LMFDB - Embedded newform 289.3.e.q.249.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,3,Mod(40,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([15]))

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

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

chi := DirichletCharacter("289.40");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	289.e (of order $16$, degree $8$, 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:	$7.87467964001$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			249.3
Character	$\chi$	$=$	289.249
Dual form			289.3.e.q.65.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09461 - 0.453400i) q^{2} +(-1.09032 - 5.48139i) q^{3} +(-1.83584 - 1.83584i) q^{4} +(0.173703 + 0.116065i) q^{5} +(-1.29180 + 6.49431i) q^{6} +(-3.34395 + 2.23436i) q^{7} +(2.99075 + 7.22031i) q^{8} +(-20.5419 + 8.50875i) q^{9} +O(q^{10})$	\(q+(-1.09461 - 0.453400i) q^{2} +(-1.09032 - 5.48139i) q^{3} +(-1.83584 - 1.83584i) q^{4} +(0.173703 + 0.116065i) q^{5} +(-1.29180 + 6.49431i) q^{6} +(-3.34395 + 2.23436i) q^{7} +(2.99075 + 7.22031i) q^{8} +(-20.5419 + 8.50875i) q^{9} +(-0.137513 - 0.205802i) q^{10} +(9.64051 + 1.91762i) q^{11} +(-8.06130 + 12.0646i) q^{12} +(-6.06272 + 6.06272i) q^{13} +(4.67337 - 0.929590i) q^{14} +(0.446804 - 1.07868i) q^{15} +1.12567i q^{16} +26.3432 q^{18} +(-16.0096 - 6.63138i) q^{19} +(-0.105815 - 0.531967i) q^{20} +(15.8933 + 15.8933i) q^{21} +(-9.68310 - 6.47004i) q^{22} +(2.94549 - 14.8080i) q^{23} +(36.3165 - 24.2659i) q^{24} +(-9.55038 - 23.0567i) q^{25} +(9.38512 - 3.88745i) q^{26} +(41.0923 + 61.4990i) q^{27} +(10.2409 + 2.03704i) q^{28} +(-9.52069 + 14.2487i) q^{29} +(-0.978149 + 0.978149i) q^{30} +(14.1967 - 2.82389i) q^{31} +(12.4734 - 30.1134i) q^{32} -54.9342i q^{33} -0.840185 q^{35} +(53.3323 + 22.0910i) q^{36} +(10.2391 + 51.4755i) q^{37} +(14.5175 + 14.5175i) q^{38} +(39.8424 + 26.6218i) q^{39} +(-0.318520 + 1.60131i) q^{40} +(-7.93493 + 5.30195i) q^{41} +(-10.1909 - 24.6030i) q^{42} +(0.301889 - 0.125047i) q^{43} +(-14.1780 - 21.2188i) q^{44} +(-4.55576 - 0.906197i) q^{45} +(-9.93809 + 14.8734i) q^{46} +(-35.1236 + 35.1236i) q^{47} +(6.17022 - 1.22733i) q^{48} +(-12.5618 + 30.3269i) q^{49} +29.5681i q^{50} +22.2603 q^{52} +(-66.5792 - 27.5780i) q^{53} +(-17.0962 - 85.9484i) q^{54} +(1.45202 + 1.45202i) q^{55} +(-26.1337 - 17.4620i) q^{56} +(-18.8937 + 94.9850i) q^{57} +(16.8818 - 11.2800i) q^{58} +(26.9981 + 65.1792i) q^{59} +(-2.80054 + 1.16002i) q^{60} +(-43.5673 - 65.2030i) q^{61} +(-16.8201 - 3.34573i) q^{62} +(49.6796 - 74.3508i) q^{63} +(-24.1230 + 24.1230i) q^{64} +(-1.75678 + 0.349445i) q^{65} +(-24.9072 + 60.1313i) q^{66} +84.8560i q^{67} -84.3798 q^{69} +(0.919671 + 0.380940i) q^{70} +(-3.67771 - 18.4891i) q^{71} +(-122.872 - 122.872i) q^{72} +(16.6405 + 11.1188i) q^{73} +(12.1312 - 60.9878i) q^{74} +(-115.970 + 77.4884i) q^{75} +(17.2168 + 41.5651i) q^{76} +(-36.5220 + 15.1279i) q^{77} +(-31.5414 - 47.2050i) q^{78} +(86.0035 + 17.1072i) q^{79} +(-0.130650 + 0.195532i) q^{80} +(150.797 - 150.797i) q^{81} +(11.0895 - 2.20584i) q^{82} +(19.1173 - 46.1534i) q^{83} -58.3552i q^{84} -0.387146 q^{86} +(88.4834 + 36.6510i) q^{87} +(14.9866 + 75.3426i) q^{88} +(37.5364 + 37.5364i) q^{89} +(4.57589 + 3.05751i) q^{90} +(6.72716 - 33.8197i) q^{91} +(-32.5925 + 21.7776i) q^{92} +(-30.9577 - 74.7386i) q^{93} +(54.3716 - 22.5214i) q^{94} +(-2.01124 - 3.01004i) q^{95} +(-178.663 - 35.5383i) q^{96} +(15.3846 - 23.0248i) q^{97} +(27.5005 - 27.5005i) q^{98} +(-214.351 + 42.6371i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 432 q^{18} + 144 q^{35} - 720 q^{52} - 432 q^{69}+O(q^{100}) $ 48 * q + 432 * q^18 + 144 * q^35 - 720 * q^52 - 432 * q^69

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{16}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.09461	−	0.453400i	−0.547303	−	0.226700i	0.0918597	−	0.995772i	$-0.470719\pi$
$2$	−1.09461	−	0.453400i	−0.547303	−	0.226700i	−0.639162	+	0.769072i	$0.720719\pi$
$3$	−1.09032	−	5.48139i	−0.363439	−	1.82713i	−0.538565	−	0.842584i	$-0.681033\pi$
$3$	−1.09032	−	5.48139i	−0.363439	−	1.82713i	0.175126	−	0.984546i	$-0.443967\pi$
$4$	−1.83584	−	1.83584i	−0.458959	−	0.458959i
$5$	0.173703	+	0.116065i	0.0347406	+	0.0232129i	0.572819	−	0.819682i	$-0.305850\pi$
$5$	0.173703	+	0.116065i	0.0347406	+	0.0232129i	−0.538079	+	0.842895i	$0.680850\pi$
$6$	−1.29180	+	6.49431i	−0.215300	+	1.08238i
$7$	−3.34395	+	2.23436i	−0.477707	+	0.319194i	−0.771007	−	0.636827i	$-0.780247\pi$
$7$	−3.34395	+	2.23436i	−0.477707	+	0.319194i	0.293300	+	0.956021i	$0.405247\pi$
$8$	2.99075	+	7.22031i	0.373844	+	0.902539i
$9$	−20.5419	+	8.50875i	−2.28244	+	0.945416i
$10$	−0.137513	−	0.205802i	−0.0137513	−	0.0205802i
$11$	9.64051	+	1.91762i	0.876410	+	0.174329i	0.612740	−	0.790284i	$-0.290067\pi$
$11$	9.64051	+	1.91762i	0.876410	+	0.174329i	0.263669	+	0.964613i	$0.415067\pi$
$12$	−8.06130	+	12.0646i	−0.671775	+	1.00538i
$13$	−6.06272	+	6.06272i	−0.466363	+	0.466363i	−0.900734	−	0.434371i	$-0.856971\pi$
$13$	−6.06272	+	6.06272i	−0.466363	+	0.466363i	0.434371	+	0.900734i	$0.356971\pi$
$14$	4.67337	−	0.929590i	0.333812	−	0.0663993i
$15$	0.446804	−	1.07868i	0.0297870	−	0.0719121i
$16$			1.12567i			0.0703542i
$17$		0			0
$17$		0			0
$18$	26.3432			1.46351
$19$	−16.0096	−	6.63138i	−0.842609	−	0.349020i	−0.0807271	−	0.996736i	$-0.525724\pi$
$19$	−16.0096	−	6.63138i	−0.842609	−	0.349020i	−0.761882	+	0.647716i	$0.775724\pi$
$20$	−0.105815	−	0.531967i	−0.00529074	−	0.0265983i
$21$	15.8933	+	15.8933i	0.756826	+	0.756826i
$22$	−9.68310	−	6.47004i	−0.440141	−	0.294093i
$23$	2.94549	−	14.8080i	0.128065	−	0.643825i	−0.862419	−	0.506195i	$-0.831052\pi$
$23$	2.94549	−	14.8080i	0.128065	−	0.643825i	0.990484	−	0.137630i	$-0.0439485\pi$
$24$	36.3165	−	24.2659i	1.51319	−	1.01108i
$25$	−9.55038	−	23.0567i	−0.382015	−	0.922267i
$26$	9.38512	−	3.88745i	0.360966	−	0.149517i
$27$	41.0923	+	61.4990i	1.52194	+	2.27774i
$28$	10.2409	+	2.03704i	0.365745	+	0.0727513i
$29$	−9.52069	+	14.2487i	−0.328300	+	0.491335i	−0.958498	−	0.285099i	$-0.907974\pi$
$29$	−9.52069	+	14.2487i	−0.328300	+	0.491335i	0.630198	+	0.776434i	$0.282974\pi$
$30$	−0.978149	+	0.978149i	−0.0326050	+	0.0326050i
$31$	14.1967	−	2.82389i	0.457957	−	0.0910934i	0.0392796	−	0.999228i	$-0.487494\pi$
$31$	14.1967	−	2.82389i	0.457957	−	0.0910934i	0.418678	+	0.908135i	$0.362494\pi$
$32$	12.4734	−	30.1134i	0.389793	−	0.941044i
$33$		−	54.9342i		−	1.66467i
$34$		0			0
$35$	−0.840185			−0.0240053
$36$	53.3323	+	22.0910i	1.48145	+	0.613638i
$37$	10.2391	+	51.4755i	0.276733	+	1.39123i	0.829785	+	0.558084i	$0.188463\pi$
$37$	10.2391	+	51.4755i	0.276733	+	1.39123i	−0.553052	+	0.833147i	$0.686537\pi$
$38$	14.5175	+	14.5175i	0.382039	+	0.382039i
$39$	39.8424	+	26.6218i	1.02160	+	0.682611i
$40$	−0.318520	+	1.60131i	−0.00796301	+	0.0400328i
$41$	−7.93493	+	5.30195i	−0.193535	+	0.129316i	−0.648562	−	0.761162i	$-0.724629\pi$
$41$	−7.93493	+	5.30195i	−0.193535	+	0.129316i	0.455028	+	0.890477i	$0.349629\pi$
$42$	−10.1909	−	24.6030i	−0.242640	−	0.585786i
$43$	0.301889	−	0.125047i	0.00702068	−	0.00290806i	−0.379170	−	0.925327i	$-0.623791\pi$
$43$	0.301889	−	0.125047i	0.00702068	−	0.00290806i	0.386191	+	0.922419i	$0.373791\pi$
$44$	−14.1780	−	21.2188i	−0.322227	−	0.482246i
$45$	−4.55576	−	0.906197i	−0.101239	−	0.0201377i
$46$	−9.93809	+	14.8734i	−0.216045	+	0.323335i
$47$	−35.1236	+	35.1236i	−0.747311	+	0.747311i	−0.973973	−	0.226662i	$-0.927219\pi$
$47$	−35.1236	+	35.1236i	−0.747311	+	0.747311i	0.226662	+	0.973973i	$0.427219\pi$
$48$	6.17022	−	1.22733i	0.128546	−	0.0255694i
$49$	−12.5618	+	30.3269i	−0.256364	+	0.618917i
$50$			29.5681i			0.591362i
$51$		0			0
$52$	22.2603			0.428083
$53$	−66.5792	−	27.5780i	−1.25621	−	0.520340i	−0.347466	−	0.937692i	$-0.612958\pi$
$53$	−66.5792	−	27.5780i	−1.25621	−	0.520340i	−0.908745	+	0.417353i	$0.862958\pi$
$54$	−17.0962	−	85.9484i	−0.316596	−	1.59164i
$55$	1.45202	+	1.45202i	0.0264003	+	0.0264003i
$56$	−26.1337	−	17.4620i	−0.466673	−	0.311821i
$57$	−18.8937	+	94.9850i	−0.331468	+	1.66640i
$58$	16.8818	−	11.2800i	0.291065	−	0.194484i
$59$	26.9981	+	65.1792i	0.457595	+	1.10473i	0.969368	+	0.245611i	$0.0789887\pi$
$59$	26.9981	+	65.1792i	0.457595	+	1.10473i	−0.511773	+	0.859120i	$0.671011\pi$
