LMFDB - Embedded newform 210.3.q.a.149.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(149,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("210.149");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.q (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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.8
Character	$\chi$	$=$	210.149
Dual form			210.3.q.a.179.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(-0.355071 + 2.97891i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.67341 + 4.71166i) q^{5} +(-3.39734 - 2.54128i) q^{6} +(-7.00000 + 0.00780758i) q^{7} +2.82843 q^{8} +(-8.74785 - 2.11545i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(-0.355071 + 2.97891i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.67341 + 4.71166i) q^{5} +(-3.39734 - 2.54128i) q^{6} +(-7.00000 + 0.00780758i) q^{7} +2.82843 q^{8} +(-8.74785 - 2.11545i) q^{9} +(-4.58730 - 5.38114i) q^{10} +(6.20051 - 3.57986i) q^{11} +(5.51470 - 2.36391i) q^{12} -7.04213i q^{13} +(4.94018 - 8.57873i) q^{14} +(-13.4414 - 6.65792i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(1.21404 + 2.10278i) q^{17} +(8.77655 - 9.21803i) q^{18} +(-12.0616 + 20.8913i) q^{19} +(9.83424 - 1.81323i) q^{20} +(2.46224 - 20.8552i) q^{21} +10.1254i q^{22} +(5.88121 - 10.1866i) q^{23} +(-1.00429 + 8.42564i) q^{24} +(-19.3994 - 15.7691i) q^{25} +(8.62482 + 4.97954i) q^{26} +(9.40786 - 25.3079i) q^{27} +(7.01352 + 12.1165i) q^{28} -8.77636i q^{29} +(17.6588 - 11.7545i) q^{30} +(-10.1062 - 17.5045i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(8.46248 + 19.7419i) q^{33} -3.43383 q^{34} +(11.6771 - 32.9946i) q^{35} +(5.08378 + 17.2672i) q^{36} +(-48.2707 - 27.8691i) q^{37} +(-17.0577 - 29.5448i) q^{38} +(20.9779 + 2.50046i) q^{39} +(-4.73312 + 13.3266i) q^{40} +52.4264i q^{41} +(23.8012 + 17.7624i) q^{42} +8.62872i q^{43} +(-12.4010 - 7.15973i) q^{44} +(24.6060 - 37.6768i) q^{45} +(8.31729 + 14.4060i) q^{46} +(-44.3039 + 76.7366i) q^{47} +(-9.60912 - 7.18783i) q^{48} +(48.9999 - 0.109306i) q^{49} +(33.0305 - 12.6089i) q^{50} +(-6.69507 + 2.86989i) q^{51} +(-12.1973 + 7.04213i) q^{52} +(-9.78573 - 16.9494i) q^{53} +(24.3434 + 29.4177i) q^{54} +(6.49110 + 35.2052i) q^{55} +(-19.7990 + 0.0220832i) q^{56} +(-57.9507 - 43.3484i) q^{57} +(10.7488 + 6.20583i) q^{58} +(-72.4908 + 41.8526i) q^{59} +(1.90959 + 29.9392i) q^{60} +(23.9426 - 41.4698i) q^{61} +28.5847 q^{62} +(61.2514 + 14.7399i) q^{63} +8.00000 q^{64} +(33.1801 + 11.7844i) q^{65} +(-30.1626 - 3.59523i) q^{66} +(-109.484 + 63.2103i) q^{67} +(2.42808 - 4.20556i) q^{68} +(28.2566 + 21.1366i) q^{69} +(32.1531 + 37.6322i) q^{70} +125.735i q^{71} +(-24.7427 - 5.98340i) q^{72} +(-65.0363 + 37.5487i) q^{73} +(68.2651 - 39.4129i) q^{74} +(53.8628 - 52.1900i) q^{75} +48.2465 q^{76} +(-43.3756 + 25.1074i) q^{77} +(-17.8960 + 23.9245i) q^{78} +(-4.09666 + 7.09562i) q^{79} +(-12.9748 - 15.2202i) q^{80} +(72.0497 + 37.0113i) q^{81} +(-64.2090 - 37.0711i) q^{82} +135.272 q^{83} +(-38.5844 + 16.5904i) q^{84} +(-11.9392 + 2.20133i) q^{85} +(-10.5680 - 6.10143i) q^{86} +(26.1440 + 3.11623i) q^{87} +(17.5377 - 10.1254i) q^{88} +(-13.4925 - 7.78991i) q^{89} +(28.7454 + 56.7776i) q^{90} +(0.0549820 + 49.2949i) q^{91} -23.5248 q^{92} +(55.7328 - 23.8902i) q^{93} +(-62.6552 - 108.522i) q^{94} +(-78.2487 - 91.7899i) q^{95} +(15.5979 - 6.68615i) q^{96} -122.825i q^{97} +(-34.5143 + 60.0896i) q^{98} +(-61.8141 + 18.1992i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 64 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) $ 64 * q - 64 * q^4 + 8 * q^6 - 4 * q^9	$ 64 q - 64 q^{4} + 8 q^{6} - 4 q^{9} - 8 q^{10} + 4 q^{15} - 128 q^{16} + 8 q^{19} - 88 q^{21} - 8 q^{24} + 12 q^{25} - 8 q^{30} + 152 q^{31} + 16 q^{36} - 208 q^{39} - 16 q^{40} + 106 q^{45} - 56 q^{46} - 64 q^{49} - 140 q^{51} - 56 q^{54} + 616 q^{55} - 4 q^{60} + 104 q^{61} + 512 q^{64} - 160 q^{66} + 456 q^{69} - 144 q^{70} + 298 q^{75} - 32 q^{76} - 360 q^{79} + 304 q^{81} - 80 q^{84} - 408 q^{85} - 688 q^{90} - 288 q^{91} + 240 q^{94} - 16 q^{96} - 568 q^{99}+O(q^{100}) $ 64 * q - 64 * q^4 + 8 * q^6 - 4 * q^9 - 8 * q^10 + 4 * q^15 - 128 * q^16 + 8 * q^19 - 88 * q^21 - 8 * q^24 + 12 * q^25 - 8 * q^30 + 152 * q^31 + 16 * q^36 - 208 * q^39 - 16 * q^40 + 106 * q^45 - 56 * q^46 - 64 * q^49 - 140 * q^51 - 56 * q^54 + 616 * q^55 - 4 * q^60 + 104 * q^61 + 512 * q^64 - 160 * q^66 + 456 * q^69 - 144 * q^70 + 298 * q^75 - 32 * q^76 - 360 * q^79 + 304 * q^81 - 80 * q^84 - 408 * q^85 - 688 * q^90 - 288 * q^91 + 240 * q^94 - 16 * q^96 - 568 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

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 $

$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$3$	−0.355071	+	2.97891i	−0.118357	+	0.992971i
$3$	−0.355071	+	2.97891i	−0.118357	+	0.992971i
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	−1.67341	+	4.71166i	−0.334682	+	0.942331i
$5$	−1.67341	+	4.71166i	−0.334682	+	0.942331i
$6$	−3.39734	−	2.54128i	−0.566223	−	0.423547i
$7$	−7.00000	+	0.00780758i	−0.999999	+	0.00111537i
$7$	−7.00000	+	0.00780758i	−0.999999	+	0.00111537i
$8$	2.82843			0.353553
$9$	−8.74785	−	2.11545i	−0.971983	−	0.235050i
$10$	−4.58730	−	5.38114i	−0.458730	−	0.538114i
$11$	6.20051	−	3.57986i	0.563682	−	0.325442i	−0.190940	−	0.981602i	$-0.561153\pi$
$11$	6.20051	−	3.57986i	0.563682	−	0.325442i	0.754622	+	0.656160i	$0.227820\pi$
$12$	5.51470	−	2.36391i	0.459558	−	0.196993i
$13$		−	7.04213i		−	0.541703i	−0.962621	−	0.270851i	$-0.912695\pi$
$13$		−	7.04213i		−	0.541703i	0.962621	−	0.270851i	$-0.0873052\pi$
$14$	4.94018	−	8.57873i	0.352870	−	0.612766i
$15$	−13.4414	−	6.65792i	−0.896096	−	0.443861i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	1.21404	+	2.10278i	0.0714142	+	0.123693i	0.899521	−	0.436877i	$-0.143915\pi$
$17$	1.21404	+	2.10278i	0.0714142	+	0.123693i	−0.828107	+	0.560570i	$0.810582\pi$
$18$	8.77655	−	9.21803i	0.487586	−	0.512113i
$19$	−12.0616	+	20.8913i	−0.634822	+	1.09954i	0.351731	+	0.936101i	$0.385593\pi$
$19$	−12.0616	+	20.8913i	−0.634822	+	1.09954i	−0.986553	+	0.163443i	$0.947740\pi$
$20$	9.83424	−	1.81323i	0.491712	−	0.0906613i
$21$	2.46224	−	20.8552i	0.117249	−	0.993102i
$22$			10.1254i			0.460245i
$23$	5.88121	−	10.1866i	0.255705	−	0.442894i	−0.709382	−	0.704824i	$-0.751026\pi$
$23$	5.88121	−	10.1866i	0.255705	−	0.442894i	0.965087	+	0.261931i	$0.0843591\pi$
$24$	−1.00429	+	8.42564i	−0.0418456	+	0.351068i
$25$	−19.3994	−	15.7691i	−0.775976	−	0.630762i
$26$	8.62482	+	4.97954i	0.331724	+	0.191521i
$27$	9.40786	−	25.3079i	0.348439	−	0.937331i
$28$	7.01352	+	12.1165i	0.250483	+	0.432734i
$29$		−	8.77636i		−	0.302633i	−0.988485	−	0.151317i	$-0.951649\pi$
$29$		−	8.77636i		−	0.302633i	0.988485	−	0.151317i	$-0.0483513\pi$
$30$	17.6588	−	11.7545i	0.588626	−	0.391816i
$31$	−10.1062	−	17.5045i	−0.326007	−	0.564661i	0.655709	−	0.755014i	$-0.272370\pi$
$31$	−10.1062	−	17.5045i	−0.326007	−	0.564661i	−0.981716	+	0.190353i	$0.939037\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$	8.46248	+	19.7419i	0.256439	+	0.598239i
$34$	−3.43383			−0.100995
$35$	11.6771	−	32.9946i	0.333631	−	0.942704i
$36$	5.08378	+	17.2672i	0.141216	+	0.479644i
$37$	−48.2707	−	27.8691i	−1.30461	−	0.753219i	−0.323422	−	0.946255i	$-0.604833\pi$
$37$	−48.2707	−	27.8691i	−1.30461	−	0.753219i	−0.981192	+	0.193036i	$0.938167\pi$
$38$	−17.0577	−	29.5448i	−0.448887	−	0.777495i
$39$	20.9779	+	2.50046i	0.537895	+	0.0641143i
$40$	−4.73312	+	13.3266i	−0.118328	+	0.333164i
$41$			52.4264i			1.27869i	0.768919	+	0.639347i	$0.220795\pi$
$41$			52.4264i			1.27869i	−0.768919	+	0.639347i	$0.779205\pi$
$42$	23.8012	+	17.7624i	0.566695	+	0.422915i
$43$			8.62872i			0.200668i	0.994954	+	0.100334i	$0.0319911\pi$
$43$			8.62872i			0.200668i	−0.994954	+	0.100334i	$0.968009\pi$
$44$	−12.4010	−	7.15973i	−0.281841	−	0.162721i
$45$	24.6060	−	37.6768i	0.546800	−	0.837263i
$46$	8.31729	+	14.4060i	0.180811	+	0.313173i
$47$	−44.3039	+	76.7366i	−0.942636	+	1.63269i	−0.182220	+	0.983258i	$0.558328\pi$
$47$	−44.3039	+	76.7366i	−0.942636	+	1.63269i	−0.760416	+	0.649436i	$0.775005\pi$
$48$	−9.60912	−	7.18783i	−0.200190	−	0.149746i
$49$	48.9999	−	0.109306i	0.999998	−	0.00223074i
$50$	33.0305	−	12.6089i	0.660610	−	0.252178i
$51$	−6.69507	+	2.86989i	−0.131276	+	0.0562723i
$52$	−12.1973	+	7.04213i	−0.234564	+	0.135426i
$53$	−9.78573	−	16.9494i	−0.184636	−	0.319800i	0.758818	−	0.651303i	$-0.225777\pi$
$53$	−9.78573	−	16.9494i	−0.184636	−	0.319800i	−0.943454	+	0.331504i	$0.892444\pi$
$54$	24.3434	+	29.4177i	0.450804	+	0.544771i
$55$	6.49110	+	35.2052i	0.118020	+	0.640095i
$56$	−19.7990	+	0.0220832i	−0.353553	+	0.000394343i
$57$	−57.9507	−	43.3484i	−1.01668	−	0.760499i
$58$	10.7488	+	6.20583i	0.185324	+	0.106997i
$59$	−72.4908	+	41.8526i	−1.22866	+	0.709366i	−0.966749	−	0.255727i	$-0.917685\pi$
$59$	−72.4908	+	41.8526i	−1.22866	+	0.709366i	−0.261908	+	0.965093i	$0.584352\pi$
$60$	1.90959	+	29.9392i	0.0318264	+	0.498986i
$61$	23.9426	−	41.4698i	0.392502	−	0.679833i	−0.600277	−	0.799792i	$-0.704943\pi$
$61$	23.9426	−	41.4698i	0.392502	−	0.679833i	0.992779	+	0.119959i	$0.0382763\pi$
$62$	28.5847			0.461044
$63$	61.2514	+	14.7399i	0.972245	+	0.233966i
