 5.95744i) q^{5} +(1.00030 - 28.0499i) q^{6} +(14.2961 - 11.7738i) q^{7} +71.1815i q^{8} +(-11.8001 - 24.2849i) q^{9} +37.1582i q^{10} +(-10.9244 + 6.30723i) q^{11} +(51.5901 + 97.2002i) q^{12} +(22.5632 + 13.0269i) q^{13} +(-35.0774 + 93.6886i) q^{14} +(16.7577 + 31.5731i) q^{15} +(-107.537 - 186.260i) q^{16} +124.623 q^{17} +(120.790 + 81.7339i) q^{18} -41.3246i q^{19} +(-72.8415 - 126.165i) q^{20} +(12.4470 + 95.4257i) q^{21} +(34.0694 - 59.0099i) q^{22} +(-97.6910 - 56.4019i) q^{23} +(-313.522 - 196.233i) q^{24} +(38.8392 + 67.2715i) q^{25} -140.733 q^{26} +(139.495 + 14.9746i) q^{27} +(-64.5583 - 386.868i) q^{28} +(114.888 - 66.3304i) q^{29} +(-163.665 - 102.438i) q^{30} +(155.062 + 89.5251i) q^{31} +(512.952 + 296.153i) q^{32} +(2.33600 - 65.5050i) q^{33} +(-582.982 + 336.585i) q^{34} +(-20.9702 - 125.664i) q^{35} +(-570.347 - 40.7306i) q^{36} +148.290 q^{37} +(111.610 + 193.315i) q^{38} +(-119.580 + 63.4683i) q^{39} +(424.060 + 244.831i) q^{40} +(93.6165 - 162.149i) q^{41} +(-315.955 - 412.781i) q^{42} +(99.1611 + 171.752i) q^{43} +267.146i q^{44} +(-185.263 - 13.2303i) q^{45} +609.326 q^{46} +(-92.1405 - 159.592i) q^{47} +(1116.85 + 39.8286i) q^{48} +(65.7542 - 336.638i) q^{49} +(-363.377 - 209.796i) q^{50} +(-343.561 + 548.909i) q^{51} +(477.838 - 275.880i) q^{52} -359.147i q^{53} +(-692.994 + 306.700i) q^{54} +86.7756i q^{55} +(838.078 + 1017.61i) q^{56} +(182.016 + 113.924i) q^{57} +(-358.293 + 620.582i) q^{58} +(-182.287 + 315.730i) q^{59} +(756.510 + 26.9783i) q^{60} +(-300.892 + 173.720i) q^{61} -967.165 q^{62} +(-454.621 - 208.246i) q^{63} -1478.83 q^{64} +(155.214 - 89.6127i) q^{65} +(165.990 + 312.739i) q^{66} +(-182.332 + 315.809i) q^{67} +(1319.62 - 2285.65i) q^{68} +(517.739 - 274.796i) q^{69} +(437.494 + 531.216i) q^{70} -565.793i q^{71} +(1728.64 - 839.949i) q^{72} -737.140i q^{73} +(-693.694 + 400.504i) q^{74} +(-403.373 - 14.3849i) q^{75} +(-757.912 - 437.580i) q^{76} +(-81.9162 + 218.791i) q^{77} +(387.973 - 619.865i) q^{78} +(-451.543 - 782.096i) q^{79} -1479.51 q^{80} +(-450.515 + 573.129i) q^{81} +1011.37i q^{82} +(382.494 + 662.499i) q^{83} +(1881.95 + 782.167i) q^{84} +(428.645 - 742.436i) q^{85} +(-927.743 - 535.633i) q^{86} +(-24.5667 + 688.887i) q^{87} +(-448.958 - 777.618i) q^{88} +395.916 q^{89} +(902.385 - 438.471i) q^{90} +(475.941 - 79.4223i) q^{91} +(-2068.87 + 1194.47i) q^{92} +(-821.793 + 436.175i) q^{93} +(862.059 + 497.710i) q^{94} +(-246.189 - 142.137i) q^{95} +(-2718.53 + 1442.89i) q^{96} +(-243.773 + 140.742i) q^{97} +(601.604 + 1752.37i) q^{98} +(282.080 + 190.873i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7	\( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7} - 18 q^{11} + 204 q^{14} + 66 q^{15} - 242 q^{16} - 210 q^{18} - 57 q^{21} - 34 q^{22} - 102 q^{23} - 352 q^{25} + 300 q^{28} + 246 q^{29} - 144 q^{30} + 1068 q^{32} - 1818 q^{36} + 328 q^{37} - 798 q^{39} - 1158 q^{42} - 170 q^{43} + 968 q^{46} - 79 q^{49} + 288 q^{50} - 204 q^{51} + 1212 q^{56} + 324 q^{57} - 538 q^{58} + 5316 q^{60} + 783 q^{63} - 808 q^{64} + 4350 q^{65} - 590 q^{67} + 384 q^{70} + 4284 q^{72} - 5304 q^{74} - 2787 q^{77} + 612 q^{78} - 302 q^{79} - 3720 q^{81} + 7050 q^{84} - 612 q^{85} - 13692 q^{86} + 1294 q^{88} + 210 q^{91} - 10194 q^{92} - 4266 q^{93} + 6336 q^{95} + 1014 q^{99}+O(q^{100}) \) 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7 - 18 * q^11 + 204 * q^14 + 66 * q^15 - 242 * q^16 - 210 * q^18 - 57 * q^21 - 34 * q^22 - 102 * q^23 - 352 * q^25 + 300 * q^28 + 246 * q^29 - 144 * q^30 + 1068 * q^32 - 1818 * q^36 + 328 * q^37 - 798 * q^39 - 1158 * q^42 - 170 * q^43 + 968 * q^46 - 79 * q^49 + 288 * q^50 - 204 * q^51 + 1212 * q^56 + 324 * q^57 - 538 * q^58 + 5316 * q^60 + 783 * q^63 - 808 * q^64 + 4350 * q^65 - 590 * q^67 + 384 * q^70 + 4284 * q^72 - 5304 * q^74 - 2787 * q^77 + 612 * q^78 - 302 * q^79 - 3720 * q^81 + 7050 * q^84 - 612 * q^85 - 13692 * q^86 + 1294 * q^88 + 210 * q^91 - 10194 * q^92 - 4266 * q^93 + 6336 * q^95 + 1014 * q^99

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