$60$	−2.80054	+	1.16002i	−0.0466757	+	0.0193337i
$61$	−43.5673	−	65.2030i	−0.714218	−	1.06890i	−0.994058	−	0.108856i	$-0.965281\pi$
$61$	−43.5673	−	65.2030i	−0.714218	−	1.06890i	0.279840	−	0.960047i	$-0.409719\pi$
$62$	−16.8201	−	3.34573i	−0.271292	−	0.0539634i
$63$	49.6796	−	74.3508i	0.788566	−	1.18017i
$64$	−24.1230	+	24.1230i	−0.376922	+	0.376922i
$65$	−1.75678	+	0.349445i	−0.0270274	+	0.00537608i
$66$	−24.9072	+	60.1313i	−0.377382	+	0.911080i
$67$			84.8560i			1.26651i	0.773945	+	0.633253i	$0.218281\pi$
$67$			84.8560i			1.26651i	−0.773945	+	0.633253i	$0.781719\pi$
$68$		0			0
$69$	−84.3798			−1.22290
$70$	0.919671	+	0.380940i	0.0131382	+	0.00544200i
$71$	−3.67771	−	18.4891i	−0.0517988	−	0.260410i	0.946205	−	0.323569i	$-0.104883\pi$
$71$	−3.67771	−	18.4891i	−0.0517988	−	0.260410i	−0.998004	+	0.0631585i	$0.979883\pi$
$72$	−122.872	−	122.872i	−1.70655	−	1.70655i
$73$	16.6405	+	11.1188i	0.227952	+	0.152312i	0.664302	−	0.747465i	$-0.268729\pi$
$73$	16.6405	+	11.1188i	0.227952	+	0.152312i	−0.436350	+	0.899777i	$0.643729\pi$
$74$	12.1312	−	60.9878i	0.163936	−	0.824160i
$75$	−115.970	+	77.4884i	−1.54626	+	1.03318i
$76$	17.2168	+	41.5651i	0.226537	+	0.546909i
$77$	−36.5220	+	15.1279i	−0.474312	+	0.196466i
$78$	−31.5414	−	47.2050i	−0.404376	−	0.605192i
$79$	86.0035	+	17.1072i	1.08865	+	0.216546i	0.706613	−	0.707600i	$-0.250222\pi$
$79$	86.0035	+	17.1072i	1.08865	+	0.216546i	0.382038	+	0.924146i	$0.375222\pi$
$80$	−0.130650	+	0.195532i	−0.00163313	+	0.00244415i
$81$	150.797	−	150.797i	1.86170	−	1.86170i
$82$	11.0895	−	2.20584i	0.135238	−	0.0269005i
$83$	19.1173	−	46.1534i	0.230329	−	0.556065i	−0.765887	−	0.642976i	$-0.777700\pi$
$83$	19.1173	−	46.1534i	0.230329	−	0.556065i	0.996216	+	0.0869111i	$0.0276996\pi$
$84$		−	58.3552i		−	0.694705i
$85$		0			0
$86$	−0.387146			−0.00450169
$87$	88.4834	+	36.6510i	1.01705	+	0.421276i
$88$	14.9866	+	75.3426i	0.170302	+	0.856165i
$89$	37.5364	+	37.5364i	0.421757	+	0.421757i	0.885808	−	0.464051i	$-0.153605\pi$
$89$	37.5364	+	37.5364i	0.421757	+	0.421757i	−0.464051	+	0.885808i	$0.653605\pi$
$90$	4.57589	+	3.05751i	0.0508432	+	0.0339724i
$91$	6.72716	−	33.8197i	0.0739248	−	0.371645i
$92$	−32.5925	+	21.7776i	−0.354266	+	0.236713i
$93$	−30.9577	−	74.7386i	−0.332879	−	0.803641i
$94$	54.3716	−	22.5214i	0.578421	−	0.239590i
$95$	−2.01124	−	3.01004i	−0.0211710	−	0.0316846i
$96$	−178.663	−	35.5383i	−1.86108	−	0.370191i
$97$	15.3846	−	23.0248i	0.158605	−	0.237369i	−0.743653	−	0.668566i	$-0.766909\pi$
$97$	15.3846	−	23.0248i	0.158605	−	0.237369i	0.902258	+	0.431197i	$0.141909\pi$
$98$	27.5005	−	27.5005i	0.280617	−	0.280617i
$99$	−214.351	+	42.6371i	−2.16516	+	0.430678i
$100$	−24.7953	+	59.8613i	−0.247953	+	0.598613i
$101$			114.575i			1.13441i	0.823578	+	0.567204i	$0.191975\pi$
$101$			114.575i			1.13441i	−0.823578	+	0.567204i	$0.808025\pi$
$102$		0			0
$103$	−78.8225			−0.765267			−0.382633	−	0.923900i	$-0.624983\pi$
$103$	−78.8225			−0.765267			−0.382633	+	0.923900i	$0.624983\pi$
$104$	−61.9068	−	25.6426i	−0.595258	−	0.246564i
$105$	0.916067	+	4.60538i	0.00872445	+	0.0438608i
$106$	60.3741	+	60.3741i	0.569567	+	0.569567i
$107$	−152.012	−	101.571i	−1.42067	−	0.949263i	−0.999098	−	0.0424697i	$-0.986477\pi$
$107$	−152.012	−	101.571i	−1.42067	−	0.949263i	−0.421575	−	0.906794i	$-0.638523\pi$
$108$	37.4634	−	188.341i	0.346883	−	1.74390i
$109$	126.102	−	84.2589i	1.15690	−	0.773018i	0.179366	−	0.983782i	$-0.442595\pi$
$109$	126.102	−	84.2589i	1.15690	−	0.773018i	0.977537	+	0.210765i	$0.0675955\pi$
$110$	−0.931041	−	2.24773i	−0.00846401	−	0.0204339i
$111$	270.994	−	112.249i	2.44138	−	1.01125i
$112$	−2.51514	−	3.76418i	−0.0224566	−	0.0336087i
$113$	−110.088	−	21.8978i	−0.974228	−	0.193786i	−0.317786	−	0.948162i	$-0.602939\pi$
$113$	−110.088	−	21.8978i	−0.974228	−	0.193786i	−0.656442	+	0.754377i	$0.727939\pi$
$114$	63.7474	−	95.4047i	0.559187	−	0.836883i
$115$	2.23032	−	2.23032i	0.0193941	−	0.0193941i
$116$	43.6368	−	8.67990i	0.376179	−	0.0748267i
$117$	72.9538	−	176.126i	0.623537	−	1.50535i
$118$		−	83.5864i		−	0.708360i
$119$		0			0
$120$	9.12469			0.0760391
$121$	−22.5273	−	9.33112i	−0.186176	−	0.0771167i
$122$	18.1259	+	91.1250i	0.148573	+	0.746927i
$123$	37.7136	+	37.7136i	0.306615	+	0.306615i
$124$	−31.2470	−	20.8786i	−0.251992	−	0.168376i
$125$	2.03605	−	10.2359i	0.0162884	−	0.0818872i
$126$	−88.0903	+	58.8601i	−0.699129	+	0.467143i
$127$	7.70528	+	18.6022i	0.0606715	+	0.146474i	0.951308	−	0.308242i	$-0.0997407\pi$
$127$	7.70528	+	18.6022i	0.0606715	+	0.146474i	−0.890636	+	0.454716i	$0.849741\pi$
$128$	−83.1111	+	34.4257i	−0.649305	+	0.268951i
$129$	−1.01458	−	1.51843i	−0.00786499	−	0.0117708i
$130$	2.08142	+	0.414020i	0.0160109	+	0.00318477i
$131$	−136.019	+	203.567i	−1.03832	+	1.55395i	−0.223095	+	0.974797i	$0.571616\pi$
$131$	−136.019	+	203.567i	−1.03832	+	1.55395i	−0.815220	+	0.579152i	$0.803384\pi$
$132$	−100.850	+	100.850i	−0.764017	+	0.764017i
$133$	68.3521	−	13.5961i	0.513925	−	0.102226i
$134$	38.4737	−	92.8838i	0.287117	−	0.693163i
$135$			15.4519i			0.114459i
$136$		0			0
$137$	−137.724			−1.00528			−0.502641	−	0.864495i	$-0.667638\pi$
$137$	−137.724			−1.00528			−0.502641	+	0.864495i	$0.667638\pi$
$138$	92.3626	+	38.2578i	0.669294	+	0.277231i
$139$	7.49235	+	37.6666i	0.0539018	+	0.270983i	0.998332	−	0.0577285i	$-0.0183858\pi$
$139$	7.49235	+	37.6666i	0.0539018	+	0.270983i	−0.944431	+	0.328711i	$0.893386\pi$
$140$	1.54244	+	1.54244i	0.0110174	+	0.0110174i
$141$	230.822	+	154.230i	1.63704	+	1.09383i
$142$	−4.35733	+	21.9058i	−0.0306854	+	0.154266i
$143$	−70.0736	+	46.8217i	−0.490025	+	0.327425i
$144$	−9.57802	−	23.1234i	−0.0665140	−	0.160579i
$145$	−3.30755	+	1.37003i	−0.0228107	+	0.00944849i
$146$	−13.1735	−	19.7155i	−0.0902293	−	0.135038i
$147$	179.930	+	35.7903i	1.22401	+	0.243472i
$148$	75.7034	−	113.298i	0.511509	−	0.765528i
$149$	81.5217	−	81.5217i	0.547125	−	0.547125i	−0.378483	−	0.925608i	$-0.623554\pi$
$149$	81.5217	−	81.5217i	0.547125	−	0.547125i	0.925608	+	0.378483i	$0.123554\pi$
$150$	162.074	−	32.2386i	1.08050	−	0.214924i
$151$	−98.9416	+	238.866i	−0.655242	+	1.58189i	0.149826	+	0.988712i	$0.452129\pi$
$151$	−98.9416	+	238.866i	−0.655242	+	1.58189i	−0.805068	+	0.593182i	$0.797871\pi$
$152$		−	135.427i		−	0.890966i
$153$		0			0
$154$	46.8362			0.304131
$155$	2.79376	+	1.15721i	0.0180243	+	0.00746589i
$156$	−24.2708	−	122.018i	−0.155582	−	0.782164i
$157$	−105.070	−	105.070i	−0.669234	−	0.669234i	0.288304	−	0.957539i	$-0.406908\pi$
$157$	−105.070	−	105.070i	−0.669234	−	0.669234i	−0.957539	+	0.288304i	$0.906908\pi$
$158$	−86.3835	−	57.7196i	−0.546731	−	0.365314i
$159$	−78.5734	+	395.015i	−0.494172	+	2.48437i
$160$	5.66177	−	3.78307i	0.0353860	−	0.0236442i
$161$	23.2367	+	56.0984i	0.144328	+	0.348437i
$162$	−233.435	+	96.6921i	−1.44096	+	0.596865i
$163$	51.8325	+	77.5728i	0.317991	+	0.475907i	0.955689	−	0.294380i	$-0.0951130\pi$
$163$	51.8325	+	77.5728i	0.317991	+	0.475907i	−0.637698	+	0.770287i	$0.720113\pi$
$164$	24.3008	+	4.83372i	0.148175	+	0.0294739i
$165$	6.37592	−	9.54223i	0.0386419	−	0.0578317i
$166$	−41.8519	+	41.8519i	−0.252120	+	0.252120i
$167$	−223.764	+	44.5093i	−1.33990	+	0.266523i	−0.812434	−	0.583053i	$-0.801858\pi$
$167$	−223.764	+	44.5093i	−1.33990	+	0.266523i	−0.527467	+	0.849576i	$0.676858\pi$
$168$	−67.2219	+	162.288i	−0.400130	+	0.966000i
$169$			95.4869i			0.565011i
$170$		0			0
$171$	385.292			2.25317
$172$	−0.783784	−	0.324654i	−0.00455689	−	0.00188752i
$173$	−61.3185	−	308.269i	−0.354442	−	1.78190i	−0.587277	−	0.809386i	$-0.699800\pi$
$173$	−61.3185	−	308.269i	−0.354442	−	1.78190i	0.232835	−	0.972516i	$-0.425200\pi$
$174$	−80.2368	−	80.2368i	−0.461131	−	0.461131i
$175$	83.4528	+	55.7614i	0.476873	+	0.318637i
$176$	−2.15860	+	10.8520i	−0.0122648	+	0.0616591i
$177$	327.836	−	219.053i	1.85218	−	1.23759i
$178$	−24.0685	−	58.1066i	−0.135217	−	0.326442i
$179$	−233.411	+	96.6819i	−1.30397	+	0.540122i	−0.923119	−	0.384514i	$-0.874369\pi$
$179$	−233.411	+	96.6819i	−1.30397	+	0.540122i	−0.380851	+	0.924636i	$0.624369\pi$
$180$	6.70001	+	10.0273i	0.0372223	+	0.0557070i
$181$	107.665	+	21.4159i	0.594835	+	0.118320i	0.483322	−	0.875443i	$-0.339430\pi$
$181$	107.665	+	21.4159i	0.594835	+	0.118320i	0.111513	+	0.993763i	$0.464430\pi$
$182$	−22.6975	+	33.9691i	−0.124711	+	0.186644i
$183$	−309.901	+	309.901i	−1.69345	+	1.69345i