$64$	8.00000			0.125000
$65$	33.1801	+	11.7844i	0.510463	+	0.181298i
$66$	−30.1626	−	3.59523i	−0.457010	−	0.0544732i
$67$	−109.484	+	63.2103i	−1.63408	+	0.943438i	−0.651267	+	0.758849i	$0.725762\pi$
$67$	−109.484	+	63.2103i	−1.63408	+	0.943438i	−0.982816	+	0.184589i	$0.940905\pi$
$68$	2.42808	−	4.20556i	0.0357071	−	0.0618465i
$69$	28.2566	+	21.1366i	0.409516	+	0.306327i
$70$	32.1531	+	37.6322i	0.459330	+	0.537602i
$71$			125.735i			1.77091i	0.464723	+	0.885456i	$0.346154\pi$
$71$			125.735i			1.77091i	−0.464723	+	0.885456i	$0.653846\pi$
$72$	−24.7427	−	5.98340i	−0.343648	−	0.0831028i
$73$	−65.0363	+	37.5487i	−0.890908	+	0.514366i	−0.874239	−	0.485495i	$-0.838639\pi$
$73$	−65.0363	+	37.5487i	−0.890908	+	0.514366i	−0.0166684	+	0.999861i	$0.505306\pi$
$74$	68.2651	−	39.4129i	0.922501	−	0.532606i
$75$	53.8628	−	52.1900i	0.718171	−	0.695867i
$76$	48.2465			0.634822
$77$	−43.3756	+	25.1074i	−0.563319	+	0.326071i
$78$	−17.8960	+	23.9245i	−0.229436	+	0.306724i
$79$	−4.09666	+	7.09562i	−0.0518565	+	0.0898180i	−0.890788	−	0.454418i	$-0.849847\pi$
$79$	−4.09666	+	7.09562i	−0.0518565	+	0.0898180i	0.838932	+	0.544236i	$0.183180\pi$
$80$	−12.9748	−	15.2202i	−0.162185	−	0.190252i
$81$	72.0497	+	37.0113i	0.889503	+	0.456930i
$82$	−64.2090	−	37.0711i	−0.783037	−	0.452086i
$83$	135.272			1.62978			0.814892	−	0.579613i	$-0.196796\pi$
$83$	135.272			1.62978			0.814892	+	0.579613i	$0.196796\pi$
$84$	−38.5844	+	16.5904i	−0.459338	+	0.197505i
$85$	−11.9392	+	2.20133i	−0.140461	+	0.0258980i
$86$	−10.5680	−	6.10143i	−0.122883	−	0.0709468i
$87$	26.1440	+	3.11623i	0.300506	+	0.0358188i
$88$	17.5377	−	10.1254i	0.199292	−	0.115061i
$89$	−13.4925	−	7.78991i	−0.151601	−	0.0875270i	0.422280	−	0.906465i	$-0.361230\pi$
$89$	−13.4925	−	7.78991i	−0.151601	−	0.0875270i	−0.573882	+	0.818938i	$0.694563\pi$
$90$	28.7454	+	56.7776i	0.319394	+	0.630863i
$91$	0.0549820	+	49.2949i	0.000604198	+	0.541702i
$92$	−23.5248			−0.255705
$93$	55.7328	−	23.8902i	0.599277	−	0.256884i
$94$	−62.6552	−	108.522i	−0.666545	−	1.15449i
$95$	−78.2487	−	91.7899i	−0.823671	−	0.966210i
$96$	15.5979	−	6.68615i	0.162478	−	0.0696474i
$97$		−	122.825i		−	1.26624i	−0.774055	−	0.633119i	$-0.781774\pi$
$97$		−	122.825i		−	1.26624i	0.774055	−	0.633119i	$-0.218226\pi$
$98$	−34.5143	+	60.0896i	−0.352186	+	0.613160i
$99$	−61.8141	+	18.1992i	−0.624385	+	0.183831i
$100$	−7.91341	+	49.3698i	−0.0791341	+	0.493698i
$101$	48.7132	−	28.1246i	0.482309	−	0.278461i	−0.239069	−	0.971003i	$-0.576842\pi$
$101$	48.7132	−	28.1246i	0.482309	−	0.278461i	0.721378	+	0.692541i	$0.243509\pi$
$102$	1.21925	−	10.2291i	0.0119535	−	0.100285i
$103$	130.134	+	75.1327i	1.26343	+	0.729443i	0.973737	−	0.227676i	$-0.0731126\pi$
$103$	130.134	+	75.1327i	1.26343	+	0.729443i	0.289696	+	0.957119i	$0.406446\pi$
$104$		−	19.9182i		−	0.191521i
$105$	94.1420	+	46.5004i	0.896590	+	0.442861i
$106$	27.6782			0.261115
$107$	2.52865	−	4.37975i	0.0236322	−	0.0409322i	−0.853967	−	0.520326i	$-0.825810\pi$
$107$	2.52865	−	4.37975i	0.0236322	−	0.0409322i	0.877600	+	0.479394i	$0.159144\pi$
$108$	−53.2425	+	9.01305i	−0.492986	+	0.0834542i
$109$	−10.1409	−	17.5645i	−0.0930357	−	0.161143i	0.815751	−	0.578403i	$-0.196324\pi$
$109$	−10.1409	−	17.5645i	−0.0930357	−	0.161143i	−0.908787	+	0.417260i	$0.862990\pi$
$110$	−47.7073	−	16.9439i	−0.433703	−	0.154036i
$111$	100.159	−	133.899i	0.902335	−	1.20629i
$112$	13.9729	−	24.2643i	0.124758	−	0.216646i
$113$	−70.8350			−0.626858			−0.313429	−	0.949612i	$-0.601478\pi$
$113$	−70.8350			−0.626858			−0.313429	+	0.949612i	$0.601478\pi$
$114$	94.0681	−	40.3229i	0.825159	−	0.353710i
$115$	38.1539	+	44.7565i	0.331773	+	0.389187i
$116$	−15.2011	+	8.77636i	−0.131044	+	0.0756583i
$117$	−14.8973	+	61.6035i	−0.127327	+	0.526526i
$118$		−	118.377i		−	1.00319i
$119$	−8.51470	−	14.7100i	−0.0715521	−	0.123613i
$120$	−38.0181	−	18.8314i	−0.316818	−	0.156929i
$121$	−34.8691	+	60.3951i	−0.288175	+	0.499133i
$122$	33.8600	+	58.6472i	0.277541	+	0.480715i
$123$	−156.174	−	18.6151i	−1.26971	−	0.151342i
$124$	−20.2124	+	35.0090i	−0.163004	+	0.282330i
$125$	106.762	−	65.0152i	0.854092	−	0.520122i
$126$	−61.3639	+	64.5947i	−0.487015	+	0.512656i
$127$			60.6241i			0.477355i	0.971099	+	0.238678i	$0.0767140\pi$
$127$			60.6241i			0.477355i	−0.971099	+	0.238678i	$0.923286\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$	−25.7042	−	3.06381i	−0.199257	−	0.0237505i
$130$	−37.8947	+	32.3044i	−0.291498	+	0.248495i
$131$	−82.7314	−	47.7650i	−0.631537	−	0.364618i	0.149810	−	0.988715i	$-0.452134\pi$
$131$	−82.7314	−	47.7650i	−0.631537	−	0.364618i	−0.781347	+	0.624097i	$0.785467\pi$
$132$	25.7315	−	34.3993i	0.194935	−	0.260601i
$133$	84.2681	−	146.333i	0.633595	−	1.10025i
$134$		−	178.786i		−	1.33422i
$135$	103.499	+	86.6772i	0.766660	+	0.642053i
$136$	3.43383	+	5.94756i	0.0252487	+	0.0437321i
$137$	−54.1084	−	93.7185i	−0.394952	−	0.684077i	0.598143	−	0.801389i	$-0.295905\pi$
$137$	−54.1084	−	93.7185i	−0.394952	−	0.684077i	−0.993095	+	0.117313i	$0.962572\pi$
$138$	−45.8674	+	19.6613i	−0.332372	+	0.142473i
$139$	−113.900			−0.819424			−0.409712	−	0.912215i	$-0.634371\pi$
$139$	−113.900			−0.819424			−0.409712	+	0.912215i	$0.634371\pi$
$140$	−68.8255	+	12.7694i	−0.491610	+	0.0912097i
$141$	−212.861	−	159.224i	−1.50965	−	1.12925i
$142$	−153.993	−	88.9079i	−1.08446	−	0.626112i
$143$	−25.2099	−	43.6648i	−0.176293	−	0.305348i
$144$	24.8238	−	26.0725i	0.172388	−	0.181059i
$145$	41.3512	+	14.6864i	0.285181	+	0.101286i
$146$		−	106.204i		−	0.727423i
$147$	−17.0728	+	146.005i	−0.116142	+	0.993233i
$148$			111.476i			0.753219i
$149$	−28.0173	−	16.1758i	−0.188036	−	0.108562i	0.403027	−	0.915188i	$-0.367958\pi$
$149$	−28.0173	−	16.1758i	−0.188036	−	0.108562i	−0.591063	+	0.806626i	$0.701291\pi$
$150$	25.8327	+	102.872i	0.172218	+	0.685814i
$151$	−107.224	−	185.718i	−0.710093	−	1.22992i	−0.964822	−	0.262905i	$-0.915319\pi$
$151$	−107.224	−	185.718i	−0.710093	−	1.22992i	0.254728	−	0.967013i	$-0.418014\pi$
$152$	−34.1154	+	59.0896i	−0.224443	+	0.388747i
$153$	−6.17191	−	20.9631i	−0.0403393	−	0.137013i
$154$	−0.0790548	−	70.8777i	−0.000513343	−	0.460245i
$155$	99.3869	−	18.3249i	0.641206	−	0.118225i
$156$	−16.6470	−	38.8353i	−0.106711	−	0.248944i
$157$	107.192	−	61.8875i	0.682753	−	0.394188i	−0.118138	−	0.992997i	$-0.537693\pi$
$157$	107.192	−	61.8875i	0.682753	−	0.394188i	0.800892	+	0.598809i	$0.204359\pi$
$158$	−5.79355	−	10.0347i	−0.0366681	−	0.0635109i
$159$	53.9654	−	23.1326i	0.339405	−	0.145488i
$160$	27.8154	−	5.12858i	0.173846	−	0.0320536i
$161$	−41.0889	+	71.3518i	−0.255211	+	0.443179i
$162$	−96.2763	+	62.0716i	−0.594298	+	0.383158i
$163$	153.419	+	88.5762i	0.941218	+	0.543412i	0.890342	−	0.455293i	$-0.150465\pi$
$163$	153.419	+	88.5762i	0.941218	+	0.543412i	0.0508759	+	0.998705i	$0.483799\pi$
$164$	90.8053	−	52.4264i	0.553691	−	0.319673i
$165$	−107.178	+	6.83606i	−0.649565	+	0.0414307i
$166$	−95.6518	+	165.674i	−0.576216	+	0.998035i
$167$	173.505			1.03895			0.519475	−	0.854486i	$-0.326128\pi$
$167$	173.505			1.03895			0.519475	+	0.854486i	$0.326128\pi$
$168$	6.96426	−	58.9873i	0.0414540	−	0.351115i
$169$	119.408			0.706558
$170$	5.74620	−	16.1790i	0.0338012	−	0.0951706i
$171$	149.708	−	157.238i	0.875484	−	0.919523i
$172$	14.9454	−	8.62872i	0.0868917	−	0.0501670i
$173$	−9.49855	+	16.4520i	−0.0549049	+	0.0950981i	−0.892172	−	0.451697i	$-0.850819\pi$
$173$	−9.49855	+	16.4520i	−0.0549049	+	0.0950981i	0.837267	+	0.546795i	$0.184152\pi$
$174$	−22.3032	+	29.8162i	−0.128179	+	0.171358i
$175$	135.919	+	110.232i	0.776679	+	0.629896i
$176$			28.6389i			0.162721i
$177$	−98.9358	−	230.804i	−0.558959	−	1.30398i
$178$	19.0813	−	11.0166i	0.107198	−	0.0618910i
$179$	−109.039	+	62.9536i	−0.609155	+	0.351696i	−0.772635	−	0.634851i	$-0.781062\pi$
$179$	−109.039	+	62.9536i	−0.609155	+	0.351696i	0.163480	+	0.986547i	$0.447728\pi$
$180$	−89.8642	−	4.94204i	−0.499246	−	0.0274558i
$181$	−138.785			−0.766771			−0.383385	−	0.923588i	$-0.625242\pi$
$181$	−138.785			−0.766771			−0.383385	+	0.923588i	$0.625242\pi$
$182$	−60.4126	−	34.7894i	−0.331937	−	0.191151i
$183$	115.034	+	86.0477i	0.628599	+	0.470206i
$184$	16.6346	−	28.8119i	0.0904053	−	0.156587i
$185$	212.086	−	180.799i	1.14641	−	0.977289i
$186$	−10.1496	+	85.1513i	−0.0545678	+	0.457803i
$187$	15.0553	+	8.69220i	0.0805098	+	0.0464824i
$188$	177.216			0.942636
$189$	−65.6574	+	177.229i	−0.347394	+	0.937719i
$190$	167.749	−	30.9295i	0.882892	−	0.162787i
$191$	224.530	+	129.633i	1.17555	+	0.678704i	0.954981	−	0.296667i	$-0.0958752\pi$
$191$	224.530	+	129.633i	1.17555	+	0.678704i	0.220569	+	0.975371i	$0.429208\pi$
$192$	−2.84057	+	23.8313i	−0.0147946	+	0.124121i
$193$	140.975	−	81.3921i	0.730442	−	0.421721i	−0.0881421	−	0.996108i	$-0.528093\pi$
$193$	140.975	−	81.3921i	0.730442	−	0.421721i	0.818584	+	0.574387i	$0.194760\pi$
$194$	150.429	+	86.8504i	0.775409	+	0.447683i
$195$	−46.8859	+	94.6564i	−0.240441	+	0.485417i
$196$	−49.1892	−	84.7610i	−0.250965	−	0.432454i
$197$	−230.629			−1.17071			−0.585354	−	0.810778i	$-0.699044\pi$
$197$	−230.629			−1.17071			−0.585354	+	0.810778i	$0.699044\pi$
$198$	21.4198	−	88.5753i	0.108181	−	0.447350i