$184$	115.727	−	23.0196i	0.628953	−	0.125107i
$185$	−4.19593	+	10.1299i	−0.0226807	+	0.0547560i
$186$			95.8455i			0.515298i
$187$		0			0
$188$	128.963			0.685971
$189$	−274.821	−	113.835i	−1.45408	−	0.602300i
$190$	0.836765	+	4.20670i	0.00440402	+	0.0221405i
$191$	59.1941	+	59.1941i	0.309917	+	0.309917i	0.844877	−	0.534960i	$-0.179673\pi$
$191$	59.1941	+	59.1941i	0.309917	+	0.309917i	−0.534960	+	0.844877i	$0.679673\pi$
$192$	158.529	+	105.926i	0.825673	+	0.551697i
$193$	−10.5281	+	52.9284i	−0.0545498	+	0.274240i	−0.998428	−	0.0560541i	$-0.982148\pi$
$193$	−10.5281	+	52.9284i	−0.0545498	+	0.274240i	0.943878	+	0.330294i	$0.107148\pi$
$194$	−27.2796	+	18.2276i	−0.140616	+	0.0939568i
$195$	3.83089	+	9.24859i	0.0196456	+	0.0474287i
$196$	78.7368	−	32.6139i	0.401718	−	0.166397i
$197$	22.7151	+	33.9955i	0.115305	+	0.172566i	0.884633	−	0.466288i	$-0.154409\pi$
$197$	22.7151	+	33.9955i	0.115305	+	0.172566i	−0.769328	+	0.638854i	$0.779409\pi$
$198$	253.962	+	50.5161i	1.28263	+	0.255132i
$199$	59.3963	−	88.8928i	0.298474	−	0.446698i	−0.651673	−	0.758500i	$-0.725933\pi$
$199$	59.3963	−	88.8928i	0.298474	−	0.446698i	0.950147	+	0.311802i	$0.100933\pi$
$200$	137.913	−	137.913i	0.689567	−	0.689567i
$201$	465.129	−	92.5198i	2.31407	−	0.460298i
$202$	51.9484	−	125.415i	0.257170	−	0.620864i
$203$		−	68.9197i		−	0.339506i
$204$		0			0
$205$	−1.99369			−0.00972532
$206$	86.2795	+	35.7381i	0.418832	+	0.173486i
$207$	65.4913	+	329.247i	0.316383	+	1.59056i
$208$	−6.82460	−	6.82460i	−0.0328106	−	0.0328106i
$209$	−141.624	−	94.6301i	−0.677626	−	0.452775i
$210$	1.08535	−	5.45642i	0.00516833	−	0.0259829i
$211$	−157.891	+	105.499i	−0.748296	+	0.499996i	−0.870293	−	0.492535i	$-0.836070\pi$
$211$	−157.891	+	105.499i	−0.748296	+	0.499996i	0.121996	+	0.992531i	$0.461070\pi$
$212$	71.5998	+	172.857i	0.337735	+	0.815365i
$213$	−97.3362	+	40.3180i	−0.456977	+	0.189286i
$214$	120.341	+	180.103i	0.562340	+	0.841601i
$215$	0.0669525	+	0.0133177i	0.000311407	+	6.19427e-5i
$216$	−321.145	+	480.628i	−1.48678	+	2.22513i
$217$	−41.1634	+	41.1634i	−0.189693	+	0.189693i
$218$	−176.235	+	35.0554i	−0.808419	+	0.160805i
$219$	42.8032	−	103.336i	0.195448	−	0.471854i
$220$		−	5.33134i		−	0.0242334i
$221$		0			0
$222$	−347.525			−1.56543
$223$	178.505	+	73.9393i	0.800472	+	0.331566i	0.745145	−	0.666902i	$-0.232380\pi$
$223$	178.505	+	73.9393i	0.800472	+	0.331566i	0.0553262	+	0.998468i	$0.482380\pi$
$224$	25.5737	+	128.568i	0.114168	+	0.573963i
$225$	392.367	+	392.367i	1.74385	+	1.74385i
$226$	110.574	+	73.8833i	0.489266	+	0.326917i
$227$	69.4449	−	349.123i	0.305925	−	1.53799i	−0.455797	−	0.890084i	$-0.650646\pi$
$227$	69.4449	−	349.123i	0.305925	−	1.53799i	0.761722	−	0.647904i	$-0.224354\pi$
$228$	209.063	−	139.691i	0.916942	−	0.612681i
$229$	−100.742	−	243.212i	−0.439920	−	1.06206i	−0.975976	−	0.217879i	$-0.930086\pi$
$229$	−100.742	−	243.212i	−0.439920	−	1.06206i	0.536055	−	0.844183i	$-0.319914\pi$
$230$	−3.45255	+	1.43009i	−0.0150111	+	0.00621780i
$231$	122.743	+	183.697i	0.531353	+	0.795226i
$232$	−131.354	−	26.1280i	−0.566182	−	0.112621i
$233$	−23.0087	+	34.4349i	−0.0987496	+	0.147789i	−0.877554	−	0.479477i	$-0.840826\pi$
$233$	−23.0087	+	34.4349i	−0.0987496	+	0.147789i	0.778805	+	0.627266i	$0.215826\pi$
$234$	−159.711	+	159.711i	−0.682527	+	0.682527i
$235$	−10.1777	+	2.02447i	−0.0433093	+	0.00861476i
$236$	70.0943	−	169.223i	0.297010	−	0.717045i
$237$		−	490.071i		−	2.06781i
$238$		0			0
$239$	255.897			1.07070			0.535348	−	0.844631i	$-0.320180\pi$
$239$	255.897			1.07070			0.535348	+	0.844631i	$0.320180\pi$
$240$	1.21424	+	0.502953i	0.00505932	+	0.00209564i
$241$	−16.6485	−	83.6977i	−0.0690810	−	0.347294i	0.930750	−	0.365655i	$-0.119155\pi$
$241$	−16.6485	−	83.6977i	−0.0690810	−	0.347294i	−0.999831	+	0.0183615i	$0.994155\pi$
$242$	20.4278	+	20.4278i	0.0844123	+	0.0844123i
$243$	−437.505	−	292.332i	−1.80043	−	1.20301i
$244$	−39.7197	+	199.685i	−0.162786	+	0.818380i
$245$	−5.70191	+	3.80990i	−0.0232731	+	0.0155506i
$246$	−24.1822	−	58.3809i	−0.0983015	−	0.237321i
$247$	137.266	−	56.8573i	0.555731	−	0.230192i
$248$	62.8481	+	94.0588i	0.253420	+	0.379270i
$249$	−273.828	−	54.4679i	−1.09971	−	0.218746i
$250$	−6.86963	+	10.2811i	−0.0274785	+	0.0411245i
$251$	195.580	−	195.580i	0.779202	−	0.779202i	−0.200493	−	0.979695i	$-0.564254\pi$
$251$	195.580	−	195.580i	0.779202	−	0.779202i	0.979695	+	0.200493i	$0.0642544\pi$
$252$	−227.700	+	45.2923i	−0.903571	+	0.179731i
$253$	56.7920	−	137.108i	0.224474	−	0.541929i
$254$		−	23.8557i		−	0.0939199i
$255$		0			0
$256$	243.043			0.949386
$257$	−164.451	−	68.1176i	−0.639885	−	0.265049i	0.0390614	−	0.999237i	$-0.487563\pi$
$257$	−164.451	−	68.1176i	−0.639885	−	0.265049i	−0.678947	+	0.734188i	$0.737563\pi$
$258$	0.422111	+	2.12210i	0.00163609	+	0.00822518i
$259$	−149.254	−	149.254i	−0.576270	−	0.576270i
$260$	3.86669	+	2.58364i	0.0148719	+	0.00993707i
$261$	74.3346	−	373.705i	0.284807	−	1.43182i
$262$	241.185	−	161.155i	0.920553	−	0.615094i
$263$	−113.108	−	273.067i	−0.430068	−	1.03828i	−0.979265	−	0.202583i	$-0.935066\pi$
$263$	−113.108	−	273.067i	−0.430068	−	1.03828i	0.549197	−	0.835693i	$-0.314934\pi$
$264$	396.642	−	164.294i	1.50243	−	0.622327i
$265$	−8.36418	−	12.5179i	−0.0315629	−	0.0472373i
$266$	−80.9830	−	16.1085i	−0.304448	−	0.0605584i
$267$	164.825	−	246.678i	0.617323	−	0.923889i
$268$	155.782	−	155.782i	0.581275	−	0.581275i
$269$	−451.802	+	89.8691i	−1.67956	+	0.334086i	−0.940563	−	0.339620i	$-0.889702\pi$
$269$	−451.802	+	89.8691i	−1.67956	+	0.334086i	−0.739000	+	0.673706i	$0.764702\pi$
$270$	7.00591	−	16.9138i	0.0259478	−	0.0626436i
$271$		−	48.9996i		−	0.180810i	−0.995905	−	0.0904051i	$-0.971184\pi$
$271$		−	48.9996i		−	0.180810i	0.995905	−	0.0904051i	$-0.0288162\pi$
$272$		0			0
$273$	−192.714			−0.705911
$274$	150.753	+	62.4440i	0.550194	+	0.227898i
$275$	−47.8567	−	240.592i	−0.174024	−	0.874880i
$276$	154.908	+	154.908i	0.561260	+	0.561260i
$277$	341.857	+	228.421i	1.23414	+	0.824626i	0.989436	−	0.144971i	$-0.0463090\pi$
$277$	341.857	+	228.421i	1.23414	+	0.824626i	0.244705	+	0.969598i	$0.421309\pi$
$278$	8.87688	−	44.6271i	0.0319312	−	0.160529i
$279$	−267.599	+	178.804i	−0.959137	+	0.640875i
$280$	−2.51278	−	6.06639i	−0.00897422	−	0.0216657i
$281$	−299.932	+	124.236i	−1.06737	+	0.442120i	−0.846063	−	0.533083i	$-0.821033\pi$
$281$	−299.932	+	124.236i	−1.06737	+	0.442120i	−0.221310	+	0.975203i	$0.571033\pi$
$282$	−182.731	−	273.476i	−0.647982	−	0.969774i
$283$	−203.123	−	40.4037i	−0.717750	−	0.142769i	−0.177314	−	0.984154i	$-0.556741\pi$
$283$	−203.123	−	40.4037i	−0.717750	−	0.142769i	−0.540436	+	0.841385i	$0.681741\pi$
$284$	−27.1913	+	40.6947i	−0.0957441	+	0.143291i
$285$	−14.3063	+	14.3063i	−0.0501975	+	0.0501975i
$286$	97.9320	−	19.4799i	0.342419	−	0.0681115i
$287$	14.6876	−	35.4589i	0.0511762	−	0.123550i
$288$			724.720i			2.51639i
$289$		0			0
$290$	4.24163			0.0146263
$291$	−142.982	−	59.2250i	−0.491346	−	0.203522i
$292$	−10.1369	−	50.9615i	−0.0347153	−	0.174526i
$293$	−217.944	−	217.944i	−0.743837	−	0.743837i	0.229477	−	0.973314i	$-0.426298\pi$
$293$	−217.944	−	217.944i	−0.743837	−	0.743837i	−0.973314	+	0.229477i	$0.926298\pi$
$294$	−180.725	−	120.757i	−0.614711	−	0.410737i
$295$	−2.87535	+	14.4553i	−0.00974694	+	0.0490012i
$296$	−341.047	+	227.880i	−1.15218	+	0.769865i
$297$	278.219	+	671.681i	0.936765	+	2.26155i
$298$	−126.196	+	52.2721i	−0.423477	+	0.175410i
$299$	71.9189	+	107.634i	0.240531	+	0.359981i
$300$	355.158	+	70.6452i	1.18386	+	0.235484i
$301$	−0.730104	+	1.09268i	−0.00242559	+	0.00363016i
$302$	216.604	−	216.604i	0.717232	−	0.717232i
$303$	628.031	−	124.923i	2.07271	−	0.412288i
$304$	7.46473	−	18.0214i	0.0245550	−	0.0592811i
$305$		−	16.3826i		−	0.0537134i
$306$		0			0
$307$	−314.446			−1.02426			−0.512128	−	0.858909i	$-0.671143\pi$
$307$	−314.446			−1.02426			−0.512128	+	0.858909i	$0.671143\pi$
$308$	94.8209	+	39.2761i	0.307860	+	0.127520i
$309$	85.9414	+	432.057i	0.278127	+	1.39824i
$310$	−2.53338	−	2.53338i	−0.00817221	−	0.00817221i
$311$	52.5786	+	35.1319i	0.169063	+	0.112964i	0.637223	−	0.770679i	$-0.280083\pi$
$311$	52.5786	+	35.1319i	0.169063	+	0.112964i	−0.468160	+	0.883644i	$0.655083\pi$
$312$	−73.0593	+	367.294i	−0.234164	+	1.17722i
$313$	−105.504	+	70.4952i	−0.337072	+	0.225224i	−0.712573	−	0.701597i	$-0.752470\pi$
$313$	−105.504	+	70.4952i	−0.337072	+	0.225224i	0.375501	+	0.926822i	$0.377470\pi$
$314$	67.3713	+	162.649i	0.214558	+	0.517989i
$315$	17.2590	−	7.14892i	0.0547905	−	0.0226950i
$316$	−126.482	−	189.294i	−0.400261	−	0.599033i
$317$	138.258	+	27.5012i	0.436145	+	0.0867546i	0.408279	−	0.912857i	$-0.366129\pi$
$317$	138.258	+	27.5012i	0.436145	+	0.0867546i	0.0278656	+	0.999612i	$0.491129\pi$
$318$	265.107	−	396.761i	0.833670	−	1.24767i
$319$	−119.108	+	119.108i	−0.373379	+	0.373379i
$320$	−6.99007	+	1.39041i	−0.0218440	+	0.00434503i
$321$	−391.010	+	943.982i	−1.21810	+	2.94075i
$322$		−	71.9412i		−	0.223420i
$323$		0			0
$324$	−553.679			−1.70889
$325$	197.687	+	81.8848i	0.608269	+	0.251953i
$326$	−21.5646	−	108.413i	−0.0661491	−	0.332554i
$327$	−599.347	−	599.347i	−1.83287	−	1.83287i
$328$	−62.0131	−	41.4358i	−0.189064	−	0.126329i
$329$	38.9730	−	195.930i	0.118459	−	0.595533i
$330$	−11.3056	+	7.55414i	−0.0342593	+	0.0228913i
$331$	−9.79472	−	23.6466i	−0.0295913	−	0.0714397i	0.908393	−	0.418117i	$-0.137310\pi$
$331$	−9.79472	−	23.6466i	−0.0295913	−	0.0714397i	−0.937984	+	0.346677i	$0.887310\pi$
$332$	−119.826	+	49.6337i	−0.360923	+	0.149499i
$333$	−648.324	−	970.285i	−1.94692	−	2.91377i
$334$	265.113	+	52.7343i	0.793752	+	0.157887i
$335$	−9.84878	+	14.7397i	−0.0293993	+	0.0439992i
$336$	−17.8906	+	17.8906i	−0.0532459	+	0.0532459i
$337$	−354.319	+	70.4785i	−1.05139	+	0.209135i	−0.690396	−	0.723432i	$-0.742564\pi$
$337$	−354.319	+	70.4785i	−1.05139	+	0.209135i	−0.360997	+	0.932567i	$0.617564\pi$
$338$	43.2938	−	104.520i	0.128088	−	0.309232i
$339$			627.309i			1.85047i
$340$		0			0
$341$	142.278			0.417238
$342$	−421.743	−	174.692i	−1.23317	−	0.510794i
$343$	−64.2005	−	322.758i	−0.187174	−	0.940985i
$344$	1.80575	+	1.80575i	0.00524927	+	0.00524927i
$345$	−14.6570	−	9.79351i	−0.0424841	−	0.0283870i
$346$	−72.6497	+	365.235i	−0.209970	+	1.05559i
$347$	−16.6380	+	11.1171i	−0.0479481	+	0.0320379i	−0.579313	−	0.815105i	$-0.696679\pi$
$347$	−16.6380	+	11.1171i	−0.0479481	+	0.0320379i	0.531365	+	0.847143i	$0.321679\pi$
$348$	−95.1558	−	229.726i	−0.273436	−	0.660133i
$349$	317.757	−	131.619i	0.910479	−	0.377133i	0.122239	−	0.992501i	$-0.460993\pi$
$349$	317.757	−	131.619i	0.910479	−	0.377133i	0.788240	+	0.615368i	$0.210993\pi$
$350$	−66.0657	−	98.8743i	−0.188759	−	0.282498i
$351$	−621.982	−	123.720i	−1.77203	−	0.352479i
$352$	177.996	−	266.389i	0.505669	−	0.756788i
$353$	37.7408	−	37.7408i	0.106915	−	0.106915i	−0.651626	−	0.758540i	$-0.725913\pi$
$353$	37.7408	−	37.7408i	0.106915	−	0.106915i	0.758540	+	0.651626i	$0.225913\pi$
$354$	−458.170	+	91.1357i	−1.29427	+	0.257445i
$355$	1.50710	−	3.63847i	0.00424536	−	0.0102492i
$356$		−	137.822i		−	0.387139i
$357$		0			0
$358$	299.328			0.836112
$359$	−5.42580	−	2.24744i	−0.0151136	−	0.00626028i	0.375114	−	0.926979i	$-0.377604\pi$
$359$	−5.42580	−	2.24744i	−0.0151136	−	0.00626028i	−0.390227	+	0.920718i	$0.627604\pi$
$360$	−7.08212	−	35.6042i	−0.0196726	−	0.0989006i
$361$	−42.9345	−	42.9345i	−0.118932	−	0.118932i
$362$	−108.141	−	72.2574i	−0.298732	−	0.199606i
$363$	−26.5856	+	133.655i	−0.0732386	+	0.368195i
$364$	−74.4375	+	49.7375i	−0.204499	+	0.136642i
$365$	1.60000	+	3.86274i	0.00438356	+	0.0105829i
$366$	479.729	−	198.710i	1.31073	−	0.542924i
$367$	−24.8417	−	37.1783i	−0.0676887	−	0.101303i	0.796081	−	0.605190i	$-0.206903\pi$
$367$	−24.8417	−	37.1783i	−0.0676887	−	0.101303i	−0.863770	+	0.503887i	$0.831903\pi$
$368$	16.6689	+	3.31564i	0.0452958	+	0.00900989i
$369$	117.886	−	176.428i	0.319474	−	0.478126i
$370$	9.18577	−	9.18577i	0.0248264	−	0.0248264i
$371$	284.257	−	56.5422i	0.766190	−	0.152405i
$372$	−80.3745	+	194.041i	−0.216061	+	0.521616i
$373$		−	488.740i		−	1.31029i	−0.755501	−	0.655147i	$-0.772607\pi$
$373$		−	488.740i		−	1.31029i	0.755501	−	0.655147i	$-0.227393\pi$
$374$		0			0
$375$	−58.3269			−0.155538
$376$	−358.649	−	148.557i	−0.953855	−	0.395100i
$377$	−28.6647	−	144.107i	−0.0760337	−	0.382247i
$378$	249.208	+	249.208i	0.659281	+	0.659281i
$379$	260.761	+	174.235i	0.688025	+	0.459723i	0.849801	−	0.527104i	$-0.176722\pi$
$379$	260.761	+	174.235i	0.688025	+	0.459723i	−0.161776	+	0.986827i	$0.551722\pi$
$380$	−1.83362	+	9.21825i	−0.00482533	+	0.0242586i
$381$	93.5647	−	62.5179i	0.245577	−	0.164089i
$382$	−37.9556	−	91.6328i	−0.0993601	−	0.239876i
$383$	184.395	−	76.3787i	0.481448	−	0.199422i	−0.128741	−	0.991678i	$-0.541094\pi$
$383$	184.395	−	76.3787i	0.481448	−	0.199422i	0.610189	+	0.792256i	$0.291094\pi$
$384$	279.318	+	418.029i	0.727391	+	1.08862i
$385$	−8.09980	−	1.61115i	−0.0210385	−	0.00418481i
$386$	35.5219	−	53.1623i	0.0920256	−	0.137726i
$387$	−5.13739	+	5.13739i	−0.0132749	+	0.0132749i
$388$	−70.5134	+	14.0260i	−0.181736	+	0.0361495i
$389$	138.254	−	333.774i	0.355408	−	0.858031i	−0.640525	−	0.767937i	$-0.721283\pi$
$389$	138.254	−	333.774i	0.355408	−	0.858031i	0.995933	−	0.0900941i	$-0.0287168\pi$
$390$		−	11.8605i		−	0.0304115i
$391$		0			0
$392$	−256.539			−0.654437
$393$	1264.14	+	523.622i	3.21663	+	1.33237i
$394$	−9.45047	−	47.5107i	−0.0239860	−	0.120586i
$395$	12.9535	+	12.9535i	0.0327937	+	0.0327937i
$396$	471.789	+	315.239i	1.19139	+	0.796058i
$397$	79.4580	−	399.462i	0.200146	−	1.00620i	−0.741847	−	0.670569i	$-0.766050\pi$
$397$	79.4580	−	399.462i	0.200146	−	1.00620i	0.941993	−	0.335633i	$-0.108950\pi$
$398$	−105.320	+	70.3723i	−0.264622	+	0.176815i
$399$	−149.051	−	359.840i	−0.373561	−	0.901856i
$400$	25.9541	−	10.7506i	0.0648853	−	0.0268764i
$401$	190.869	+	285.655i	0.475981	+	0.712357i	0.989309	−	0.145836i	$-0.0465873\pi$
$401$	190.869	+	285.655i	0.475981	+	0.712357i	−0.513327	+	0.858193i	$0.671587\pi$
$402$	−551.081	−	109.617i	−1.37085	−	0.272679i
$403$	−68.9500	+	103.191i	−0.171092	+	0.256057i
$404$	210.341	−	210.341i	0.520647	−	0.520647i
$405$	43.6962	−	8.69172i	0.107892	−	0.0214610i
$406$	−31.2482	+	75.4399i	−0.0769660	+	0.185812i
$407$			515.885i			1.26753i
$408$		0			0
$409$	−541.811			−1.32472			−0.662361	−	0.749185i	$-0.730445\pi$
$409$	−541.811			−1.32472			−0.662361	+	0.749185i	$0.730445\pi$
$410$	2.18230	+	0.903940i	0.00532269	+	0.00220473i
$411$	150.162	+	754.917i	0.365359	+	1.83678i
$412$	144.705	+	144.705i	0.351226	+	0.351226i
$413$	−235.914	−	157.633i	−0.571220	−	0.381677i
$414$	77.5936	−	390.089i	0.187424	−	0.942244i
$415$	8.67752	−	5.79813i	0.0209097	−	0.0139714i
$416$	106.946	+	258.192i	0.257083	+	0.620653i
$417$	198.296	−	82.1369i	0.475530	−	0.196971i
$418$	112.117	+	167.795i	0.268222	+	0.401423i
$419$	−115.942	−	23.0624i	−0.276712	−	0.0550414i	0.0547835	−	0.998498i	$-0.482553\pi$
$419$	−115.942	−	23.0624i	−0.276712	−	0.0550414i	−0.331495	+	0.943457i	$0.607553\pi$
$420$	6.77298	−	10.1365i	0.0161261	−	0.0241345i
$421$	−115.542	+	115.542i	−0.274447	+	0.274447i	−0.830887	−	0.556441i	$-0.812167\pi$
$421$	−115.542	+	115.542i	−0.274447	+	0.274447i	0.556441	+	0.830887i	$0.312167\pi$
$422$	220.661	−	43.8922i	0.522894	−	0.104010i
$423$	422.649	−	1020.36i	0.999170	−	2.41221i
$424$		−	563.201i		−	1.32830i
$425$		0			0
$426$	124.825			0.293016
$427$	291.374	+	120.691i	0.682374	+	0.282649i
$428$	92.6012	+	465.538i	0.216358	+	1.08770i
$429$	333.050	+	333.050i	0.776341	+	0.776341i
$430$	−0.0672484	−	0.0449339i	−0.000156392	−	0.000104497i
$431$	15.8856	−	79.8623i	0.0368576	−	0.185295i	−0.957971	−	0.286866i	$-0.907387\pi$
$431$	15.8856	−	79.8623i	0.0368576	−	0.185295i	0.994828	+	0.101570i	$0.0323867\pi$
$432$	−69.2274	+	46.2563i	−0.160249	+	0.107075i
$433$	130.853	+	315.906i	0.302200	+	0.729575i	0.999913	+	0.0131977i	$0.00420107\pi$
$433$	130.853	+	315.906i	0.302200	+	0.729575i	−0.697713	+	0.716377i	$0.745799\pi$
$434$	63.7212	−	26.3942i	0.146823	−	0.0608161i
$435$	11.1159	+	16.6362i	0.0255539	+	0.0382441i
$436$	−386.189	−	76.8178i	−0.885755	−	0.176188i
$437$	−145.353	+	217.537i	−0.332616	+	0.497795i
$438$	−93.7051	+	93.7051i	−0.213939	+	0.213939i
$439$	336.965	−	67.0265i	0.767574	−	0.152680i	0.204253	−	0.978918i	$-0.434524\pi$
$439$	336.965	−	67.0265i	0.767574	−	0.152680i	0.563321	+	0.826238i	$0.309524\pi$
$440$	−6.14140	+	14.8266i	−0.0139577	+	0.0336969i
$441$		−	729.859i		−	1.65501i
$442$		0			0
$443$	150.115			0.338861			0.169430	−	0.985542i	$-0.445807\pi$
$443$	150.115			0.338861			0.169430	+	0.985542i	$0.445807\pi$