$199$	138.508	+	239.904i	0.696022	+	1.20555i	0.969835	+	0.243763i	$0.0783818\pi$
$199$	138.508	+	239.904i	0.696022	+	1.20555i	−0.273813	+	0.961783i	$0.588285\pi$
$200$	−54.8698	−	44.6016i	−0.274349	−	0.223008i
$201$	−149.424	−	348.586i	−0.743401	−	1.73426i
$202$			79.5483i			0.393804i
$203$	0.0685222	+	61.4345i	0.000337548	+	0.302633i
$204$	11.6659	+	8.72632i	0.0571856	+	0.0427761i
$205$	−247.015	−	87.7309i	−1.20495	−	0.427956i
$206$	−184.037	+	106.254i	−0.893382	+	0.515794i
$207$	−72.9971	+	76.6690i	−0.352643	+	0.370382i
$208$	24.3947	+	14.0843i	0.117282	+	0.0677128i
$209$			172.716i			0.826391i
$210$	−123.520	+	82.4191i	−0.588189	+	0.392472i
$211$	85.1155			0.403391			0.201695	−	0.979448i	$-0.435355\pi$
$211$	85.1155			0.403391			0.201695	+	0.979448i	$0.435355\pi$
$212$	−19.5715	+	33.8988i	−0.0923182	+	0.159900i
$213$	−374.553	−	44.6448i	−1.75846	−	0.209600i
$214$	3.57605	+	6.19390i	0.0167105	+	0.0289434i
$215$	−40.6556	−	14.4394i	−0.189096	−	0.0671599i
$216$	26.6095	−	71.5817i	0.123192	−	0.331397i
$217$	70.8801	+	122.452i	0.326637	+	0.564297i
$218$	28.6828			0.131572
$219$	−88.7618	−	207.070i	−0.405305	−	0.945524i
$220$	54.4862	−	46.4482i	0.247664	−	0.211128i
$221$	14.8081	−	8.54944i	0.0670048	−	0.0386852i
$222$	93.1685	+	217.350i	0.419678	+	0.979055i
$223$		−	355.525i		−	1.59428i	−0.603793	−	0.797141i	$-0.706344\pi$
$223$		−	355.525i		−	1.59428i	0.603793	−	0.797141i	$-0.293656\pi$
$224$	19.8372	+	34.2708i	0.0885590	+	0.152994i
$225$	136.344	+	178.984i	0.605975	+	0.795484i
$226$	50.0879	−	86.7548i	0.221628	−	0.383871i
$227$	161.450	+	279.640i	0.711235	+	1.23190i	0.964394	+	0.264470i	$0.0851971\pi$
$227$	161.450	+	279.640i	0.711235	+	1.23190i	−0.253159	+	0.967425i	$0.581470\pi$
$228$	−17.1309	+	143.722i	−0.0751357	+	0.630360i
$229$	−73.9973	+	128.167i	−0.323132	+	0.559682i	−0.981133	−	0.193336i	$-0.938069\pi$
$229$	−73.9973	+	128.167i	−0.323132	+	0.559682i	0.658000	+	0.753018i	$0.271403\pi$
$230$	−81.7942	+	15.0811i	−0.355627	+	0.0655701i
$231$	−59.3915	−	138.127i	−0.257106	−	0.597952i
$232$		−	24.8233i		−	0.106997i
$233$	−128.110	+	221.893i	−0.549829	+	0.952332i	0.448457	+	0.893804i	$0.351974\pi$
$233$	−128.110	+	221.893i	−0.549829	+	0.952332i	−0.998286	+	0.0585271i	$0.981360\pi$
$234$	−64.9146	−	61.8057i	−0.277413	−	0.264127i
$235$	−287.418	−	337.157i	−1.22306	−	1.43471i
$236$	144.982	+	83.7051i	0.614329	+	0.354683i
$237$	−19.6826	−	14.7231i	−0.0830491	−	0.0621226i
$238$	24.0368	−	0.0268099i	0.100995	−	0.000112647i
$239$			85.0303i			0.355775i	0.984051	+	0.177888i	$0.0569263\pi$
$239$			85.0303i			0.355775i	−0.984051	+	0.177888i	$0.943074\pi$
$240$	49.9466	−	33.2467i	0.208111	−	0.138528i
$241$	184.501	+	319.566i	0.765566	+	1.32600i	0.939947	+	0.341321i	$0.110874\pi$
$241$	184.501	+	319.566i	0.765566	+	1.32600i	−0.174381	+	0.984678i	$0.555792\pi$
$242$	−49.3124	−	85.4116i	−0.203770	−	0.352940i
$243$	−135.836	+	201.488i	−0.558997	+	0.829170i
$244$	−95.7705			−0.392502
$245$	−81.4818	+	231.053i	−0.332579	+	0.943075i
$246$	133.230	−	178.110i	0.541587	−	0.724025i
$247$	147.120	+	84.9395i	0.595626	+	0.343885i
$248$	−28.5847	−	49.5102i	−0.115261	−	0.199638i
$249$	−48.0312	+	402.964i	−0.192896	+	1.61833i
$250$	4.13525	+	176.728i	0.0165410	+	0.706913i
$251$			423.245i			1.68623i	0.537731	+	0.843117i	$0.319282\pi$
$251$			423.245i			1.68623i	−0.537731	+	0.843117i	$0.680718\pi$
$252$	−35.7212	−	120.830i	−0.141751	−	0.479486i
$253$		−	84.2158i		−	0.332869i
$254$	−74.2491	−	42.8677i	−0.292319	−	0.168771i
$255$	−2.31832	−	36.3474i	−0.00909144	−	0.142539i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	85.7431	−	148.511i	0.333631	−	0.577865i	−0.649590	−	0.760285i	$-0.725059\pi$
$257$	85.7431	−	148.511i	0.333631	−	0.577865i	0.983221	+	0.182419i	$0.0583928\pi$
$258$	21.9280	−	29.3147i	0.0849923	−	0.113623i
$259$	338.112	+	194.707i	1.30545	+	0.751764i
$260$	−12.7690	−	69.2540i	−0.0491115	−	0.266362i
$261$	−18.5660	+	76.7743i	−0.0711340	+	0.294154i
$262$	117.000	−	67.5499i	0.446564	−	0.257824i
$263$	−175.037	−	303.173i	−0.665539	−	1.15275i	−0.979139	−	0.203193i	$-0.934868\pi$
$263$	−175.037	−	303.173i	−0.665539	−	1.15275i	0.313599	−	0.949555i	$-0.398465\pi$
$264$	23.9355	+	55.8385i	0.0906648	+	0.211509i
$265$	96.2352	−	17.7437i	0.363152	−	0.0669575i
$266$	119.635	+	206.680i	0.449754	+	0.776994i
$267$	27.9963	−	37.4271i	0.104855	−	0.140176i
$268$	218.967	+	126.421i	0.817041	+	0.471719i
$269$	−27.4482	+	15.8472i	−0.102038	+	0.0589117i	−0.550151	−	0.835065i	$-0.685430\pi$
$269$	−27.4482	+	15.8472i	−0.102038	+	0.0589117i	0.448113	+	0.893977i	$0.352096\pi$
$270$	−179.342	+	65.4700i	−0.664231	+	0.242482i
$271$	85.2758	−	147.702i	0.314671	−	0.545026i	−0.664697	−	0.747113i	$-0.731439\pi$
$271$	85.2758	−	147.702i	0.314671	−	0.545026i	0.979367	+	0.202087i	$0.0647725\pi$
$272$	−9.71233			−0.0357071
$273$	−146.865	−	17.3394i	−0.537966	−	0.0635144i
$274$	153.042			0.558546
$275$	−176.737	−	28.3289i	−0.642681	−	0.103014i
$276$	8.35300	−	70.0785i	0.0302645	−	0.253908i
$277$	297.279	−	171.634i	1.07321	−	0.619617i	0.144152	−	0.989556i	$-0.453955\pi$
$277$	297.279	−	171.634i	1.07321	−	0.619617i	0.929056	+	0.369938i	$0.120621\pi$
$278$	80.5394	−	139.498i	0.289710	−	0.501793i
$279$	51.3778	+	174.506i	0.184150	+	0.625469i
$280$	33.0277	−	93.3229i	0.117956	−	0.333296i
$281$		−	13.8269i		−	0.0492062i	−0.999697	−	0.0246031i	$-0.992168\pi$
$281$		−	13.8269i		−	0.0492062i	0.999697	−	0.0246031i	$-0.00783220\pi$
$282$	345.525	−	148.111i	1.22526	−	0.525217i
$283$	−359.947	+	207.815i	−1.27190	+	0.734330i	−0.975345	−	0.220687i	$-0.929170\pi$
$283$	−359.947	+	207.815i	−1.27190	+	0.734330i	−0.296552	+	0.955017i	$0.595837\pi$
$284$	217.779	−	125.735i	0.766828	−	0.442728i
$285$	301.218	−	200.504i	1.05691	−	0.703524i
$286$	71.3043			0.249316
$287$	−0.409324	−	366.985i	−0.00142622	−	1.27869i
$288$	14.3791	+	48.8389i	0.0499274	+	0.169580i
$289$	141.552	−	245.176i	0.489800	−	0.848359i
$290$	−47.2269	+	40.2598i	−0.162851	+	0.138827i
$291$	365.885	+	43.6116i	1.25734	+	0.149868i
$292$	130.073	+	75.0974i	0.445454	+	0.257183i
$293$	−113.109			−0.386039			−0.193019	−	0.981195i	$-0.561828\pi$
$293$	−113.109			−0.386039			−0.193019	+	0.981195i	$0.561828\pi$
$294$	−166.747	−	124.151i	−0.567166	−	0.422283i
$295$	−75.8882	−	411.588i	−0.257248	−	1.39521i
$296$	−136.530	−	78.8257i	−0.461251	−	0.266303i
$297$	−32.2655	−	190.601i	−0.108638	−	0.641754i
$298$	39.6225	−	22.8761i	0.132961	−	0.0767653i
$299$	−71.7351	−	41.4163i	−0.239917	−	0.138516i
$300$	−144.259	−	41.1032i	−0.480862	−	0.137011i
$301$	−0.0673694	−	60.4010i	−0.000223819	−	0.200668i
$302$	303.276			1.00422
$303$	66.4840	+	155.099i	0.219419	+	0.511877i
$304$	−48.2465	−	83.5653i	−0.158705	−	0.274886i
$305$	155.326	+	182.205i	0.509265	+	0.597395i
$306$	30.0386	+	7.26410i	0.0981653	+	0.0237389i
$307$			205.675i			0.669952i	0.942227	+	0.334976i	$0.108728\pi$
$307$			205.675i			0.669952i	−0.942227	+	0.334976i	$0.891272\pi$
$308$	86.8630	+	50.0213i	0.282023	+	0.162407i
$309$	−270.020	+	360.979i	−0.873852	+	1.16822i
$310$	−47.8339	+	134.681i	−0.154303	+	0.434456i
$311$	−155.578	+	89.8230i	−0.500251	+	0.288820i	−0.728817	−	0.684708i	$-0.759930\pi$
$311$	−155.578	+	89.8230i	−0.500251	+	0.288820i	0.228566	+	0.973528i	$0.426596\pi$
$312$	59.3345	+	7.07237i	0.190175	+	0.0226678i
$313$	−207.288	−	119.678i	−0.662261	−	0.382357i	0.130877	−	0.991399i	$-0.458221\pi$
$313$	−207.288	−	119.678i	−0.662261	−	0.382357i	−0.793138	+	0.609042i	$0.791554\pi$
$314$			175.044i			0.557466i
$315$	−171.948	+	263.930i	−0.545866	+	0.837872i
$316$	16.3866			0.0518565
$317$	167.654	−	290.385i	0.528876	−	0.916040i	−0.470557	−	0.882369i	$-0.655947\pi$
$317$	167.654	−	290.385i	0.528876	−	0.916040i	0.999433	−	0.0336702i	$-0.0107196\pi$
$318$	−9.82774	+	82.4510i	−0.0309049	+	0.259280i
$319$	−31.4182	−	54.4179i	−0.0984896	−	0.170589i
$320$	−13.3873	+	37.6932i	−0.0418352	+	0.117791i
$321$	12.1490	+	9.08774i	0.0378475	+	0.0283107i
$322$	−58.3335	−	100.777i	−0.181160	−	0.312971i
$323$	−58.5732			−0.181341
$324$	−7.94422	−	161.805i	−0.0245192	−	0.499398i
$325$	−111.048	+	136.613i	−0.341686	+	0.420348i
$326$	−216.967	+	125.266i	−0.665541	+	0.384251i
$327$	55.9240	−	23.9722i	0.171021	−	0.0733094i
$328$			148.284i			0.452086i
$329$	309.528	−	537.502i	0.940815	−	1.63374i
$330$	67.4140	−	136.100i	0.204285	−	0.412423i
$331$	38.0065	−	65.8292i	0.114823	−	0.198880i	−0.802886	−	0.596133i	$-0.796703\pi$
$331$	38.0065	−	65.8292i	0.114823	−	0.198880i	0.917709	+	0.397253i	$0.130036\pi$
$332$	−135.272	−	234.298i	−0.407446	−	0.705717i
$333$	363.309	+	345.909i	1.09102	+	1.03877i
$334$	−122.686	+	212.499i	−0.367324	+	0.636224i
$335$	−114.615	−	621.626i	−0.342133	−	1.85560i
$336$	67.3199	+	50.2398i	0.200357	+	0.149523i
$337$			644.608i			1.91278i	0.292085	+	0.956392i	$0.405651\pi$
$337$			644.608i			1.91278i	−0.292085	+	0.956392i	$0.594349\pi$
$338$	−84.4345	+	146.245i	−0.249806	+	0.432677i
$339$	25.1515	−	211.011i	0.0741931	−	0.622452i
$340$	15.7520	+	18.4779i	0.0463294	+	0.0543468i
$341$	−125.327	−	72.3578i	−0.367529	−	0.212193i
$342$	86.7175	+	294.538i	0.253560	+	0.861223i
$343$	−342.998	+	1.14771i	−0.999994	+	0.00334610i
$344$			24.4057i			0.0709468i
$345$	−146.873	+	97.7653i	−0.425719	+	0.283378i