$444$	−703.572	−	291.429i	−1.58462	−	0.656372i
$445$	2.16354	+	10.8768i	0.00486188	+	0.0244423i
$446$	−161.869	−	161.869i	−0.362934	−	0.362934i
$447$	−535.737	−	357.968i	−1.19852	−	0.800823i
$448$	26.7667	−	134.566i	0.0597472	−	0.300369i
$449$	633.631	−	423.379i	1.41120	−	0.942937i	0.411705	−	0.911317i	$-0.364933\pi$
$449$	633.631	−	423.379i	1.41120	−	0.942937i	0.999500	−	0.0316198i	$-0.0100666\pi$
$450$	−251.587	−	607.386i	−0.559083	−	1.34975i
$451$	−86.6638	+	35.8973i	−0.192159	+	0.0795949i
$452$	161.902	+	242.304i	0.358191	+	0.536071i
$453$	1417.20	+	281.898i	3.12847	+	0.622291i
$454$	−234.307	+	350.666i	−0.516096	+	0.772392i
$455$	5.09380	−	5.09380i	0.0111952	−	0.0111952i
$456$	−742.327	+	147.658i	−1.62791	+	0.323812i
$457$	−31.0768	+	75.0260i	−0.0680017	+	0.164171i	−0.954227	−	0.299085i	$-0.903319\pi$
$457$	−31.0768	+	75.0260i	−0.0680017	+	0.164171i	0.886225	+	0.463255i	$0.153319\pi$
$458$			311.898i			0.680999i
$459$		0			0
$460$	−8.18902			−0.0178022
$461$	−440.721	−	182.552i	−0.956010	−	0.395992i	−0.150524	−	0.988606i	$-0.548096\pi$
$461$	−440.721	−	182.552i	−0.956010	−	0.395992i	−0.805487	+	0.592614i	$0.798096\pi$
$462$	−51.0663	−	256.728i	−0.110533	−	0.555687i
$463$	311.442	+	311.442i	0.672660	+	0.672660i	0.958329	−	0.285668i	$-0.0922155\pi$
$463$	311.442	+	311.442i	0.672660	+	0.672660i	−0.285668	+	0.958329i	$0.592216\pi$
$464$	−16.0393	−	10.7171i	−0.0345675	−	0.0230973i
$465$	3.29706	−	16.5754i	0.00709044	−	0.0356461i
$466$	40.7982	−	27.2605i	0.0875498	−	0.0584989i
$467$	−219.722	−	530.456i	−0.470497	−	1.13588i	−0.963944	−	0.266104i	$-0.914263\pi$
$467$	−219.722	−	530.456i	−0.470497	−	1.13588i	0.493447	−	0.869776i	$-0.335737\pi$
$468$	−457.270	+	189.407i	−0.977073	+	0.404717i
$469$	−189.598	−	283.754i	−0.404261	−	0.605020i
$470$	12.0585	+	2.39858i	0.0256563	+	0.00510335i
$471$	−461.369	+	690.488i	−0.979552	+	1.46600i
$472$	−389.869	+	389.869i	−0.825994	+	0.825994i
$473$	3.15015	−	0.626605i	0.00665995	−	0.00132475i
$474$	−222.198	+	536.434i	−0.468773	+	1.13172i
$475$			432.459i			0.910441i
$476$		0			0
$477$	1602.32			3.35916
$478$	−280.106	−	116.024i	−0.585995	−	0.242727i
$479$	−36.0006	−	180.987i	−0.0751578	−	0.377844i	0.924839	−	0.380359i	$-0.124199\pi$
$479$	−36.0006	−	180.987i	−0.0751578	−	0.377844i	−0.999997	+	0.00251498i	$0.999199\pi$
$480$	−26.9096	−	26.9096i	−0.0560617	−	0.0560617i
$481$	−374.159	−	250.005i	−0.777877	−	0.519760i
$482$	−19.7250	+	99.1645i	−0.0409233	+	0.205735i
$483$	282.162	−	188.535i	0.584186	−	0.390341i
$484$	24.2261	+	58.4869i	0.0500539	+	0.120841i
$485$	5.34472	−	2.21386i	0.0110200	−	0.00456465i
$486$	346.352	+	518.353i	0.712659	+	1.06657i
$487$	−443.883	−	88.2938i	−0.911464	−	0.181301i	−0.282982	−	0.959125i	$-0.591324\pi$
$487$	−443.883	−	88.2938i	−0.911464	−	0.181301i	−0.628482	+	0.777824i	$0.716324\pi$
$488$	340.487	−	509.575i	0.697720	−	1.04421i
$489$	368.693	−	368.693i	0.753974	−	0.753974i
$490$	7.96876	−	1.58508i	0.0162628	−	0.00323487i
$491$	−167.530	+	404.453i	−0.341202	+	0.823734i	0.656393	+	0.754419i	$0.272081\pi$
$491$	−167.530	+	404.453i	−0.341202	+	0.823734i	−0.997595	+	0.0693148i	$0.977919\pi$
$492$		−	138.472i		−	0.281448i
$493$		0			0
$494$	−176.031			−0.356338
$495$	−42.1821	−	17.4724i	−0.0852164	−	0.0352978i
$496$	3.17877	+	15.9807i	0.00640880	+	0.0322192i
$497$	53.6094	+	53.6094i	0.107866	+	0.107866i
$498$	275.038	+	183.775i	0.552286	+	0.369026i
$499$	−132.516	+	666.204i	−0.265564	+	1.33508i	0.585780	+	0.810470i	$0.300788\pi$
$499$	−132.516	+	666.204i	−0.265564	+	1.33508i	−0.851344	+	0.524608i	$0.824212\pi$
$500$	−22.5293	+	15.0536i	−0.0450586	+	0.0301072i
$501$	487.946	+	1178.01i	0.973944	+	2.35131i
$502$	−302.759	+	125.407i	−0.603105	+	0.249814i
$503$	−179.818	−	269.116i	−0.357490	−	0.535022i	0.608516	−	0.793542i	$-0.291765\pi$
$503$	−179.818	−	269.116i	−0.357490	−	0.535022i	−0.966006	+	0.258520i	$0.916765\pi$
$504$	685.415	+	136.338i	1.35995	+	0.270511i
$505$	−13.2981	+	19.9021i	−0.0263329	+	0.0394100i
$506$	−124.330	+	124.330i	−0.245711	+	0.245711i
$507$	523.401	−	104.111i	1.03235	−	0.205347i
$508$	20.0050	−	48.2963i	0.0393799	−	0.0950714i
$509$			145.680i			0.286209i	0.989708	+	0.143105i	$0.0457085\pi$
$509$			145.680i			0.286209i	−0.989708	+	0.143105i	$0.954291\pi$
$510$		0			0
$511$	−80.4883			−0.157511
$512$	66.4083	+	27.5072i	0.129704	+	0.0537251i
$513$	−250.047	−	1257.07i	−0.487421	−	2.45043i
$514$	149.124	+	149.124i	0.290124	+	0.290124i
$515$	−13.6917	−	9.14850i	−0.0265858	−	0.0177641i
$516$	−0.924983	+	4.65020i	−0.00179260	+	0.00901202i
$517$	−405.963	+	271.256i	−0.785228	+	0.524673i
$518$	95.7023	+	231.046i	0.184754	+	0.446035i
$519$	−1622.89	+	672.222i	−3.12695	+	1.29522i
$520$	−7.77719	−	11.6394i	−0.0149561	−	0.0223834i
$521$	12.3204	+	2.45067i	0.0236475	+	0.00470378i	0.206900	−	0.978362i	$-0.433663\pi$
$521$	12.3204	+	2.45067i	0.0236475	+	0.00470378i	−0.183252	+	0.983066i	$0.558663\pi$
$522$	−250.805	+	375.357i	−0.480470	+	0.719074i
$523$	68.6445	−	68.6445i	0.131251	−	0.131251i	−0.638429	−	0.769681i	$-0.720415\pi$
$523$	68.6445	−	68.6445i	0.131251	−	0.131251i	0.769681	+	0.638429i	$0.220415\pi$
$524$	623.426	−	124.007i	1.18974	−	0.236655i
$525$	214.660	−	518.235i	0.408876	−	0.987115i
$526$			350.183i			0.665748i
$527$		0			0
$528$	61.8376			0.117117
$529$	278.132	+	115.206i	0.525769	+	0.217781i
$530$	3.47986	+	17.4945i	0.00656578	+	0.0330084i
$531$	−1109.19	−	1109.19i	−2.08886	−	2.08886i
$532$	−150.444	−	100.523i	−0.282789	−	0.188953i
$533$	15.9630	−	80.2514i	0.0299493	−	0.150566i
$534$	−292.263	+	195.284i	−0.547308	+	0.365700i
$535$	−14.6161	−	35.2864i	−0.0273199	−	0.0659560i
$536$	−612.686	+	253.783i	−1.14307	+	0.473476i
$537$	784.442	+	1174.00i	1.46079	+	2.18622i
$538$	535.292	+	106.476i	0.994967	+	0.197911i
$539$	−179.258	+	268.278i	−0.332575	+	0.497733i
$540$	28.3672	−	28.3672i	0.0525319	−	0.0525319i
$541$	−299.438	+	59.5618i	−0.553489	+	0.110096i	−0.463907	−	0.885884i	$-0.653553\pi$
$541$	−299.438	+	59.5618i	−0.553489	+	0.110096i	−0.0895816	+	0.995979i	$0.528553\pi$
$542$	−22.2164	+	53.6352i	−0.0409897	+	0.0989580i
$543$		−	613.505i		−	1.12984i
$544$		0			0
$545$	31.6839			0.0581355
$546$	210.946	+	87.3765i	0.386347	+	0.160030i
$547$	110.074	+	553.378i	0.201232	+	1.01166i	0.940899	+	0.338687i	$0.109983\pi$
$547$	110.074	+	553.378i	0.201232	+	1.01166i	−0.739667	+	0.672973i	$0.765017\pi$
$548$	252.838	+	252.838i	0.461384	+	0.461384i
$549$	1449.75	+	968.693i	2.64071	+	1.76447i
$550$	−56.7003	+	285.052i	−0.103091	+	0.518275i
$551$	246.911	−	164.981i	0.448114	−	0.299420i
$552$	−252.359	−	609.248i	−0.457172	−	1.10371i
$553$	−325.815	+	134.957i	−0.589177	+	0.244045i
$554$	−270.632	−	405.029i	−0.488506	−	0.731100i
$555$	60.1006	+	11.9548i	0.108289	+	0.0215401i
$556$	55.3950	−	82.9044i	0.0996313	−	0.149109i
$557$	−638.055	+	638.055i	−1.14552	+	1.14552i	−0.158097	+	0.987424i	$0.550536\pi$
$557$	−638.055	+	638.055i	−1.14552	+	1.14552i	−0.987424	+	0.158097i	$0.949464\pi$
$558$	373.986	−	74.3904i	0.670225	−	0.133316i
$559$	−1.07215	+	2.58839i	−0.00191797	+	0.00463039i
$560$		−	0.945768i		−	0.00168887i
$561$		0			0
$562$	384.636			0.684405
$563$	−242.249	−	100.343i	−0.430282	−	0.178228i	0.157022	−	0.987595i	$-0.449811\pi$
$563$	−242.249	−	100.343i	−0.430282	−	0.178228i	−0.587304	+	0.809367i	$0.699811\pi$
$564$	−140.610	−	706.894i	−0.249308	−	1.25336i
$565$	−16.5810	−	16.5810i	−0.0293469	−	0.0293469i
$566$	204.021	+	136.322i	0.360461	+	0.240852i
$567$	−167.324	+	841.194i	−0.295104	+	1.48359i
$568$	122.498	−	81.8506i	0.215666	−	0.144103i
$569$	319.837	+	772.154i	0.562103	+	1.35704i	0.908081	+	0.418794i	$0.137547\pi$
$569$	319.837	+	772.154i	0.562103	+	1.35704i	−0.345978	+	0.938243i	$0.612453\pi$
$570$	22.1462	−	9.17327i	0.0388530	−	0.0160934i
$571$	−64.9499	−	97.2045i	−0.113748	−	0.170235i	0.770228	−	0.637769i	$-0.220143\pi$
$571$	−64.9499	−	97.2045i	−0.113748	−	0.170235i	−0.883975	+	0.467534i	$0.845143\pi$
$572$	214.601	+	42.6868i	0.375176	+	0.0746272i
$573$	259.926	−	389.006i	0.453622	−	0.678894i
$574$	−32.1542	+	32.1542i	−0.0560177	+	0.0560177i
$575$	−369.553	+	73.5087i	−0.642701	+	0.127841i
$576$	290.276	−	700.789i	0.503952	−	1.21665i
$577$			416.487i			0.721814i	0.932602	+	0.360907i	$0.117533\pi$
$577$			416.487i			0.721814i	−0.932602	+	0.360907i	$0.882467\pi$
$578$		0			0
$579$	301.600			0.520898
$580$	8.58727	+	3.55697i	0.0148056	+	0.00613270i
$581$	39.1956	+	197.050i	0.0674623	+	0.339156i
$582$	129.656	+	129.656i	0.222777	+	0.222777i
$583$	−588.973	−	393.539i	−1.01025	−	0.675024i
$584$	−30.5138	+	153.403i	−0.0522496	+	0.262676i
$585$	33.1143	−	22.1263i	0.0566057	−	0.0378227i
$586$	139.747	+	337.379i	0.238476	+	0.575732i
$587$	976.853	−	404.626i	1.66415	−	0.689312i	0.665763	−	0.746163i	$-0.268106\pi$
$587$	976.853	−	404.626i	1.66415	−	0.689312i	0.998383	+	0.0568517i	$0.0181062\pi$
$588$	−264.617	−	396.028i	−0.450029	−	0.673517i
$589$	−246.009	−	48.9342i	−0.417672	−	0.0830802i
$590$	9.70143	−	14.5192i	0.0164431	−	0.0246088i
$591$	161.576	−	161.576i	0.273394	−	0.273394i
$592$	−57.9443	+	11.5258i	−0.0978789	+	0.0194693i
$593$	−301.246	+	727.272i	−0.508004	+	1.22643i	0.437027	+	0.899448i	$0.356031\pi$
$593$	−301.246	+	727.272i	−0.508004	+	1.22643i	−0.945031	+	0.326981i	$0.893969\pi$
$594$		−	861.370i		−	1.45012i
$595$		0			0
$596$	−299.321			−0.502217
$597$	−552.017	−	228.653i	−0.924651	−	0.383003i
$598$	−29.9214	−	150.425i	−0.0500358	−	0.251547i
$599$	677.644	+	677.644i	1.13129	+	1.13129i	0.989963	+	0.141329i	$0.0451375\pi$
$599$	677.644	+	677.644i	1.13129	+	1.13129i	0.141329	+	0.989963i	$0.454862\pi$
$600$	−906.327	−	605.588i	−1.51054	−	1.00931i
$601$	75.7925	−	381.035i	0.126111	−	0.634001i	−0.865088	−	0.501620i	$-0.832738\pi$
$601$	75.7925	−	381.035i	0.126111	−	0.634001i	0.991199	−	0.132381i	$-0.0422624\pi$
$602$	1.29460	−	0.865021i	0.00215049	−	0.00143691i
$603$	−722.018	−	1743.10i	−1.19738	−	2.89072i
$604$	620.160	−	256.879i	1.02675	−	0.425296i
$605$	−2.83005	−	4.23547i	−0.00467777	−	0.00700077i
$606$	−744.086	−	148.008i	−1.22787	−	0.244238i
$607$	−476.707	+	713.443i	−0.785349	+	1.17536i	0.195522	+	0.980699i	$0.437360\pi$
$607$	−476.707	+	713.443i	−0.785349	+	1.17536i	−0.980871	+	0.194659i	$0.937640\pi$
$608$	−399.387	+	399.387i	−0.656886	+	0.656886i
$609$	−377.776	+	75.1442i	−0.620321	+	0.123390i
$610$	−7.42787	+	17.9325i	−0.0121768	+	0.0293975i
$611$		−	425.889i		−	0.697036i
$612$		0			0
$613$	−468.221			−0.763819			−0.381909	−	0.924200i	$-0.624733\pi$
$613$	−468.221			−0.763819			−0.381909	+	0.924200i	$0.624733\pi$
$614$	344.195	+	142.570i	0.560578	+	0.232199i
$615$	2.17375	+	10.9282i	0.00353456	+	0.0177694i
$616$	−218.457	−	218.457i	−0.354637	−	0.354637i
$617$	106.861	+	71.4022i	0.173194	+	0.115725i	0.639146	−	0.769085i	$-0.279288\pi$
$617$	106.861	+	71.4022i	0.173194	+	0.115725i	−0.465952	+	0.884810i	$0.654288\pi$
$618$	101.823	−	511.897i	0.164762	−	0.828313i
$619$	87.1955	−	58.2622i	0.140865	−	0.0941231i	−0.483141	−	0.875543i	$-0.660504\pi$
$619$	87.1955	−	58.2622i	0.140865	−	0.0941231i	0.624006	+	0.781420i	$0.285504\pi$
$620$	−3.00443	−	7.25335i	−0.00484586	−	0.0116989i
$621$	1031.71	−	427.349i	1.66137	−	0.688163i
$622$	−41.6240	−	62.2948i	−0.0669197	−	0.100152i
$623$	−209.390	−	41.6502i	−0.336099	−	0.0668542i
$624$	−29.9673	+	44.8493i	−0.0480246	+	0.0718738i
$625$	−439.629	+	439.629i	−0.703406	+	0.703406i
$626$	147.447	−	29.3291i	0.235539	−	0.0468516i
$627$	−364.289	+	879.472i	−0.581004	+	1.40267i
$628$			385.782i			0.614303i
$629$		0			0
$630$	−22.1331			−0.0351320
$631$	−542.031	−	224.517i	−0.859004	−	0.355811i	−0.0906858	−	0.995880i	$-0.528906\pi$
$631$	−542.031	−	224.517i	−0.859004	−	0.355811i	−0.768318	+	0.640069i	$0.778906\pi$
$632$	133.696	+	672.135i	0.211544	+	1.06350i
$633$	750.432	+	750.432i	1.18552	+	1.18552i
$634$	−138.869	−	92.7892i	−0.219036	−	0.146355i
$635$	−0.820627	+	4.12557i	−0.00129233	+	0.00649696i
$636$	869.432	−	580.936i	1.36703	−	0.913421i
$637$	−107.705	−	260.022i	−0.169081	−	0.408199i
$638$	184.380	−	76.3726i	0.288996	−	0.119706i
$639$	232.867	+	348.509i	0.364423	+	0.545398i
$640$	−18.4323	−	3.66640i	−0.0288004	−	0.00572876i
$641$	359.042	−	537.344i	0.560128	−	0.838290i	−0.438030	−	0.898960i	$-0.644324\pi$
$641$	359.042	−	537.344i	0.560128	−	0.838290i	0.998158	+	0.0606699i	$0.0193237\pi$
$642$	856.003	−	856.003i	1.33334	−	1.33334i
$643$	487.602	−	96.9901i	0.758324	−	0.150840i	0.199239	−	0.979951i	$-0.436153\pi$
$643$	487.602	−	96.9901i	0.758324	−	0.150840i	0.559084	+	0.829111i	$0.311153\pi$
$644$	60.3287	−	145.646i	0.0936782	−	0.226159i
$645$		−	0.381513i		−	0.000591494i
$646$		0			0
$647$	−62.0539			−0.0959102			−0.0479551	−	0.998849i	$-0.515270\pi$
$647$	−62.0539			−0.0959102			−0.0479551	+	0.998849i	$0.515270\pi$
$648$	1539.80	+	637.807i	2.37624	+	0.984270i
$649$	135.287	+	680.132i	0.208454	+	1.04797i
$650$	−179.263	−	179.263i	−0.275789	−	0.275789i
$651$	270.514	+	180.752i	0.415536	+	0.277652i
$652$	47.2551	−	237.567i	0.0724771	−	0.364367i
$653$	7.83499	−	5.23517i	0.0119984	−	0.00801711i	−0.549557	−	0.835457i	$-0.685203\pi$
$653$	7.83499	−	5.23517i	0.0119984	−	0.00801711i	0.561555	+	0.827439i	$0.310203\pi$
$654$	384.305	+	927.793i	0.587622	+	1.41864i
$655$	−47.2539	+	19.5732i	−0.0721434	+	0.0298828i
$656$	−5.96823	−	8.93209i	−0.00909791	−	0.0136160i
$657$	−436.435	−	86.8122i	−0.664284	−	0.132134i
$658$	−131.495	+	196.796i	−0.199840	+	0.299082i
$659$	−248.723	+	248.723i	−0.377426	+	0.377426i	−0.870173	−	0.492747i	$-0.835993\pi$
$659$	−248.723	+	248.723i	−0.377426	+	0.377426i	0.492747	+	0.870173i	$0.335993\pi$
$660$	−29.2231	+	5.81285i	−0.0442775	+	0.00880734i
$661$	437.551	−	1056.34i	0.661953	−	1.59810i	−0.132786	−	0.991145i	$-0.542392\pi$
$661$	437.551	−	1056.34i	0.661953	−	1.59810i	0.794739	−	0.606951i	$-0.207608\pi$
$662$			30.3246i			0.0458075i
$663$		0			0
$664$	390.417			0.587977
$665$	13.4510	+	5.57158i	0.0202271	+	0.00837832i
$666$	269.731	+	1356.03i	0.405002	+	2.03608i
$667$	182.952	+	182.952i	0.274290	+	0.274290i
$668$	492.505	+	329.082i	0.737284	+	0.492637i
$669$	210.663	−	1059.07i	0.314892	−	1.58307i
$670$	17.4635	−	11.6688i	0.0260650	−	0.0174161i
$671$	−294.976	−	712.136i	−0.439607	−	1.06131i
$672$	676.846	−	280.359i	1.00721	−	0.417201i
$673$	35.3346	+	52.8819i	0.0525031	+	0.0785764i	0.856792	−	0.515661i	$-0.172454\pi$
$673$	35.3346	+	52.8819i	0.0525031	+	0.0785764i	−0.804289	+	0.594238i	$0.797454\pi$
$674$	419.795	+	83.5024i	0.622841	+	0.123891i
$675$	1025.51	−	1534.79i	1.51928	−	2.27376i
$676$	175.298	−	175.298i	0.259317	−	0.259317i
$677$	293.289	−	58.3388i	0.433218	−	0.0861725i	0.0263362	−	0.999653i	$-0.491616\pi$
$677$	293.289	−	58.3388i	0.433218	−	0.0861725i	0.406882	+	0.913481i	$0.366616\pi$
$678$	284.422	−	686.656i	0.419502	−	1.01277i
$679$			111.368i			0.164018i
$680$		0			0
$681$	−1989.40			−2.92129
$682$	−155.739	−	64.5090i	−0.228356	−	0.0945880i
$683$	87.9838	+	442.324i	0.128820	+	0.647620i	0.990200	+	0.139659i	$0.0446006\pi$
$683$	87.9838	+	442.324i	0.128820	+	0.647620i	−0.861380	+	0.507961i	$0.830399\pi$
$684$	−707.334	−	707.334i	−1.03411	−	1.03411i
$685$	−23.9230	−	15.9849i	−0.0349241	−	0.0233356i
$686$	−76.0643	+	382.401i	−0.110881	+	0.557436i
$687$	−1223.30	+	817.383i	−1.78064	+	1.18979i
$688$	0.140761	+	0.339827i	0.000204594	+	0.000493934i
$689$	570.848	−	236.453i	0.828517	−	0.343183i
$690$	11.6033	+	17.3655i	0.0168164	+	0.0251674i
$691$	329.736	+	65.5886i	0.477187	+	0.0949184i	0.427823	−	0.903862i	$-0.359281\pi$
$691$	329.736	+	65.5886i	0.477187	+	0.0949184i	0.0493638	+	0.998781i	$0.484281\pi$
$692$	−453.361	+	678.503i	−0.655146	+	0.980496i
$693$	621.513	−	621.513i	0.896844	−	0.896844i
$694$	23.2525	−	4.62522i	0.0335051	−	0.00666458i
$695$	−3.07031	+	7.41240i	−0.00441772	+	0.0106653i
$696$			748.491i			1.07542i
$697$		0			0
$698$	−407.495			−0.583804
$699$	213.838	+	88.5745i	0.305920	+	0.126716i
$700$	−50.8370	−	255.575i	−0.0726243	−	0.365107i
$701$	−593.627	−	593.627i	−0.846828	−	0.846828i	0.142908	−	0.989736i	$-0.454355\pi$
$701$	−593.627	−	593.627i	−0.846828	−	0.846828i	−0.989736	+	0.142908i	$0.954355\pi$
$702$	624.731	+	417.432i	0.889930	+	0.594632i
$703$	177.430	−	892.001i	0.252390	−	1.26885i
$704$	−278.817	+	186.299i	−0.396046	+	0.264630i
$705$	22.1938	+	53.5806i	0.0314806	+	0.0760008i
$706$	−58.4231	+	24.1996i	−0.0827522	+	0.0342771i
$707$	−256.002	−	383.134i	−0.362096	−	0.541915i
$708$	−1004.00	−	199.708i	−1.41808	−	0.282073i
$709$	365.345	−	546.777i	0.515296	−	0.771195i	−0.479004	−	0.877813i	$-0.659002\pi$
$709$	365.345	−	546.777i	0.515296	−	0.771195i	0.994300	+	0.106618i	$0.0340021\pi$
$710$	−3.29937	+	3.29937i	−0.00464700	+	0.00464700i