$346$	−13.4330	−	23.2666i	−0.0388237	−	0.0672445i
$347$	224.279	+	388.462i	0.646336	+	1.11949i	0.983991	+	0.178217i	$0.0570328\pi$
$347$	224.279	+	388.462i	0.646336	+	1.11949i	−0.337656	+	0.941270i	$0.609634\pi$
$348$	−20.7465	−	48.3990i	−0.0596165	−	0.139078i
$349$	−606.769			−1.73859			−0.869296	−	0.494292i	$-0.835427\pi$
$349$	−606.769			−1.73859			−0.869296	+	0.494292i	$0.835427\pi$
$350$	−231.115	+	88.5202i	−0.660329	+	0.252915i
$351$	−178.222	−	66.2514i	−0.507755	−	0.188750i
$352$	−35.0754	−	20.2508i	−0.0996459	−	0.0575306i
$353$	214.130	+	370.884i	0.606601	+	1.05066i	0.991796	+	0.127828i	$0.0408006\pi$
$353$	214.130	+	370.884i	0.606601	+	1.05066i	−0.385196	+	0.922835i	$0.625866\pi$
$354$	352.635	+	42.0323i	0.996143	+	0.118735i
$355$	−592.419	−	210.406i	−1.66879	−	0.592692i
$356$			31.1596i			0.0875270i
$357$	46.8431	−	20.1415i	0.131213	−	0.0564187i
$358$		−	178.060i		−	0.497373i
$359$	−607.369	−	350.664i	−1.69183	−	0.976781i	−0.953037	−	0.302854i	$-0.902061\pi$
$359$	−607.369	−	350.664i	−1.69183	−	0.976781i	−0.738798	−	0.673927i	$-0.764606\pi$
$360$	69.5963	−	106.566i	0.193323	−	0.296017i
$361$	−110.465	−	191.331i	−0.305998	−	0.530003i
$362$	98.1362	−	169.977i	0.271094	−	0.469549i
$363$	−167.531	−	125.317i	−0.461517	−	0.345225i
$364$	85.3263	−	49.3901i	0.234413	−	0.135687i
$365$	−68.0843	−	369.263i	−0.186532	−	1.01168i
$366$	−186.728	+	80.0420i	−0.510185	+	0.218694i
$367$	378.737	−	218.664i	1.03198	−	0.595815i	0.114430	−	0.993431i	$-0.463496\pi$
$367$	378.737	−	218.664i	1.03198	−	0.595815i	0.917552	+	0.397616i	$0.130162\pi$
$368$	23.5248	+	40.7462i	0.0639262	+	0.110723i
$369$	110.906	−	458.619i	0.300557	−	1.24287i
$370$	71.4644	+	387.595i	0.193147	+	1.04756i
$371$	68.6324	+	118.569i	0.184993	+	0.319594i
$372$	−97.1118	−	72.6418i	−0.261053	−	0.195274i
$373$	−179.844	−	103.833i	−0.482156	−	0.278373i	0.239158	−	0.970981i	$-0.423129\pi$
$373$	−179.844	−	103.833i	−0.482156	−	0.278373i	−0.721315	+	0.692607i	$0.756462\pi$
$374$	−21.2915	+	12.2926i	−0.0569291	+	0.0328680i
$375$	155.767	+	341.118i	0.415378	+	0.909649i
$376$	−125.310	+	217.044i	−0.333272	+	0.577244i
$377$	−61.8043			−0.163937
$378$	−170.633	−	205.733i	−0.451411	−	0.544268i
$379$	−426.364			−1.12497			−0.562486	−	0.826807i	$-0.690155\pi$
$379$	−426.364			−1.12497			−0.562486	+	0.826807i	$0.690155\pi$
$380$	−80.7361	+	227.321i	−0.212463	+	0.598212i
$381$	−180.594	−	21.5259i	−0.474000	−	0.0564984i
$382$	−317.534	+	183.328i	−0.831240	+	0.479916i
$383$	92.8852	−	160.882i	0.242520	−	0.420057i	−0.718911	−	0.695102i	$-0.755359\pi$
$383$	92.8852	−	160.882i	0.242520	−	0.420057i	0.961431	+	0.275045i	$0.0886927\pi$
$384$	−27.1787	−	20.3303i	−0.0707778	−	0.0529434i
$385$	−45.7126	−	246.386i	−0.118734	−	0.639963i
$386$			230.212i			0.596403i
$387$	18.2536	−	75.4827i	0.0471671	−	0.195046i
$388$	−212.739	+	122.825i	−0.548297	+	0.316559i
$389$	469.908	−	271.302i	1.20799	−	0.697433i	0.245670	−	0.969353i	$-0.420992\pi$
$389$	469.908	−	271.302i	1.20799	−	0.697433i	0.962320	+	0.271920i	$0.0876587\pi$
$390$	−82.7766	−	124.355i	−0.212248	−	0.318860i
$391$	28.5601			0.0730438
$392$	138.593	−	0.309164i	0.353553	−	0.000788685i
$393$	171.663	−	229.490i	0.436802	−	0.583943i
$394$	163.080	−	282.462i	0.413908	−	0.716909i
$395$	−26.5768	−	31.1759i	−0.0672829	−	0.0789264i
$396$	93.3361	+	88.8660i	0.235697	+	0.224409i
$397$	227.395	+	131.286i	0.572782	+	0.330696i	0.758260	−	0.651953i	$-0.226050\pi$
$397$	227.395	+	131.286i	0.572782	+	0.330696i	−0.185478	+	0.982648i	$0.559383\pi$
$398$	−391.761			−0.984324
$399$	405.993	+	302.986i	1.01753	+	0.759364i
$400$	93.4244	−	35.6634i	0.233561	−	0.0891584i
$401$	99.9285	+	57.6937i	0.249198	+	0.143875i	0.619397	−	0.785078i	$-0.287377\pi$
$401$	99.9285	+	57.6937i	0.249198	+	0.143875i	−0.370199	+	0.928953i	$0.620710\pi$
$402$	532.588	+	63.4817i	1.32484	+	0.157915i
$403$	−123.269	+	71.1693i	−0.305878	+	0.176599i
$404$	−97.4264	−	56.2492i	−0.241154	−	0.139231i
$405$	−294.953	+	277.538i	−0.728280	+	0.685280i
$406$	−75.2900	−	43.3568i	−0.185443	−	0.106790i
$407$	−399.071			−0.980517
$408$	−18.9365	+	8.11726i	−0.0464130	+	0.0198953i
$409$	−205.919	−	356.662i	−0.503469	−	0.872033i	−0.999992	−	0.00400996i	$-0.998724\pi$
$409$	−205.919	−	356.662i	−0.503469	−	0.872033i	0.496523	−	0.868023i	$-0.334610\pi$
$410$	282.114	−	240.496i	0.688083	−	0.586575i
$411$	298.392	−	127.908i	0.726014	−	0.311210i
$412$		−	300.531i		−	0.729443i
$413$	507.108	−	293.534i	1.22787	−	0.710736i
$414$	−42.2832	−	143.616i	−0.102133	−	0.346899i
$415$	−226.366	+	637.355i	−0.545459	+	1.53580i
$416$	−34.4993	+	19.9182i	−0.0829309	+	0.0478802i
$417$	40.4426	−	339.298i	0.0969847	−	0.813664i
$418$	−211.533	−	122.129i	−0.506059	−	0.292173i
$419$		−	187.984i		−	0.448649i	−0.974515	−	0.224325i	$-0.927982\pi$
$419$		−	187.984i		−	0.448649i	0.974515	−	0.224325i	$-0.0720176\pi$
$420$	−13.6009	−	209.559i	−0.0323830	−	0.498950i
$421$	278.344			0.661149			0.330574	−	0.943780i	$-0.392758\pi$
$421$	278.344			0.661149			0.330574	+	0.943780i	$0.392758\pi$
$422$	−60.1857	+	104.245i	−0.142620	+	0.247025i
$423$	549.897	−	577.557i	1.29999	−	1.36538i
$424$	−27.6782	−	47.9401i	−0.0652788	−	0.113066i
$425$	9.60720	−	59.9370i	0.0226052	−	0.141028i
$426$	319.527	−	427.163i	0.750065	−	1.00273i
$427$	−167.274	+	290.476i	−0.391743	+	0.680271i
$428$	−10.1146			−0.0236322
$429$	139.025	−	59.5939i	0.324068	−	0.138914i
$430$	46.4324	−	39.5825i	0.107982	−	0.0920523i
$431$	−250.523	+	144.639i	−0.581259	+	0.335590i	−0.761634	−	0.648008i	$-0.775602\pi$
$431$	−250.523	+	144.639i	−0.581259	+	0.335590i	0.180374	+	0.983598i	$0.442269\pi$
$432$	68.8536	+	83.2057i	0.159383	+	0.192606i
$433$			565.286i			1.30551i	0.757569	+	0.652755i	$0.226387\pi$
$433$			565.286i			1.30551i	−0.757569	+	0.652755i	$0.773613\pi$
$434$	−200.093	+	0.223177i	−0.461043	+	0.000514234i
$435$	−58.4323	+	117.967i	−0.134327	+	0.271188i
$436$	−20.2818	+	35.1291i	−0.0465178	+	0.0805713i
$437$	141.874	+	245.733i	0.324654	+	0.562317i
$438$	316.372	+	37.7099i	0.722310	+	0.0860957i
$439$	−154.519	+	267.635i	−0.351980	+	0.609647i	−0.986596	−	0.163180i	$-0.947825\pi$
$439$	−154.519	+	267.635i	−0.351980	+	0.609647i	0.634616	+	0.772827i	$0.281158\pi$
$440$	18.3596	+	99.5754i	0.0417264	+	0.226308i
$441$	−428.875	−	102.701i	−0.972505	−	0.232882i
$442$			24.1815i			0.0547092i
$443$	−96.6911	+	167.474i	−0.218264	+	0.378045i	−0.954277	−	0.298922i	$-0.903373\pi$
$443$	−96.6911	+	167.474i	−0.218264	+	0.378045i	0.736013	+	0.676967i	$0.236706\pi$
$444$	−332.079	−	39.5821i	−0.747925	−	0.0891488i
$445$	59.2819	−	50.5364i	0.133218	−	0.113565i
$446$	435.428	+	251.394i	0.976295	+	0.563664i
$447$	58.1345	−	77.7176i	0.130055	−	0.173865i
$448$	−56.0000	+	0.0624607i	−0.125000	+	0.000139421i
$449$			241.376i			0.537587i	0.963198	+	0.268793i	$0.0866249\pi$
$449$			241.376i			0.537587i	−0.963198	+	0.268793i	$0.913375\pi$
$450$	−315.620	+	40.4263i	−0.701377	+	0.0898362i
$451$	187.680	+	325.071i	0.416141	+	0.720777i
$452$	70.8350	+	122.690i	0.156715	+	0.271438i
$453$	591.309	−	253.468i	1.30532	−	0.559533i
$454$	−456.650			−1.00584
$455$	−232.353	−	82.2315i	−0.510665	−	0.180729i
$456$	−163.909	−	122.608i	−0.359450	−	0.268877i
$457$	−5.49041	−	3.16989i	−0.0120140	−	0.00693630i	0.493981	−	0.869473i	$-0.335541\pi$
$457$	−5.49041	−	3.16989i	−0.0120140	−	0.00693630i	−0.505995	+	0.862536i	$0.668875\pi$
$458$	−104.648	−	181.256i	−0.228489	−	0.395755i
$459$	64.6386	−	10.9422i	0.140825	−	0.0238392i
$460$	39.3667	−	110.841i	0.0855798	−	0.240959i
$461$		−	63.0320i		−	0.136729i	−0.997660	−	0.0683644i	$-0.978222\pi$
$461$		−	63.0320i		−	0.136729i	0.997660	−	0.0683644i	$-0.0217781\pi$
$462$	211.166	+	24.9311i	0.457070	+	0.0539635i
$463$			170.842i			0.368990i	0.982833	+	0.184495i	$0.0590649\pi$
$463$			170.842i			0.368990i	−0.982833	+	0.184495i	$0.940935\pi$
$464$	30.4022	+	17.5527i	0.0655220	+	0.0378291i
$465$	19.2987	+	302.572i	0.0415026	+	0.650692i
$466$	−181.175	−	313.804i	−0.388788	−	0.673400i
$467$	120.590	−	208.868i	0.258223	−	0.447255i	−0.707543	−	0.706670i	$-0.750197\pi$
$467$	120.590	−	208.868i	0.258223	−	0.447255i	0.965766	+	0.259415i	$0.0835299\pi$
$468$	121.598	−	35.8006i	0.259824	−	0.0764971i
$469$	765.891	−	443.327i	1.63303	−	0.945260i
$470$	616.166	−	113.608i	1.31099	−	0.241719i
$471$	146.297	+	341.291i	0.310608	+	0.724609i
$472$	−205.035	+	118.377i	−0.434396	+	0.250799i
$473$	30.8896	+	53.5024i	0.0653058	+	0.113113i
$474$	31.9497	−	13.6954i	0.0674045	−	0.0288934i
$475$	563.425	−	215.079i	1.18616	−	0.452798i
$476$	−16.9637	+	29.4579i	−0.0356381	+	0.0618863i
$477$	49.7485	+	168.972i	0.104294	+	0.354239i
$478$	−104.140	−	60.1255i	−0.217867	−	0.125786i
$479$	−94.9661	+	54.8287i	−0.198259	+	0.114465i	−0.595843	−	0.803101i	$-0.703182\pi$
$479$	−94.9661	+	54.8287i	−0.198259	+	0.114465i	0.397584	+	0.917566i	$0.369849\pi$
$480$	5.40113	+	84.6807i	0.0112523	+	0.176418i
$481$	−196.258	+	339.929i	−0.408021	+	0.706713i
$482$	−521.849			−1.08267
$483$	−197.961	−	147.735i	−0.409858	−	0.305870i
$484$	139.477			0.288175
$485$	578.709	+	205.537i	1.19322	+	0.423787i
$486$	−150.721	−	308.839i	−0.310125	−	0.635470i
$487$	564.917	−	326.155i	1.15999	−	0.669723i	0.208691	−	0.977982i	$-0.433080\pi$
$487$	564.917	−	326.155i	1.15999	−	0.669723i	0.951302	+	0.308259i	$0.0997463\pi$
$488$	67.7200	−	117.294i	0.138770	−	0.240357i
$489$	−318.335	+	425.570i	−0.650993	+	0.870285i
$490$	−225.365	−	263.174i	−0.459929	−	0.537090i
$491$			176.921i			0.360328i	0.983637	+	0.180164i	$0.0576628\pi$
$491$			176.921i			0.360328i	−0.983637	+	0.180164i	$0.942337\pi$
$492$	123.931	+	289.116i	0.251893	+	0.587634i
$493$	18.4548	−	10.6549i	0.0374336	−	0.0216123i
$494$	−208.058	+	120.123i	−0.421171	+	0.243163i
$495$	17.6918	−	321.702i	0.0357411	−	0.649902i
$496$	80.8497			0.163004
$497$	−0.981685	−	880.143i	−0.00197522	−	1.77091i
$498$	−459.564	−	343.764i	−0.922820	−	0.690290i
$499$	107.821	−	186.751i	0.216074	−	0.374251i	−0.737530	−	0.675314i	$-0.764008\pi$
$499$	107.821	−	186.751i	0.216074	−	0.374251i	0.953604	+	0.301063i	$0.0973415\pi$
$500$	−219.371	−	119.901i	−0.438742	−	0.239802i
$501$	−61.6065	+	516.855i	−0.122967	+	1.03165i
$502$	−518.367	−	299.279i	−1.03260	−	0.596174i
$503$	−333.396			−0.662815			−0.331408	−	0.943488i	$-0.607524\pi$
$503$	−333.396			−0.662815			−0.331408	+	0.943488i	$0.607524\pi$
$504$	173.245	+	41.6906i	0.343740	+	0.0827195i
$505$	50.9962	+	276.584i	0.100983	+	0.547691i
$506$	103.143	+	59.5495i	0.203840	+	0.117687i
$507$	−42.3985	+	355.707i	−0.0836262	+	0.701592i
$508$	105.004	−	60.6241i	0.206701	−	0.119339i
$509$	38.1549	+	22.0287i	0.0749604	+	0.0432784i	0.537012	−	0.843575i	$-0.319553\pi$
$509$	38.1549	+	22.0287i	0.0749604	+	0.0432784i	−0.462051	+	0.886853i	$0.652886\pi$
$510$	46.1556	+	22.8621i	0.0905011	+	0.0448277i
$511$	454.960	−	263.349i	0.890333	−	0.515359i
$512$	22.6274			0.0441942
$513$	415.243	+	501.797i	0.809440	+	0.978163i
$514$	121.259	+	210.027i	0.235913	+	0.408612i
$515$	−571.766	+	487.417i	−1.11023	+	0.946441i
$516$	20.3975	+	47.5848i	0.0395301	+	0.0922186i
$517$			634.408i			1.22709i
$518$	−477.548	+	276.423i	−0.921907	+	0.533635i
$519$	−45.6363	−	34.1370i	−0.0879313	−	0.0657745i
$520$	93.8475	+	33.3312i	0.180476	+	0.0640985i
$521$	367.661	−	212.269i	0.705684	−	0.407427i	−0.103777	−	0.994601i	$-0.533093\pi$
$521$	367.661	−	212.269i	0.705684	−	0.407427i	0.809461	+	0.587174i	$0.199759\pi$
$522$	−80.9008	−	77.0262i	−0.154982	−	0.147560i
$523$	−220.292	−	127.186i	−0.421208	−	0.243185i	0.274386	−	0.961620i	$-0.411525\pi$
$523$	−220.292	−	127.186i	−0.421208	−	0.243185i	−0.695594	+	0.718435i	$0.744859\pi$
$524$			191.060i			0.364618i
$525$	−376.632	+	365.750i	−0.717394	+	0.696667i
$526$	495.079			0.941215
$527$	24.5387	−	42.5023i	0.0465630	−	0.0806496i
$528$	−85.3129	−	10.1689i	−0.161577	−	0.0192592i
$529$	195.323	+	338.309i	0.369230	+	0.639525i
$530$	−46.3170	+	130.410i	−0.0873906	+	0.246057i
$531$	722.676	−	212.769i	1.36097	−	0.400695i
$532$	−337.725	+	0.376688i	−0.634821	+	0.000708061i
$533$	369.194			0.692672
$534$	26.0422	+	60.7532i	0.0487683	+	0.113770i
$535$	16.4044	+	19.2432i	0.0306624	+	0.0359686i
$536$	−309.666	+	178.786i	−0.577735	+	0.333556i
$537$	−148.817	−	347.170i	−0.277126	−	0.646499i
$538$		−	44.8228i		−	0.0833137i
$539$	303.433	−	176.091i	0.562955	−	0.326699i
$540$	46.6301	−	265.943i	0.0863521	−	0.492487i
$541$	−416.076	+	720.665i	−0.769087	+	1.33210i	0.168972	+	0.985621i	$0.445955\pi$
$541$	−416.076	+	720.665i	−0.769087	+	1.33210i	−0.938059	+	0.346477i	$0.887378\pi$
$542$	120.598	+	208.882i	0.222506	+	0.385392i
$543$	49.2787	−	413.430i	0.0907527	−	0.761381i
$544$	6.86765	−	11.8951i	0.0126244	−	0.0218660i
$545$	99.7279	−	18.3877i	0.182987	−	0.0337389i
$546$	125.085	−	167.611i	0.229094	−	0.306980i
$547$		−	609.451i		−	1.11417i	−0.830455	−	0.557085i	$-0.811920\pi$
$547$		−	609.451i		−	1.11417i	0.830455	−	0.557085i	$-0.188080\pi$
$548$	−108.217	+	187.437i	−0.197476	+	0.342038i
$549$	−297.174	+	312.122i	−0.541300	+	0.568529i
$550$	159.668	−	196.426i	0.290305	−	0.357139i
$551$	183.350	+	105.857i	0.332758	+	0.192118i
$552$	79.9218	+	59.7833i	0.144786	+	0.108303i
$553$	28.6212	−	49.7013i	0.0517563	−	0.0898758i
$554$			485.454i			0.876271i
$555$	463.277	+	695.983i	0.834734	+	1.25402i
$556$	113.900	+	197.280i	0.204856	+	0.354821i
$557$	420.634	+	728.559i	0.755177	+	1.30801i	0.945286	+	0.326242i	$0.105783\pi$
$557$	420.634	+	728.559i	0.755177	+	1.30801i	−0.190109	+	0.981763i	$0.560884\pi$
$558$	−250.055	−	60.4696i	−0.448127	−	0.108368i
$559$	60.7646			0.108702
$560$	90.9426	+	106.440i	0.162398	+	0.190071i
$561$	−31.2390	+	41.7622i	−0.0556846	+	0.0744424i
$562$	16.9345	+	9.77712i	0.0301325	+	0.0173970i
$563$	63.6150	+	110.184i	0.112993	+	0.195709i	0.916976	−	0.398943i	$-0.130623\pi$
$563$	63.6150	+	110.184i	0.112993	+	0.195709i	−0.803983	+	0.594653i	$0.797290\pi$
$564$	−62.9242	+	527.910i	−0.111568	+	0.936011i
$565$	118.536	−	333.750i	0.209798	−	0.590708i
$566$		−	587.791i		−	1.03850i
$567$	−504.637	−	258.517i	−0.890012	−	0.455938i
$568$			355.632i			0.626112i
$569$	437.386	+	252.525i	0.768692	+	0.443805i	0.832408	−	0.554164i	$-0.186962\pi$
$569$	437.386	+	252.525i	0.768692	+	0.443805i	−0.0637158	+	0.997968i	$0.520295\pi$
$570$	32.5732	+	510.693i	0.0571459	+	0.895953i
$571$	−567.899	−	983.631i	−0.994570	−	1.72265i	−0.587413	−	0.809287i	$-0.699853\pi$
$571$	−567.899	−	983.631i	−0.994570	−	1.72265i	−0.407157	−	0.913358i	$-0.633480\pi$
$572$	−50.4198	+	87.3296i	−0.0881465	+	0.152674i
$573$	−465.888	+	622.827i	−0.813068	+	1.08696i
$574$	449.752	+	258.996i	0.783540	+	0.451213i
$575$	−274.724	+	104.872i	−0.477782	+	0.182386i
$576$	−69.9828	−	16.9236i	−0.121498	−	0.0293813i
$577$	−310.137	+	179.058i	−0.537499	+	0.310325i	−0.744065	−	0.668107i	$-0.767105\pi$
$577$	−310.137	+	179.058i	−0.537499	+	0.310325i	0.206565	+	0.978433i	$0.433771\pi$
$578$	200.185	+	346.731i	0.346341	+	0.599880i
$579$	192.404	+	448.853i	0.332303	+	0.775221i
$580$	−15.9135	−	86.3088i	−0.0274371	−	0.148808i
$581$	−946.904	+	1.05615i	−1.62978	+	0.00181781i
$582$	−312.133	+	417.278i	−0.536311	+	0.716972i
$583$	−121.353	−	70.0632i	−0.208153	−	0.120177i
$584$	−183.950	+	106.204i	−0.314983	+	0.181856i
$585$	−265.325	−	173.279i	−0.453548	−	0.296203i
$586$	79.9804	−	138.530i	0.136485	−	0.236400i
$587$	−637.230			−1.08557			−0.542786	−	0.839871i	$-0.682630\pi$
$587$	−637.230			−1.08557			−0.542786	+	0.839871i	$0.682630\pi$
$588$	269.961	−	116.434i	0.459118	−	0.198017i
$589$	487.589			0.827826
$590$	557.751	+	198.093i	0.945341	+	0.335751i
$591$	81.8899	−	687.025i	0.138562	−	1.16248i
$592$	193.083	−	111.476i	0.326153	−	0.188305i
$593$	−283.144	+	490.421i	−0.477478	+	0.827016i	−0.999667	−	0.0258139i	$-0.991782\pi$
$593$	−283.144	+	490.421i	−0.477478	+	0.827016i	0.522189	+	0.852830i	$0.325116\pi$
$594$	256.253	+	95.2582i	0.431402	+	0.160367i
$595$	83.5569	−	15.5025i	0.140432	−	0.0260547i
$596$			64.7032i			0.108562i
$597$	−763.832	+	327.422i	−1.27945	+	0.548445i
$598$	101.449	−	58.5715i	0.169647	−	0.0979456i
$599$	−134.396	+	77.5938i	−0.224368	+	0.129539i	−0.607971	−	0.793959i	$-0.708016\pi$
$599$	−134.396	+	77.5938i	−0.224368	+	0.129539i	0.383603	+	0.923498i	$0.374683\pi$
$600$	152.347	−	147.616i	0.253912	−	0.246026i
$601$	−852.137			−1.41786			−0.708932	−	0.705276i	$-0.750823\pi$
$601$	−852.137			−1.41786			−0.708932	+	0.705276i	$0.750823\pi$
$602$	74.0234	+	42.6274i	0.122963	+	0.0708097i
$603$	1091.46	−	321.347i	1.81006	−	0.532914i
$604$	−214.448	+	371.435i	−0.355047	+	0.614959i
$605$	−226.211	−	265.357i	−0.373902	−	0.438607i
$606$	−236.968	−	28.2453i	−0.391036	−	0.0466094i
$607$	256.188	+	147.910i	0.422056	+	0.243674i	0.695957	−	0.718084i	$-0.254981\pi$
$607$	256.188	+	147.910i	0.422056	+	0.243674i	−0.273900	+	0.961758i	$0.588314\pi$
$608$	136.462			0.224443
$609$	−183.032	−	21.6095i	−0.300546	−	0.0354836i
$610$	−332.987	+	61.3958i	−0.545880	+	0.100649i
$611$	540.390	+	311.994i	0.884435	+	0.510629i
$612$	−30.1372	+	31.6531i	−0.0492437	+	0.0517208i
$613$	−619.980	+	357.946i	−1.01139	+	0.583925i	−0.911598	−	0.411084i	$-0.865150\pi$
$613$	−619.980	+	357.946i	−1.01139	+	0.583925i	−0.0997897	+	0.995009i	$0.531817\pi$
$614$	−251.900	−	145.434i	−0.410260	−	0.236864i
$615$	349.051	−	704.687i	0.567562	−	1.14583i
$616$	−122.685	+	71.0146i	−0.199163	+	0.115283i
$617$	546.134			0.885145			0.442572	−	0.896733i	$-0.354066\pi$
$617$	546.134			0.885145			0.442572	+	0.896733i	$0.354066\pi$
$618$	−251.174	−	585.957i	−0.406431	−	0.948150i
$619$	−445.587	−	771.779i	−0.719849	−	1.24682i	−0.961059	−	0.276343i	$-0.910878\pi$
$619$	−445.587	−	771.779i	−0.719849	−	1.24682i	0.241210	−	0.970473i	$-0.422456\pi$
$620$	−131.127	−	153.818i	−0.211494	−	0.248094i
$621$	−202.471	−	244.675i	−0.326041	−	0.394002i
$622$		−	254.058i		−	0.408453i
$623$	94.5084	+	54.4240i	0.151699	+	0.0873579i
$624$	−50.6177	+	67.6687i	−0.0811180	+	0.108443i
$625$	127.674	+	611.821i	0.204278	+	0.978913i
$626$	293.149	−	169.250i	0.468289	−	0.270367i
$627$	−514.505	−	61.3264i	−0.820583	−	0.0978093i
$628$	−214.384	−	123.775i	−0.341377	−	0.197094i
$629$		−	135.337i		−	0.215162i
$630$	−201.661	−	397.219i	−0.320097	−	0.630506i
$631$	302.275			0.479041			0.239520	−	0.970891i	$-0.423010\pi$
$631$	302.275			0.479041			0.239520	+	0.970891i	$0.423010\pi$
$632$	−11.5871	+	20.0695i	−0.0183340	+	0.0317555i