$711$	−1912.24	+	380.368i	−2.68950	+	0.534976i
$712$	−158.762	+	383.287i	−0.222981	+	0.538324i
$713$		−	218.542i		−	0.306510i
$714$		0			0
$715$	−17.6064			−0.0246243
$716$	605.996	+	251.012i	0.846364	+	0.350575i
$717$	−279.008	−	1402.67i	−0.389133	−	1.95630i
$718$	4.92012	+	4.92012i	0.00685253	+	0.00685253i
$719$	−90.0560	−	60.1735i	−0.125252	−	0.0836905i	0.491366	−	0.870953i	$-0.336498\pi$
$719$	−90.0560	−	60.1735i	−0.125252	−	0.0836905i	−0.616618	+	0.787263i	$0.711498\pi$
$720$	1.02008	−	5.12827i	0.00141677	−	0.00712260i
$721$	263.578	−	176.117i	0.365573	−	0.244268i
$722$	27.5298	+	66.4629i	0.0381300	+	0.0920539i
$723$	−440.628	+	182.514i	−0.609444	+	0.252440i
$724$	−158.340	−	236.972i	−0.218701	−	0.327309i
$725$	419.454	+	83.4347i	0.578558	+	0.115082i
$726$	89.6999	−	134.245i	0.123554	−	0.184911i
$727$	882.782	−	882.782i	1.21428	−	1.21428i	0.244676	−	0.969605i	$-0.421318\pi$
$727$	882.782	−	882.782i	1.21428	−	1.21428i	0.969605	−	0.244676i	$-0.0786817\pi$
$728$	264.308	−	52.5741i	0.363061	−	0.0722172i
$729$	−390.866	+	943.633i	−0.536167	+	1.29442i
$730$		−	4.95362i		−	0.00678578i
$731$		0			0
$732$	1137.86			1.55445
$733$	−905.225	−	374.956i	−1.23496	−	0.511537i	−0.332823	−	0.942989i	$-0.608001\pi$
$733$	−905.225	−	374.956i	−1.23496	−	0.511537i	−0.902136	+	0.431453i	$0.858001\pi$
$734$	10.3353	+	51.9588i	0.0140807	+	0.0707886i
$735$	27.1004	+	27.1004i	0.0368713	+	0.0368713i
$736$	−409.178	−	273.404i	−0.555949	−	0.371473i
$737$	−162.721	+	818.054i	−0.220789	+	1.10998i
$738$	−209.031	+	139.670i	−0.283240	+	0.189255i
$739$	178.399	+	430.693i	0.241406	+	0.582806i	0.997423	−	0.0717465i	$-0.0228572\pi$
$739$	178.399	+	430.693i	0.241406	+	0.582806i	−0.756017	+	0.654552i	$0.772857\pi$
$740$	26.2998	−	10.8937i	0.0355403	−	0.0147213i
$741$	−461.320	−	690.414i	−0.622564	−	0.931733i
$742$	−336.785	−	66.9907i	−0.453888	−	0.0902840i
$743$	590.914	−	884.366i	0.795309	−	1.19026i	−0.183000	−	0.983113i	$-0.558581\pi$
$743$	590.914	−	884.366i	0.795309	−	1.19026i	0.978309	−	0.207151i	$-0.0664191\pi$
$744$	447.049	−	447.049i	0.600872	−	0.600872i
$745$	23.6224	−	4.69878i	0.0317079	−	0.00630708i
$746$	−221.595	+	534.978i	−0.297044	+	0.717128i
$747$			1110.74i			1.48694i
$748$		0			0
$749$	735.267			0.981665
$750$	63.8449	+	26.4454i	0.0851265	+	0.0352606i
$751$	−111.852	−	562.317i	−0.148937	−	0.748757i	−0.980990	−	0.194060i	$-0.937834\pi$
$751$	−111.852	−	562.317i	−0.148937	−	0.748757i	0.832052	−	0.554697i	$-0.187166\pi$
$752$	−39.5375	−	39.5375i	−0.0525765	−	0.0525765i
$753$	−1285.29	−	858.805i	−1.70690	−	1.14051i
$754$	−33.9617	+	170.737i	−0.0450421	+	0.226442i
$755$	−44.9104	+	30.0081i	−0.0594839	+	0.0397459i
$756$	295.545	+	713.510i	0.390933	+	0.943796i
$757$	−480.991	+	199.233i	−0.635391	+	0.263188i	−0.677042	−	0.735945i	$-0.736738\pi$
$757$	−480.991	+	199.233i	−0.635391	+	0.263188i	0.0416507	+	0.999132i	$0.486738\pi$
$758$	−206.432	−	308.948i	−0.272338	−	0.407583i
$759$	−813.464	−	161.808i	−1.07176	−	0.213186i
$760$	15.7183	−	23.5241i	0.0206819	−	0.0309527i
$761$	−577.095	+	577.095i	−0.758338	+	0.758338i	−0.976020	−	0.217682i	$-0.930150\pi$
$761$	−577.095	+	577.095i	−0.758338	+	0.758338i	0.217682	+	0.976020i	$0.430150\pi$
$762$	−130.762	+	26.0102i	−0.171604	+	0.0341341i
$763$	−233.416	+	563.515i	−0.305918	+	0.738552i
$764$		−	217.341i		−	0.284478i
$765$		0			0
$766$	−236.469			−0.308707
$767$	−558.845	−	231.481i	−0.728611	−	0.301801i
$768$	−264.993	−	1332.21i	−0.345044	−	1.73465i
$769$	−21.1831	−	21.1831i	−0.0275462	−	0.0275462i	0.693200	−	0.720746i	$-0.256200\pi$
$769$	−21.1831	−	21.1831i	−0.0275462	−	0.0275462i	−0.720746	+	0.693200i	$0.756200\pi$
$770$	8.13559	+	5.43603i	0.0105657	+	0.00705978i
$771$	−194.076	+	975.687i	−0.251720	+	1.26548i
$772$	116.496	−	77.8400i	0.150901	−	0.100829i
$773$	−318.138	−	768.053i	−0.411563	−	0.993601i	−0.984718	−	0.174154i	$-0.944281\pi$
$773$	−318.138	−	768.053i	−0.411563	−	0.993601i	0.573155	−	0.819447i	$-0.305719\pi$
$774$	7.95272	−	3.29412i	0.0102748	−	0.00425597i
$775$	−200.693	−	300.359i	−0.258959	−	0.387560i
$776$	212.257	+	42.2206i	0.273528	+	0.0544080i
$777$	−655.385	+	980.853i	−0.843481	+	1.26236i
$778$	−302.667	+	302.667i	−0.389032	+	0.389032i
$779$	162.194	−	32.2624i	0.208208	−	0.0414151i
$780$	9.94602	−	24.0118i	0.0127513	−	0.0307844i
$781$		−	185.297i		−	0.237256i
$782$		0			0
$783$	−1267.51			−1.61879
$784$	−34.1380	−	14.1404i	−0.0435434	−	0.0180363i
$785$	−6.05605	−	30.4458i	−0.00771472	−	0.0387845i
$786$	−1146.32	−	1146.32i	−1.45842	−	1.45842i
$787$	474.713	+	317.193i	0.603193	+	0.403041i	0.819330	−	0.573322i	$-0.194346\pi$
$787$	474.713	+	317.193i	0.603193	+	0.403041i	−0.216137	+	0.976363i	$0.569346\pi$
$788$	20.7091	−	104.112i	0.0262805	−	0.132121i
$789$	−1373.46	+	917.717i	−1.74076	+	1.16314i
$790$	−8.30587	−	20.0521i	−0.0105138	−	0.0253825i
$791$	417.056	−	172.750i	0.527251	−	0.218395i
$792$	−948.924	−	1420.16i	−1.19814	−	1.79314i
$793$	659.444	+	131.172i	0.831581	+	0.165412i
$794$	−268.092	+	401.227i	−0.337647	+	0.505324i
$795$	−59.4957	+	59.4957i	−0.0748374	+	0.0748374i
$796$	−272.235	+	54.1509i	−0.342003	+	0.0680287i
$797$	−177.637	+	428.854i	−0.222882	+	0.538086i	−0.995279	−	0.0970548i	$-0.969058\pi$
$797$	−177.637	+	428.854i	−0.222882	+	0.538086i	0.772397	+	0.635140i	$0.219058\pi$
$798$			461.463i			0.578274i
$799$		0			0
$800$	−813.440			−1.01680
$801$	−1090.46	−	451.682i	−1.36137	−	0.563898i
$802$	−79.4097	−	399.219i	−0.0990146	−	0.497780i
$803$	139.101	+	139.101i	0.173227	+	0.173227i
$804$	−1023.75	−	684.049i	−1.27332	−	0.850807i
$805$	−2.47475	+	12.4414i	−0.00307423	+	0.0154552i
$806$	122.260	−	81.6914i	0.151687	−	0.101354i
$807$	985.215	+	2378.52i	1.22084	+	2.94736i
$808$	−827.268	+	342.666i	−1.02385	+	0.424091i
$809$	−474.913	−	710.757i	−0.587037	−	0.878563i	0.412437	−	0.910986i	$-0.364678\pi$
$809$	−474.913	−	710.757i	−0.587037	−	0.878563i	−0.999474	+	0.0324231i	$0.989678\pi$
$810$	−51.7710	−	10.2979i	−0.0639148	−	0.0127134i
$811$	4.89963	−	7.33282i	0.00604147	−	0.00904170i	−0.828437	−	0.560083i	$-0.810769\pi$
$811$	4.89963	−	7.33282i	0.00604147	−	0.00904170i	0.834478	+	0.551041i	$0.185769\pi$
$812$	−126.525	+	126.525i	−0.155819	+	0.155819i
$813$	−268.586	+	53.4250i	−0.330364	+	0.0657134i
$814$	233.903	−	564.691i	0.287350	−	0.693723i
$815$			19.4906i			0.0239148i
$816$		0			0
$817$	−5.66234			−0.00693065
$818$	593.069	+	245.657i	0.725024	+	0.300315i
$819$	149.574	+	751.962i	0.182631	+	0.918146i
$820$	3.66009	+	3.66009i	0.00446353	+	0.00446353i
$821$	765.495	+	511.487i	0.932393	+	0.623005i	0.926223	−	0.376976i	$-0.123036\pi$
$821$	765.495	+	511.487i	0.932393	+	0.623005i	0.00616997	+	0.999981i	$0.498036\pi$
$822$	177.911	−	894.420i	0.216437	−	1.08810i
$823$	−1215.17	+	811.948i	−1.47651	+	0.986571i	−0.482661	+	0.875807i	$0.660330\pi$
$823$	−1215.17	+	811.948i	−1.47651	+	0.986571i	−0.993847	+	0.110764i	$0.964670\pi$
$824$	−235.738	−	569.123i	−0.286090	−	0.690683i
$825$	−1266.60	+	524.643i	−1.53527	+	0.635930i
$826$	186.762	+	279.509i	0.226104	+	0.338389i
$827$	67.0395	+	13.3350i	0.0810635	+	0.0161245i	0.235455	−	0.971885i	$-0.424342\pi$
$827$	67.0395	+	13.3350i	0.0810635	+	0.0161245i	−0.154392	+	0.988010i	$0.549342\pi$
$828$	484.212	−	724.675i	0.584798	−	0.875211i
$829$	932.147	−	932.147i	1.12442	−	1.12442i	0.133354	−	0.991068i	$-0.457425\pi$
$829$	932.147	−	932.147i	1.12442	−	1.12442i	0.991068	−	0.133354i	$-0.0425749\pi$
$830$	−12.1273	+	2.41228i	−0.0146112	+	0.00290636i
$831$	879.335	−	2122.90i	1.05816	−	2.55464i
$832$		−	292.502i		−	0.351565i
$833$		0			0
$834$	−254.297			−0.304912
$835$	−44.0344	−	18.2396i	−0.0527358	−	0.0218439i
$836$	86.2730	+	433.724i	0.103197	+	0.518809i
$837$	757.041	+	757.041i	0.904470	+	0.904470i
$838$	116.455	+	77.8125i	0.138967	+	0.0928550i
$839$	−217.570	+	1093.80i	−0.259320	+	1.30369i	0.603168	+	0.797614i	$0.293905\pi$
$839$	−217.570	+	1093.80i	−0.259320	+	1.30369i	−0.862488	+	0.506077i	$0.831095\pi$
$840$	−30.5125	+	20.3878i	−0.0363244	+	0.0242712i
$841$	209.454	+	505.667i	0.249054	+	0.601269i
$842$	178.860	−	74.0861i	0.212423	−	0.0879883i
$843$	1008.01	+	1508.59i	1.19574	+	1.78955i
$844$	483.541	+	96.1822i	0.572915	+	0.113960i
$845$	−11.0827	+	16.5864i	−0.0131156	+	0.0196288i
$846$	−925.268	+	925.268i	−1.09370	+	1.09370i
$847$	96.1793	−	19.1312i	0.113553	−	0.0225871i