$633$	−30.2221	+	253.552i	−0.0477442	+	0.400555i
$634$	237.098	+	410.666i	0.373972	+	0.647738i
$635$	−285.640	−	101.449i	−0.449827	−	0.159762i
$636$	−94.0322	−	70.3382i	−0.147849	−	0.110595i
$637$	−0.769748	−	345.064i	−0.00120840	−	0.541701i
$638$	88.8641			0.139285
$639$	265.986	−	1099.91i	0.416254	−	1.72130i
$640$	−36.6984	−	43.0491i	−0.0573412	−	0.0672643i
$641$	408.095	−	235.614i	0.636654	−	0.367572i	−0.146671	−	0.989185i	$-0.546856\pi$
$641$	408.095	−	235.614i	0.636654	−	0.367572i	0.783324	+	0.621613i	$0.213522\pi$
$642$	−19.7208	+	8.45346i	−0.0307178	+	0.0131674i
$643$			645.383i			1.00371i	0.864953	+	0.501853i	$0.167348\pi$
$643$			645.383i			1.00371i	−0.864953	+	0.501853i	$0.832652\pi$
$644$	164.674	−	0.183672i	0.255705	−	0.000285205i
$645$	57.4493	−	115.982i	0.0890686	−	0.179818i
$646$	41.4175	−	71.7372i	0.0641138	−	0.111048i
$647$	−295.133	−	511.186i	−0.456157	−	0.790086i	0.542597	−	0.839993i	$-0.317441\pi$
$647$	−295.133	−	511.186i	−0.456157	−	0.790086i	−0.998754	+	0.0499067i	$0.984108\pi$
$648$	203.787	+	104.684i	0.314487	+	0.161549i
$649$	−299.653	+	519.014i	−0.461715	+	0.799714i
$650$	−88.7936	−	232.605i	−0.136606	−	0.357854i
$651$	−389.943	+	167.666i	−0.598990	+	0.257552i
$652$		−	354.305i		−	0.543412i
$653$	546.903	−	947.264i	0.837524	−	1.45063i	−0.0544355	−	0.998517i	$-0.517336\pi$
$653$	546.903	−	947.264i	0.837524	−	1.45063i	0.891959	−	0.452116i	$-0.149331\pi$
$654$	−10.1844	+	85.4435i	−0.0155725	+	0.130648i
$655$	363.496	−	309.871i	0.554955	−	0.473086i
$656$	−181.611	−	104.853i	−0.276845	−	0.159837i
$657$	648.360	−	190.889i	0.986849	−	0.290547i
$658$	439.433	+	759.164i	0.667832	+	1.15374i
$659$		−	165.177i		−	0.250648i	−0.992116	−	0.125324i	$-0.960003\pi$
$659$		−	165.177i		−	0.250648i	0.992116	−	0.125324i	$-0.0399971\pi$
$660$	119.019	+	178.802i	0.180331	+	0.270912i
$661$	128.965	+	223.374i	0.195106	+	0.337934i	0.946935	−	0.321424i	$-0.104162\pi$
$661$	128.965	+	223.374i	0.195106	+	0.337934i	−0.751829	+	0.659358i	$0.770828\pi$
$662$	53.7493	+	93.0965i	0.0811923	+	0.140629i
$663$	20.2101	+	47.1476i	0.0304828	+	0.0711125i
$664$	382.607			0.576216
$665$	548.457	+	641.918i	0.824748	+	0.965291i
$666$	−680.549	+	200.366i	−1.02184	+	0.300850i
$667$	−89.4009	−	51.6156i	−0.134034	−	0.0773848i
$668$	−173.505	−	300.519i	−0.259737	−	0.449878i
$669$	1059.08	+	126.237i	1.58308	+	0.188695i
$670$	842.377	+	299.182i	1.25728	+	0.446540i
$671$		−	342.845i		−	0.510947i
$672$	−109.133	+	46.9248i	−0.162401	+	0.0698286i
$673$		−	982.005i		−	1.45915i	−0.683903	−	0.729573i	$-0.739719\pi$
$673$		−	982.005i		−	1.45915i	0.683903	−	0.729573i	$-0.260281\pi$
$674$	−789.481	−	455.807i	−1.17134	−	0.676272i
$675$	−581.589	+	342.606i	−0.861614	+	0.507564i
$676$	−119.408	−	206.821i	−0.176640	−	0.305949i
$677$	−397.241	+	688.041i	−0.586766	+	1.01631i	0.407887	+	0.913033i	$0.366266\pi$
$677$	−397.241	+	688.041i	−0.586766	+	1.01631i	−0.994653	+	0.103276i	$0.967067\pi$
$678$	240.650	+	180.012i	0.354941	+	0.265504i
$679$	0.958967	+	859.775i	0.00141232	+	1.26624i
$680$	−33.7691	+	6.22630i	−0.0496604	+	0.00915633i
$681$	−890.350	+	381.654i	−1.30742	+	0.560432i
$682$	177.240	−	102.329i	0.259882	−	0.150043i
$683$	92.7635	+	160.671i	0.135818	+	0.235243i	0.925910	−	0.377745i	$-0.123300\pi$
$683$	92.7635	+	160.671i	0.135818	+	0.235243i	−0.790092	+	0.612989i	$0.789967\pi$
$684$	−422.053	−	102.063i	−0.617036	−	0.149215i
$685$	532.115	−	98.1108i	0.776810	−	0.143227i
$686$	241.131	−	420.897i	0.351502	−	0.613552i
$687$	−355.524	−	265.940i	−0.517503	−	0.387103i
$688$	−29.8908	−	17.2574i	−0.0434459	−	0.0250835i
$689$	−119.360	+	68.9124i	−0.173236	+	0.100018i
$690$	−15.8826	−	249.013i	−0.0230182	−	0.360888i
$691$	−32.7555	+	56.7341i	−0.0474030	+	0.0821044i	−0.888753	−	0.458386i	$-0.848428\pi$
$691$	−32.7555	+	56.7341i	−0.0474030	+	0.0821044i	0.841350	+	0.540490i	$0.181761\pi$
$692$	37.9942			0.0549049
$693$	432.557	−	127.877i	0.624180	−	0.184527i
$694$	−634.355			−0.914057
$695$	190.601	−	536.657i	0.274246	−	0.772169i
$696$	73.9465	+	8.81404i	0.106245	+	0.0126639i
$697$	−110.241	+	63.6478i	−0.158165	+	0.0913168i
$698$	429.050	−	743.137i	0.614685	−	1.06467i
$699$	−615.513	−	460.417i	−0.880562	−	0.658679i
$700$	55.0084	−	345.650i	0.0785834	−	0.493786i
$701$		−	965.721i		−	1.37763i	−0.724936	−	0.688816i	$-0.758131\pi$
$701$		−	965.721i		−	1.37763i	0.724936	−	0.688816i	$-0.241869\pi$
$702$	207.163	−	171.430i	0.295104	−	0.244202i
$703$	1164.45	−	672.293i	1.65639	−	0.956320i
$704$	49.6041	−	28.6389i	0.0704603	−	0.0406803i
$705$	1106.41	−	736.479i	1.56938	−	1.04465i
$706$	−605.651			−0.857863
$707$	−340.773	+	197.252i	−0.481998	+	0.278999i
$708$	−300.829	+	402.166i	−0.424900	+	0.568031i
$709$	351.730	−	609.214i	0.496093	−	0.859258i	−0.503897	−	0.863764i	$-0.668101\pi$
$709$	351.730	−	609.214i	0.496093	−	0.859258i	0.999990	+	0.00450607i	$0.00143433\pi$
$710$	676.597	−	576.783i	0.952953	−	0.812370i
$711$	50.8474	−	53.4052i	0.0715154	−	0.0751127i
$712$	−38.1626	−	22.0332i	−0.0535991	−	0.0309455i
$713$	−237.747			−0.333446
$714$	−8.45490	+	71.6130i	−0.0118416	+	0.100298i
$715$	247.920	−	45.7112i	0.346741	−	0.0639318i
$716$	218.078	+	125.907i	0.304578	+	0.175848i
$717$	−253.298	−	30.1918i	−0.353274	−	0.0421085i
$718$	858.949	−	495.914i	1.19631	−	0.690689i
$719$	649.908	+	375.224i	0.903905	+	0.521870i	0.878465	−	0.477807i	$-0.158568\pi$
$719$	649.908	+	375.224i	0.903905	+	0.521870i	0.0254398	+	0.999676i	$0.491901\pi$
$720$	81.3043	+	160.591i	0.112923	+	0.223044i
$721$	−911.521	−	524.912i	−1.26425	−	0.728034i
$722$	312.443			0.432746
$723$	−1017.47	+	436.145i	−1.40729	+	0.603243i
$724$	138.785	+	240.384i	0.191693	+	0.332021i
$725$	−138.395	+	170.256i	−0.190890	+	0.234836i
$726$	271.943	−	116.570i	0.374577	−	0.160565i
$727$		−	674.589i		−	0.927908i	−0.885859	−	0.463954i	$-0.846430\pi$
$727$		−	674.589i		−	0.927908i	0.885859	−	0.463954i	$-0.153570\pi$
$728$	0.155513	+	139.427i	0.000213616	+	0.191521i
$729$	−551.984	−	476.187i	−0.757180	−	0.653206i
$730$	500.396	+	177.722i	0.685473	+	0.243455i
$731$	−18.1443	+	10.4756i	−0.0248212	+	0.0143305i
$732$	34.0053	−	285.292i	0.0464554	−	0.389743i
$733$	330.354	+	190.730i	0.450688	+	0.260205i	0.708121	−	0.706091i	$-0.249543\pi$
$733$	330.354	+	190.730i	0.450688	+	0.260205i	−0.257433	+	0.966296i	$0.582877\pi$
$734$			618.475i			0.842610i
$735$	−659.356	−	324.768i	−0.897084	−	0.441861i
$736$	−66.5383			−0.0904053
$737$	−452.569	+	783.872i	−0.614069	+	1.06360i
$738$	483.269	+	460.123i	0.654835	+	0.623473i
$739$	88.3245	+	152.983i	0.119519	+	0.207013i	0.919577	−	0.392910i	$-0.128531\pi$
$739$	88.3245	+	152.983i	0.119519	+	0.207013i	−0.800058	+	0.599922i	$0.795198\pi$
$740$	−525.239	−	186.546i	−0.709782	−	0.252089i
$741$	−305.265	+	408.097i	−0.411964	+	0.550738i
$742$	−193.747	+	0.216100i	−0.261115	+	0.000291240i
$743$	−722.670			−0.972637			−0.486319	−	0.873781i	$-0.661661\pi$
$743$	−722.670			−0.972637			−0.486319	+	0.873781i	$0.661661\pi$
$744$	157.636	−	67.5717i	0.211876	−	0.0908222i
$745$	123.099	−	104.939i	0.165234	−	0.140858i
$746$	254.338	−	146.842i	0.340936	−	0.196840i
$747$	−1183.34	−	286.162i	−1.58412	−	0.383081i
$748$		−	34.7688i		−	0.0464824i
$749$	−17.6663	+	30.6779i	−0.0235866	+	0.0409585i
$750$	−527.927	−	50.4326i	−0.703902	−	0.0672435i
$751$	324.799	−	562.568i	0.432489	−	0.749092i	−0.564598	−	0.825366i	$-0.690969\pi$
$751$	324.799	−	562.568i	0.432489	−	0.749092i	0.997087	+	0.0762737i	$0.0243023\pi$
$752$	−177.216	−	306.946i	−0.235659	−	0.408173i
$753$	−1260.81	−	150.282i	−1.67438	−	0.199578i
$754$	43.7023	−	75.6945i	0.0579606	−	0.100391i
$755$	1054.47	−	194.421i	1.39665	−	0.257512i
$756$	372.627	−	63.5070i	0.492893	−	0.0840040i
$757$		−	181.051i		−	0.239169i	−0.992824	−	0.119584i	$-0.961844\pi$
$757$		−	181.051i		−	0.239169i	0.992824	−	0.119584i	$-0.0381562\pi$
$758$	301.485	−	522.188i	0.397738	−	0.688902i
$759$	250.871	+	29.9026i	0.330529	+	0.0393974i
$760$	−221.321	−	259.621i	−0.291212	−	0.341607i
$761$	−1061.73	−	612.990i	−1.39518	−	0.805506i	−0.401295	−	0.915949i	$-0.631440\pi$
$761$	−1061.73	−	612.990i	−1.39518	−	0.805506i	−0.993882	+	0.110443i	$0.964773\pi$
$762$	154.063	−	205.961i	0.202182	−	0.270289i
$763$	71.1233	+	122.873i	0.0932154	+	0.161039i
$764$		−	518.530i		−	0.678704i
$765$	109.099	+	5.99984i	0.142613	+	0.00784293i
$766$	131.359	+	227.521i	0.171488	+	0.297025i
$767$	294.731	+	510.490i	0.384265	+	0.665567i
$768$	44.1176	−	18.9113i	0.0574448	−	0.0246241i
$769$	−741.584			−0.964349			−0.482174	−	0.876075i	$-0.660153\pi$
$769$	−741.584			−0.964349			−0.482174	+	0.876075i	$0.660153\pi$
$770$	334.083	+	118.235i	0.433875	+	0.153552i
$771$	411.958	+	308.153i	0.534316	+	0.399680i
$772$	−281.950	−	162.784i	−0.365221	−	0.210860i
$773$	0.777017	+	1.34583i	0.00100520	+	0.00174105i	0.866528	−	0.499129i	$-0.166347\pi$
$773$	0.777017	+	1.34583i	0.00100520	+	0.00174105i	−0.865522	+	0.500870i	$0.833013\pi$
$774$	79.5398	+	75.7304i	0.102765	+	0.0978429i
$775$	−79.9746	+	498.942i	−0.103193	+	0.643796i
$776$		−	347.402i		−	0.447683i
$777$	−700.068	+	938.073i	−0.900989	+	1.20730i
$778$			767.357i			0.986320i
$779$	−1095.26	−	632.348i	−1.40598	−	0.811743i
$780$	210.836	−	13.4476i	0.270302	−	0.0172405i
$781$	450.114	+	779.619i	0.576330	+	0.998232i
$782$	−20.1951	+	34.9789i	−0.0258249	+	0.0447300i
$783$	−222.112	−	82.5668i	−0.283668	−	0.105449i
$784$	−97.6211	+	169.959i	−0.124517	+	0.216785i
$785$	112.216	+	608.616i	0.142950	+	0.775307i
$786$	159.682	+	372.517i	0.203158	+	0.473941i
$787$	−516.324	+	298.100i	−0.656066	+	0.378780i	−0.790776	−	0.612105i	$-0.790323\pi$
$787$	−516.324	+	298.100i	−0.656066	+	0.378780i	0.134711	+	0.990885i	$0.456990\pi$
$788$	230.629	+	399.462i	0.292677	+	0.506931i
$789$	965.276	−	413.772i	1.22342	−	0.524426i
$790$	56.9752	−	10.5050i	0.0721205	−	0.0132975i
$791$	495.844	−	0.553050i	0.626858	−	0.000699178i
$792$	−174.837	+	51.4752i	−0.220754	+	0.0649939i
$793$	−292.036	−	168.607i	−0.368268	−	0.212619i
$794$	−321.584	+	185.667i	−0.405018	+	0.233837i
$795$	18.6867	+	292.977i	0.0235053	+	0.368524i
$796$	277.017	−	479.807i	0.348011	−	0.602773i
$797$	−796.553			−0.999439			−0.499720	−	0.866187i	$-0.666564\pi$
$797$	−796.553			−0.999439			−0.499720	+	0.866187i	$0.666564\pi$
$798$	−658.162	+	282.995i	−0.824764	+	0.354630i
$799$	−215.147			−0.269270
$800$	−22.3825	+	139.639i	−0.0279781	+	0.174549i
$801$	101.551	+	96.6877i	0.126781	+	0.120709i
$802$	−141.320	+	81.5912i	−0.176210	+	0.101735i
$803$	−268.839	+	465.642i	−0.334793	+	0.579878i
$804$	−454.345	+	607.396i	−0.565106	+	0.755467i
$805$	−267.426	−	312.998i	−0.332207	−	0.388817i
$806$		−	201.297i		−	0.249749i
$807$	−37.4615	−	87.3928i	−0.0464207	−	0.108293i
$808$	137.782	−	79.5483i	0.170522	−	0.0984509i
$809$	956.082	−	551.994i	1.18181	−	0.682317i	0.225376	−	0.974272i	$-0.427639\pi$
$809$	956.082	−	551.994i	1.18181	−	0.682317i	0.956432	+	0.291955i	$0.0943058\pi$
$810$	−131.350	−	557.492i	−0.162161	−	0.688262i
$811$	1030.67			1.27087			0.635435	−	0.772155i	$-0.280821\pi$
$811$	1030.67			1.27087			0.635435	+	0.772155i	$0.280821\pi$
$812$	106.339	−	61.5532i	0.130960	−	0.0758044i
$813$	409.713	+	306.474i	0.503951	+	0.376967i
$814$	282.185	−	488.760i	0.346665	−	0.600442i
$815$	−674.073	+	574.631i	−0.827083	+	0.705069i
$816$	3.44857	−	28.9322i	0.00422619	−	0.0354561i
$817$	−180.265	−	104.076i	−0.220643	−	0.127388i
$818$	582.426			0.712012
$819$	103.800	−	431.341i	0.126740	−	0.526668i
$820$	95.0610	+	515.574i	0.115928	+	0.628749i
$821$	−539.449	−	311.451i	−0.657063	−	0.379355i	0.134094	−	0.990969i	$-0.457188\pi$
$821$	−539.449	−	311.451i	−0.657063	−	0.379355i	−0.791157	+	0.611613i	$0.790521\pi$
$822$	−54.3407	+	455.898i	−0.0661079	+	0.554620i
$823$	−236.754	+	136.690i	−0.287672	+	0.166088i	−0.636892	−	0.770953i	$-0.719780\pi$
$823$	−236.754	+	136.690i	−0.287672	+	0.166088i	0.349219	+	0.937041i	$0.386447\pi$
$824$	368.073	+	212.507i	0.446691	+	0.257897i
$825$	147.144	−	516.426i	0.178356	−	0.625971i
$826$	0.924238	+	828.638i	0.00111893	+	1.00319i
$827$	−679.547			−0.821701			−0.410850	−	0.911703i	$-0.634768\pi$
$827$	−679.547			−0.821701			−0.410850	+	0.911703i	$0.634768\pi$
$828$	205.792	+	49.7657i	0.248541	+	0.0601035i
$829$	−536.469	−	929.192i	−0.647128	−	1.12086i	−0.983806	−	0.179239i	$-0.942637\pi$
$829$	−536.469	−	929.192i	−0.647128	−	1.12086i	0.336678	−	0.941620i	$-0.390697\pi$
$830$	−620.533	−	727.918i	−0.747630	−	0.877010i
$831$	405.728	+	946.510i	0.488240	+	1.13900i
$832$		−	56.3371i		−	0.0677128i
$833$	59.7177	+	102.903i	0.0716899	+	0.123533i
$834$	386.956	+	289.452i	0.463976	+	0.347065i
$835$	−290.344	+	817.494i	−0.347718	+	0.979034i
$836$	299.153	−	172.716i	0.357838	−	0.206598i
$837$	−538.080	+	91.0879i	−0.642868	+	0.108827i
$838$	230.232	+	132.925i	0.274740	+	0.158621i
$839$			1354.96i			1.61497i	0.589885	+	0.807487i	$0.299173\pi$
$839$			1354.96i			1.61497i	−0.589885	+	0.807487i	$0.700827\pi$
$840$	266.274	+	131.523i	0.316992	+	0.156575i
$841$	763.975			0.908413
$842$	−196.819	+	340.900i	−0.233751	+	0.404869i
$843$	41.1892	+	4.90955i	0.0488603	+	0.00582390i
$844$	−85.1155	−	147.424i	−0.100848	−	0.174673i
$845$	−199.819	+	562.611i	−0.236472	+	0.665812i
$846$	318.525	+	1081.88i	0.376507	+	1.27882i
$847$	243.612	−	423.038i	0.287618	−	0.499454i
$848$	78.2858			0.0923182
$849$	−491.257	−	1146.04i	−0.578631	−	1.34987i
$850$	66.6142	+	54.1482i	0.0783696	+	0.0637038i
$851$	−567.780	+	327.808i	−0.667192	+	0.385204i
$852$	297.226	+	693.390i	0.348857	+	0.813838i
$853$		−	447.622i		−	0.524762i	−0.964964	−	0.262381i	$-0.915492\pi$
$853$		−	447.622i		−	0.524762i	0.964964	−	0.262381i	$-0.0845077\pi$
$854$	−237.478	−	410.266i	−0.278077	−	0.480405i
$855$	490.331	+	968.496i	0.573486	+	1.13274i
$856$	7.15210	−	12.3878i	0.00835525	−	0.0144717i
$857$	583.427	+	1010.53i	0.680778	+	1.17914i	0.974744	+	0.223326i	$0.0716916\pi$
$857$	583.427	+	1010.53i	0.680778	+	1.17914i	−0.293965	+	0.955816i	$0.594975\pi$
$858$	−25.3181	+	212.409i	−0.0295083	+	0.247563i
$859$	−242.597	+	420.191i	−0.282418	+	0.489163i	−0.971980	−	0.235064i	$-0.924470\pi$
$859$	−242.597	+	420.191i	−0.282418	+	0.489163i	0.689561	+	0.724227i	$0.257803\pi$
$860$	15.6458	+	84.8569i	0.0181928	+	0.0986708i
$861$	1093.36	+	129.086i	1.26987	+	0.149926i
$862$		−	409.102i		−	0.474596i
$863$	476.994	−	826.178i	0.552716	−	0.957333i	−0.445361	−	0.895351i	$-0.646925\pi$
$863$	476.994	−	826.178i	0.552716	−	0.957333i	0.998077	−	0.0619817i	$-0.0197421\pi$
$864$	−150.593	+	25.4928i	−0.174297	+	0.0295055i
$865$	−61.6211	−	72.2848i	−0.0712382	−	0.0835663i
$866$	−692.331	−	399.717i	−0.799458	−	0.461567i
$867$	680.096	+	508.727i	0.784424	+	0.586767i
$868$	141.214	−	245.220i	0.162689	−	0.282512i
$869$			58.6620i			0.0675051i
$870$	−103.162	−	154.980i	−0.118576	−	0.178138i
$871$	445.136	+	770.998i	0.511063	+	0.885187i
$872$	−28.6828	−	49.6800i	−0.0328931	−	0.0569725i
$873$	−259.831	+	1074.45i	−0.297630	+	1.23076i
$874$	−401.280			−0.459130
$875$	−746.823	+	455.940i	−0.853512	+	0.521074i
$876$	−269.894	+	360.810i	−0.308098	+	0.411883i
$877$	636.114	+	367.261i	0.725329	+	0.418769i	0.816711	−	0.577047i	$-0.195795\pi$
$877$	636.114	+	367.261i	0.725329	+	0.418769i	−0.0913816	+	0.995816i	$0.529128\pi$
$878$	−218.523	−	378.493i	−0.248887	−	0.431085i
$879$	40.1619	−	336.943i	0.0456904	−	0.383325i
$880$	−134.937	−	47.9246i	−0.153337	−	0.0544598i
$881$			939.200i			1.06606i	0.846096	+	0.533031i	$0.178947\pi$
$881$			939.200i			1.06606i	−0.846096	+	0.533031i	$0.821053\pi$
$882$	429.042	−	452.642i	0.486443	−	0.513199i
$883$			58.4468i			0.0661911i	0.999452	+	0.0330956i	$0.0105366\pi$
$883$			58.4468i			0.0661911i	−0.999452	+	0.0330956i	$0.989463\pi$
$884$	−29.6161	−	17.0989i	−0.0335024	−	0.0193426i
$885$	1253.03	−	79.9211i	1.41585	−	0.0903063i
$886$	−136.742	−	236.844i	−0.154336	−	0.267318i
$887$	393.337	−	681.280i	0.443446	−	0.768072i	−0.554496	−	0.832186i	$-0.687089\pi$
$887$	393.337	−	681.280i	0.443446	−	0.768072i	0.997943	+	0.0641147i	$0.0204223\pi$
$888$	283.293	−	378.723i	0.319024	−	0.426490i
$889$	−0.473328	−	424.369i	−0.000532427	−	0.477355i
$890$	19.9756	+	108.340i	0.0224445	+	0.121730i
$891$	579.240	−	28.4392i	0.650101	−	0.0319183i
$892$	−615.788	+	355.525i	−0.690345	+	0.398571i
$893$	−1068.75	−	1851.14i	−1.19681	−	2.07294i
$894$	54.0770	+	126.155i	0.0604888	+	0.141113i
$895$	−114.149	−	619.100i	−0.127541	−	0.691732i
$896$	39.5215	−	68.6298i	0.0441088	−	0.0765958i
$897$	148.847	−	198.987i	0.165938	−	0.221836i
$898$	−295.625	−	170.679i	−0.329203	−	0.190066i
$899$	−153.626	+	88.6958i	−0.170885	+	0.0986606i
$900$	173.665	−	415.139i	0.192961	−	0.461266i
$901$	23.7606	−	41.1545i	0.0263713	−	0.0456765i
$902$	−530.838			−0.588512
$903$	179.953	+	21.2460i	0.199284	+	0.0235282i
$904$	−200.352			−0.221628
$905$	232.245	−	653.909i	0.256624	−	0.722552i
$906$	−107.684	+	903.431i	−0.118857	+	0.997165i
$907$	−172.579	+	99.6384i	−0.190274	+	0.109855i	−0.592111	−	0.805856i	$-0.701705\pi$
$907$	−172.579	+	99.6384i	−0.190274	+	0.109855i	0.401837	+	0.915711i	$0.368372\pi$
$908$	322.901	−	559.280i	0.355617	−	0.615948i
$909$	−485.632	+	142.979i	−0.534248	+	0.157293i
$910$	265.011	−	226.426i	0.291221	−	0.248820i
$911$		−	31.2958i		−	0.0343532i	−0.999852	−	0.0171766i	$-0.994532\pi$
$911$		−	31.2958i		−	0.0343532i	0.999852	−	0.0171766i	$-0.00546775\pi$
$912$	266.065	−	114.050i	0.291738	−	0.125055i
$913$	838.755	−	484.256i	0.918680	−	0.530400i
$914$	7.76461	−	4.48290i	0.00849520	−	0.00490471i
$915$	−597.926	+	398.006i	−0.653471	+	0.434979i
$916$	295.989			0.323132
$917$	579.492	+	333.709i	0.631944	+	0.363914i
$918$	−32.3050	+	86.9031i	−0.0351906	+	0.0946657i
$919$	784.863	−	1359.42i	0.854040	−	1.47924i	−0.0234927	−	0.999724i	$-0.507479\pi$
$919$	784.863	−	1359.42i	0.854040	−	1.47924i	0.877533	−	0.479517i	$-0.159188\pi$
$920$	107.915	+	126.591i	0.117299	+	0.137598i
$921$	−612.689	−	73.0294i	−0.665243	−	0.0792936i
$922$	77.1981	+	44.5704i	0.0837290	+	0.0483410i
$923$	885.441			0.959308
$924$	−179.852	+	240.996i	−0.194644	+	0.260818i
$925$	496.953	+	1301.83i	0.537247	+	1.40738i
$926$	−209.238	−	120.804i	−0.225959	−	0.130458i
$927$	−979.449	−	932.541i	−1.05658	−	1.00598i
$928$	−42.9952	+	24.8233i	−0.0463311	+	0.0267492i
$929$	1359.58	+	784.952i	1.46349	+	0.844943i	0.999170	−	0.0407268i	$-0.0129673\pi$
$929$	1359.58	+	784.952i	1.46349	+	0.844943i	0.464315	+	0.885670i	$0.346301\pi$
$930$	−384.219	−	190.315i	−0.413139	−	0.204639i
$931$	−588.734	+	1024.99i	−0.632367	+	1.10096i
$932$	512.441			0.549829
$933$	−212.334	−	495.347i	−0.227582	−	0.530918i
$934$	170.540	+	295.384i	0.182591	+	0.316257i
$935$	−66.1484	+	56.3900i	−0.0707470	+	0.0603101i
$936$	−42.1359	+	174.241i	−0.0450170	+	0.186155i
$937$		−	1487.98i		−	1.58803i	−0.607901	−	0.794013i	$-0.707988\pi$
$937$		−	1487.98i		−	1.58803i	0.607901	−	0.794013i	$-0.292012\pi$
$938$	1.39589	+	1251.50i	0.00148815	+	1.33422i
$939$	430.111	−	574.998i	0.458052	−	0.612352i
$940$	−296.554	+	834.979i	−0.315483	+	0.888276i
$941$	−444.759	+	256.782i	−0.472645	+	0.272882i	−0.717346	−	0.696717i	$-0.754643\pi$
$941$	−444.759	+	256.782i	−0.472645	+	0.272882i	0.244702	+	0.969598i	$0.421310\pi$
$942$	−521.441	−	62.1532i	−0.553547	−	0.0659800i
$943$	534.045	+	308.331i	0.566325	+	0.326968i
$944$		−	334.821i		−	0.354683i
$945$	−725.170	−	605.932i	−0.767376	−	0.641198i
$946$	−87.3691			−0.0923563
$947$	537.505	−	930.985i	0.567587	−	0.983089i	−0.429217	−	0.903201i	$-0.641210\pi$
$947$	537.505	−	930.985i	0.567587	−	0.983089i	0.996804	−	0.0798878i	$-0.0254562\pi$
$948$	−5.81843	+	48.8144i	−0.00613758	+	0.0514920i
$949$	264.423	+	457.994i	0.278633	+	0.482607i
$950$	−134.985	+	842.135i	−0.142089	+	0.886458i
$951$	805.502	+	602.533i	0.847005	+	0.633578i
$952$	−24.0832	−	41.6061i	−0.0252975	−	0.0437039i
$953$	−1252.50			−1.31427			−0.657133	−	0.753774i	$-0.728231\pi$
$953$	−1252.50			−1.31427			−0.657133	+	0.753774i	$0.728231\pi$
$954$	−242.125	−	58.5520i	−0.253800	−	0.0613752i
$955$	−986.515	+	840.980i	−1.03300	+	0.880608i
$956$	147.277	−	85.0303i	0.154055	−	0.0889438i
$957$	173.262	−	74.2698i	0.181047	−	0.0776069i
$958$		−	155.079i		−	0.161878i
$959$	379.490	+	655.607i	0.395715	+	0.683636i
$960$	−107.531	−	53.2633i	−0.112012	−	0.0554826i
$961$	276.229	−	478.442i	0.287439	−	0.497859i
$962$	−277.551	−	480.732i	−0.288514	−	0.499721i
$963$	−31.3854	+	32.9641i	−0.0325912	+	0.0342307i
$964$	369.003	−	639.132i	0.382783	−	0.662999i
$965$	147.582	+	800.429i	0.152935	+	0.829460i
$966$	320.918	−	137.987i	0.332213	−	0.142844i
$967$			1694.07i			1.75188i	0.482420	+	0.875940i	$0.339758\pi$
$967$			1694.07i			1.75188i	−0.482420	+	0.875940i	$0.660242\pi$
$968$	−98.6248	+	170.823i	−0.101885	+	0.176470i
$969$	20.7977	−	174.484i	0.0214630	−	0.180066i
$970$	−660.939	+	563.435i	−0.681381	+	0.580861i
$971$	1127.86	+	651.170i	1.16154	+	0.670618i	0.951674	−	0.307111i	$-0.0993622\pi$
$971$	1127.86	+	651.170i	1.16154	+	0.670618i	0.209871	+	0.977729i	$0.432696\pi$
$972$	484.824	+	33.7872i	0.498790	+	0.0347605i
$973$	797.299	−	0.889283i	0.819424	−	0.000913960i
$974$			922.505i			0.947131i
$975$	−367.529	−	379.309i	−0.376953	−	0.389035i
$976$	95.7705	+	165.879i	0.0981255	+	0.169958i
$977$	−287.292	−	497.605i	−0.294056	−	0.509319i	0.680709	−	0.732554i	$-0.261672\pi$
$977$	−287.292	−	497.605i	−0.294056	−	0.509319i	−0.974765	+	0.223235i	$0.928338\pi$
$978$	−296.117	−	690.803i	−0.302778	−	0.706342i
$979$	−111.547			−0.113940
$980$	481.678	−	89.9228i	0.491508	−	0.0917579i
$981$	51.5540	+	175.104i	0.0525525	+	0.178496i
$982$	−216.683	−	125.102i	−0.220655	−	0.127395i
$983$	619.075	+	1072.27i	0.629781	+	1.09081i	0.987595	+	0.157021i	$0.0501889\pi$
$983$	619.075	+	1072.27i	0.629781	+	1.09081i	−0.357814	+	0.933793i	$0.616478\pi$
$984$	−441.726	−	52.6515i	−0.448909	−	0.0535076i
$985$	385.937	−	1086.65i	0.391815	−	1.10319i
$986$			30.1365i			0.0305644i
$987$	1491.27	+	1112.91i	1.51091	+	1.12757i
$988$		−	339.758i		−	0.343885i
$989$	87.8969	+	50.7473i	0.0888746	+	0.0513117i
$990$	381.492	+	249.145i	0.385346	+	0.251662i
$991$	−262.675	−	454.967i	−0.265061	−	0.459098i	0.702519	−	0.711665i	$-0.252059\pi$
$991$	−262.675	−	454.967i	−0.265061	−	0.459098i	−0.967579	+	0.252567i	$0.918725\pi$
$992$	−57.1694	+	99.0203i	−0.0576304	+	0.0998189i
$993$	182.604	+	136.592i	0.183892	+	0.137555i
$994$	1078.64	+	621.153i	1.08516	+	0.624902i
$995$	−1362.12	+	251.147i	−1.36897	+	0.252409i
$996$	745.985	−	319.771i	0.748981	−	0.321055i
$997$	−7.87841	+	4.54860i	−0.00790211	+	0.00456229i	−0.503946	−	0.863735i	$-0.668119\pi$
$997$	−7.87841	+	4.54860i	−0.00790211	+	0.00456229i	0.496044	+	0.868298i	$0.334786\pi$
$998$	152.482	+	264.106i	0.152787	+	0.264635i
$999$	−1159.43	+	959.444i	−1.16059	+	0.960404i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.q.a.149.8	✓	64
3.2	odd	2	inner	210.3.q.a.149.19	yes	64
5.4	even	2	inner	210.3.q.a.149.25	yes	64
7.4	even	3	inner	210.3.q.a.179.14	yes	64
15.14	odd	2	inner	210.3.q.a.149.14	yes	64
21.11	odd	6	inner	210.3.q.a.179.25	yes	64
35.4	even	6	inner	210.3.q.a.179.19	yes	64
105.74	odd	6	inner	210.3.q.a.179.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.q.a.149.8	✓	64	1.1	even	1	trivial
210.3.q.a.149.14	yes	64	15.14	odd	2	inner
210.3.q.a.149.19	yes	64	3.2	odd	2	inner
210.3.q.a.149.25	yes	64	5.4	even	2	inner
210.3.q.a.179.8	yes	64	105.74	odd	6	inner
210.3.q.a.179.14	yes	64	7.4	even	3	inner
210.3.q.a.179.19	yes	64	35.4	even	6	inner
210.3.q.a.179.25	yes	64	21.11	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-0.355071 + 2.97891i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.67341 + 4.71166i) q^{5} +(-3.39734 - 2.54128i) q^{6} +(-7.00000 + 0.00780758i) q^{7} +2.82843 q^{8} +(-8.74785 - 2.11545i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-0.355071 + 2.97891i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.67341 + 4.71166i) q^{5} +(-3.39734 - 2.54128i) q^{6} +(-7.00000 + 0.00780758i) q^{7} +2.82843 q^{8} +(-8.74785 - 2.11545i) q^{9} +(-4.58730 - 5.38114i) q^{10} +(6.20051 - 3.57986i) q^{11} +(5.51470 - 2.36391i) q^{12} -7.04213i q^{13} +(4.94018 - 8.57873i) q^{14} +(-13.4414 - 6.65792i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(1.21404 + 2.10278i) q^{17} +(8.77655 - 9.21803i) q^{18} +(-12.0616 + 20.8913i) q^{19} +(9.83424 - 1.81323i) q^{20} +(2.46224 - 20.8552i) q^{21} +10.1254i q^{22} +(5.88121 - 10.1866i) q^{23} +(-1.00429 + 8.42564i) q^{24} +(-19.3994 - 15.7691i) q^{25} +(8.62482 + 4.97954i) q^{26} +(9.40786 - 25.3079i) q^{27} +(7.01352 + 12.1165i) q^{28} -8.77636i q^{29} +(17.6588 - 11.7545i) q^{30} +(-10.1062 - 17.5045i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(8.46248 + 19.7419i) q^{33} -3.43383 q^{34} +(11.6771 - 32.9946i) q^{35} +(5.08378 + 17.2672i) q^{36} +(-48.2707 - 27.8691i) q^{37} +(-17.0577 - 29.5448i) q^{38} +(20.9779 + 2.50046i) q^{39} +(-4.73312 + 13.3266i) q^{40} +52.4264i q^{41} +(23.8012 + 17.7624i) q^{42} +8.62872i q^{43} +(-12.4010 - 7.15973i) q^{44} +(24.6060 - 37.6768i) q^{45} +(8.31729 + 14.4060i) q^{46} +(-44.3039 + 76.7366i) q^{47} +(-9.60912 - 7.18783i) q^{48} +(48.9999 - 0.109306i) q^{49} +(33.0305 - 12.6089i) q^{50} +(-6.69507 + 2.86989i) q^{51} +(-12.1973 + 7.04213i) q^{52} +(-9.78573 - 16.9494i) q^{53} +(24.3434 + 29.4177i) q^{54} +(6.49110 + 35.2052i) q^{55} +(-19.7990 + 0.0220832i) q^{56} +(-57.9507 - 43.3484i) q^{57} +(10.7488 + 6.20583i) q^{58} +(-72.4908 + 41.8526i) q^{59} +(1.90959 + 29.9392i) q^{60} +(23.9426 - 41.4698i) q^{61} +28.5847 q^{62} +(61.2514 + 14.7399i) q^{63} +8.00000 q^{64} +(33.1801 + 11.7844i) q^{65} +(-30.1626 - 3.59523i) q^{66} +(-109.484 + 63.2103i) q^{67} +(2.42808 - 4.20556i) q^{68} +(28.2566 + 21.1366i) q^{69} +(32.1531 + 37.6322i) q^{70} +125.735i q^{71} +(-24.7427 - 5.98340i) q^{72} +(-65.0363 + 37.5487i) q^{73} +(68.2651 - 39.4129i) q^{74} +(53.8628 - 52.1900i) q^{75} +48.2465 q^{76} +(-43.3756 + 25.1074i) q^{77} +(-17.8960 + 23.9245i) q^{78} +(-4.09666 + 7.09562i) q^{79} +(-12.9748 - 15.2202i) q^{80} +(72.0497 + 37.0113i) q^{81} +(-64.2090 - 37.0711i) q^{82} +135.272 q^{83} +(-38.5844 + 16.5904i) q^{84} +(-11.9392 + 2.20133i) q^{85} +(-10.5680 - 6.10143i) q^{86} +(26.1440 + 3.11623i) q^{87} +(17.5377 - 10.1254i) q^{88} +(-13.4925 - 7.78991i) q^{89} +(28.7454 + 56.7776i) q^{90} +(0.0549820 + 49.2949i) q^{91} -23.5248 q^{92} +(55.7328 - 23.8902i) q^{93} +(-62.6552 - 108.522i) q^{94} +(-78.2487 - 91.7899i) q^{95} +(15.5979 - 6.68615i) q^{96} -122.825i q^{97} +(-34.5143 + 60.0896i) q^{98} +(-61.8141 + 18.1992i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) \) 64 * q - 64 * q^4 + 8 * q^6 - 4 * q^9	\( 64 q - 64 q^{4} + 8 q^{6} - 4 q^{9} - 8 q^{10} + 4 q^{15} - 128 q^{16} + 8 q^{19} - 88 q^{21} - 8 q^{24} + 12 q^{25} - 8 q^{30} + 152 q^{31} + 16 q^{36} - 208 q^{39} - 16 q^{40} + 106 q^{45} - 56 q^{46} - 64 q^{49} - 140 q^{51} - 56 q^{54} + 616 q^{55} - 4 q^{60} + 104 q^{61} + 512 q^{64} - 160 q^{66} + 456 q^{69} - 144 q^{70} + 298 q^{75} - 32 q^{76} - 360 q^{79} + 304 q^{81} - 80 q^{84} - 408 q^{85} - 688 q^{90} - 288 q^{91} + 240 q^{94} - 16 q^{96} - 568 q^{99}+O(q^{100}) \) 64 * q - 64 * q^4 + 8 * q^6 - 4 * q^9 - 8 * q^10 + 4 * q^15 - 128 * q^16 + 8 * q^19 - 88 * q^21 - 8 * q^24 + 12 * q^25 - 8 * q^30 + 152 * q^31 + 16 * q^36 - 208 * q^39 - 16 * q^40 + 106 * q^45 - 56 * q^46 - 64 * q^49 - 140 * q^51 - 56 * q^54 + 616 * q^55 - 4 * q^60 + 104 * q^61 + 512 * q^64 - 160 * q^66 + 456 * q^69 - 144 * q^70 + 298 * q^75 - 32 * q^76 - 360 * q^79 + 304 * q^81 - 80 * q^84 - 408 * q^85 - 688 * q^90 - 288 * q^91 + 240 * q^94 - 16 * q^96 - 568 * q^99

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