$848$	31.0437	−	74.9460i	0.0366081	−	0.0883797i
$849$			1157.45i			1.36331i
$850$		0			0
$851$	792.408			0.931149
$852$	252.711	+	104.676i	0.296609	+	0.122859i
$853$	230.147	+	1157.03i	0.269808	+	1.35642i	0.843404	+	0.537280i	$0.180548\pi$
$853$	230.147	+	1157.03i	0.269808	+	1.35642i	−0.573595	+	0.819139i	$0.694452\pi$
$854$	−264.218	−	264.218i	−0.309389	−	0.309389i
$855$	66.9264	+	44.7188i	0.0782765	+	0.0523027i
$856$	278.745	−	1401.35i	0.325637	−	1.63709i
$857$	997.368	−	666.420i	1.16379	−	0.777619i	0.185051	−	0.982729i	$-0.440755\pi$
$857$	997.368	−	666.420i	1.16379	−	0.777619i	0.978739	+	0.205109i	$0.0657550\pi$
$858$	−213.554	−	515.564i	−0.248897	−	0.600891i
$859$	602.760	−	249.671i	0.701699	−	0.290653i	−0.00316564	−	0.999995i	$-0.501008\pi$
$859$	602.760	−	249.671i	0.701699	−	0.290653i	0.704865	+	0.709342i	$0.251008\pi$
$860$	−0.0984649	−	0.147363i	−0.000114494	−	0.000171352i
$861$	−210.378	−	41.8468i	−0.244342	−	0.0486026i
$862$	−53.5981	+	80.2152i	−0.0621788	+	0.0930571i
$863$	−277.083	+	277.083i	−0.321070	+	0.321070i	−0.849177	−	0.528108i	$-0.822902\pi$
$863$	−277.083	+	277.083i	−0.321070	+	0.321070i	0.528108	+	0.849177i	$0.322902\pi$
$864$	2364.50	−	470.329i	2.73670	−	0.544362i
$865$	25.1279	−	60.6642i	0.0290496	−	0.0701320i
$866$		−	405.121i		−	0.467807i
$867$		0			0
$868$	151.139			0.174123
$869$	796.312	+	329.843i	0.916354	+	0.379566i
$870$	−4.62472	−	23.2500i	−0.00531577	−	0.0267242i
$871$	−514.458	−	514.458i	−0.590652	−	0.590652i
$872$	985.516	+	658.501i	1.13018	+	0.755162i
$873$	−120.119	+	603.877i	−0.137593	+	0.691726i
$874$	257.736	−	172.214i	0.294892	−	0.197041i
$875$	16.0622	+	38.7776i	0.0183568	+	0.0443172i
$876$	−268.288	+	111.128i	−0.306264	+	0.126859i
$877$	382.543	+	572.516i	0.436195	+	0.652812i	0.982820	−	0.184565i	$-0.0590877\pi$
$877$	382.543	+	572.516i	0.436195	+	0.652812i	−0.546625	+	0.837377i	$0.684088\pi$
$878$	−399.233	−	79.4125i	−0.454708	−	0.0904470i
$879$	−957.009	+	1432.27i	−1.08875	+	1.62943i
$880$	−1.63449	+	1.63449i	−0.00185737	+	0.00185737i
$881$	−1090.08	+	216.830i	−1.23732	+	0.246118i	−0.770042	−	0.637994i	$-0.779765\pi$
$881$	−1090.08	+	216.830i	−1.23732	+	0.246118i	−0.467276	+	0.884111i	$0.654765\pi$
$882$	−330.918	+	798.908i	−0.375191	+	0.905791i
$883$		−	248.129i		−	0.281007i	−0.990080	−	0.140503i	$-0.955128\pi$
$883$		−	248.129i		−	0.281007i	0.990080	−	0.140503i	$-0.0448721\pi$
$884$		0			0
$885$	82.3704			0.0930739
$886$	−164.317	−	68.0623i	−0.185459	−	0.0768198i
$887$	−247.355	−	1243.54i	−0.278867	−	1.40196i	−0.825412	−	0.564530i	$-0.809057\pi$
$887$	−247.355	−	1243.54i	−0.278867	−	1.40196i	0.546545	−	0.837430i	$-0.315943\pi$
$888$	1620.95	+	1620.95i	1.82539	+	1.82539i
$889$	−67.3301	−	44.9885i	−0.0757368	−	0.0506057i
$890$	2.56334	−	12.8868i	0.00288016	−	0.0144795i
$891$	1742.93	−	1164.59i	1.95616	−	1.30706i
$892$	−191.966	−	463.447i	−0.215209	−	0.519559i
$893$	795.232	−	329.396i	0.890517	−	0.368864i
$894$	424.117	+	634.737i	0.474404	+	0.709996i
$895$	−51.7655	−	10.2968i	−0.0578385	−	0.0115048i
$896$	201.000	−	300.818i	0.224330	−	0.335734i
$897$	511.571	−	511.571i	0.570313	−	0.570313i
$898$	−885.536	+	176.144i	−0.986120	+	0.196152i
$899$	−94.9253	+	229.170i	−0.105590	+	0.254917i
$900$		−	1440.64i		−	1.60071i
$901$		0			0
$902$	111.139			0.123213
$903$	6.78543	+	2.81062i	0.00751432	+	0.00311254i
$904$	−171.136	−	860.359i	−0.189310	−	0.951724i
$905$	16.2161	+	16.2161i	0.0179184	+	0.0179184i
$906$	−1423.46	−	951.124i	−1.57115	−	1.04981i
$907$	245.644	−	1234.94i	0.270831	−	1.36156i	−0.570614	−	0.821218i	$-0.693295\pi$
$907$	245.644	−	1234.94i	0.270831	−	1.36156i	0.841446	−	0.540342i	$-0.181705\pi$
$908$	−768.423	+	513.444i	−0.846281	+	0.565467i
$909$	−974.891	−	2353.59i	−1.07249	−	2.58921i
$910$	−7.88524	+	3.26617i	−0.00866509	+	0.00358920i
$911$	713.375	+	1067.64i	0.783068	+	1.17194i	0.981431	+	0.191816i	$0.0614377\pi$
$911$	713.375	+	1067.64i	0.783068	+	1.17194i	−0.198363	+	0.980129i	$0.563562\pi$
$912$	−106.921	−	21.2680i	−0.117238	−	0.0233202i
$913$	272.805	−	408.282i	0.298801	−	0.447187i
$914$	68.0336	−	68.0336i	0.0744351	−	0.0744351i
$915$	−89.7994	+	17.8622i	−0.0981414	+	0.0195215i
$916$	−261.552	+	631.443i	−0.285538	+	0.689349i
$917$		−	984.635i		−	1.07376i
$918$		0			0
$919$	1532.68			1.66777			0.833886	−	0.551937i	$-0.186111\pi$
$919$	1532.68			1.66777			0.833886	+	0.551937i	$0.186111\pi$
$920$	22.7740	+	9.43329i	0.0247543	+	0.0102536i
$921$	342.846	+	1723.60i	0.372254	+	1.87145i
$922$	399.646	+	399.646i	0.433455	+	0.433455i
$923$	134.391	+	89.7974i	0.145603	+	0.0972886i
$924$	111.903	−	562.574i	0.121107	−	0.608846i
$925$	1089.07	−	727.691i	1.17737	−	0.786693i
$926$	−199.698	−	482.114i	−0.215657	−	0.520641i
$927$	1619.17	−	670.680i	1.74667	−	0.723495i
$928$	310.322	+	464.430i	0.334399	+	0.500464i
$929$	−1611.03	−	320.454i	−1.73416	−	0.344945i	−0.775901	−	0.630855i	$-0.782704\pi$
$929$	−1611.03	−	320.454i	−1.73416	−	0.344945i	−0.958257	+	0.285909i	$0.907704\pi$
$930$	−11.1243	+	16.6487i	−0.0119616	+	0.0179018i
$931$	402.219	−	402.219i	0.432029	−	0.432029i
$932$	105.457	−	20.9767i	0.113151	−	0.0225072i
$933$	135.244	−	326.509i	0.144956	−	0.349956i
$934$			680.262i			0.728332i
$935$		0			0
$936$	1489.87			1.59174
$937$	1179.70	+	488.648i	1.25902	+	0.521502i	0.909608	−	0.415468i	$-0.136382\pi$
$937$	1179.70	+	488.648i	1.25902	+	0.521502i	0.349410	+	0.936970i	$0.386382\pi$
$938$	78.8813	+	396.563i	0.0840952	+	0.422775i
$939$	501.444	+	501.444i	0.534019	+	0.534019i
$940$	22.4012	+	14.9680i	0.0238311	+	0.0159234i
$941$	−330.228	+	1660.17i	−0.350933	+	1.76426i	0.253236	+	0.967405i	$0.418505\pi$
$941$	−330.228	+	1660.17i	−0.350933	+	1.76426i	−0.604169	+	0.796856i	$0.706495\pi$
$942$	818.085	−	546.627i	0.868455	−	0.580283i
$943$	55.1389	+	133.117i	0.0584718	+	0.141163i
$944$	−73.3701	+	30.3909i	−0.0777225	+	0.0321937i
$945$	−34.5251	−	51.6705i	−0.0365345	−	0.0546778i
$946$	−3.73228	−	0.742397i	−0.00394533	−	0.000784774i
$947$	430.349	−	644.063i	0.454434	−	0.680109i	−0.531535	−	0.847036i	$-0.678384\pi$
$947$	430.349	−	644.063i	0.454434	−	0.680109i	0.985969	+	0.166927i	$0.0533845\pi$
$948$	−899.690	+	899.690i	−0.949040	+	0.949040i
$949$	−168.297	+	33.4763i	−0.177341	+	0.0352753i
$950$	196.077	−	473.373i	0.206397	−	0.498287i
$951$		−	787.831i		−	0.828423i
$952$		0			0
$953$	−103.362			−0.108460			−0.0542299	−	0.998528i	$-0.517270\pi$
$953$	−103.362			−0.108460			−0.0542299	+	0.998528i	$0.517270\pi$
$954$	−1753.91	−	726.492i	−1.83848	−	0.761522i
$955$	3.41185	+	17.1525i	0.00357262	+	0.0179608i
$956$	−469.784	−	469.784i	−0.491406	−	0.491406i
$957$	782.742	+	523.011i	0.817912	+	0.546511i
$958$	−42.6532	+	214.432i	−0.0445232	+	0.223833i
$959$	460.541	−	307.724i	0.480231	−	0.320880i
$960$	15.2428	+	36.7993i	0.0158779	+	0.0383326i
$961$	−694.277	+	287.579i	−0.722453	+	0.299250i
$962$	296.204	+	443.300i	0.307904	+	0.460811i
$963$	3986.86	+	793.036i	4.14004	+	0.823506i
$964$	−123.092	+	184.219i	−0.127688	+	0.191099i
$965$	−7.97188	+	7.97188i	−0.00826102	+	0.00826102i
$966$	−394.338	+	78.4387i	−0.408217	+	0.0811994i
$967$	225.886	−	545.336i	0.233594	−	0.563946i	−0.763001	−	0.646397i	$-0.776275\pi$
$967$	225.886	−	545.336i	0.233594	−	0.563946i	0.996595	+	0.0824511i	$0.0262748\pi$
$968$		−	190.561i		−	0.196861i
$969$		0			0
$970$	−6.85412			−0.00706611
$971$	723.680	+	299.758i	0.745293	+	0.308711i	0.722820	−	0.691037i	$-0.242846\pi$
$971$	723.680	+	299.758i	0.745293	+	0.308711i	0.0224739	+	0.999747i	$0.492846\pi$
$972$	266.515	+	1339.86i	0.274192	+	1.37846i
$973$	−109.215	−	109.215i	−0.112245	−	0.112245i
$974$	445.844	+	297.904i	0.457746	+	0.305856i
$975$	233.301	−	1172.88i	0.239283	−	1.20296i
$976$	73.3969	−	49.0423i	0.0752018	−	0.0502482i
$977$	−382.117	−	922.512i	−0.391113	−	0.944229i	−0.989698	−	0.143170i	$-0.954270\pi$
$977$	−382.117	−	922.512i	−0.391113	−	0.944229i	0.598586	−	0.801059i	$-0.295730\pi$
$978$	−570.739	+	236.408i	−0.583578	+	0.241726i
$979$	289.890	+	433.850i	0.296108	+	0.443157i
$980$	17.4621	+	3.47344i	0.0178185	+	0.00354432i
$981$	−1873.45	+	2803.81i	−1.90973	+	2.85812i
$982$	366.759	−	366.759i	0.373481	−	0.373481i
$983$	1801.37	−	358.315i	1.83252	−	0.364512i	0.846670	−	0.532119i	$-0.178604\pi$
$983$	1801.37	−	358.315i	1.83252	−	0.364512i	0.985854	+	0.167607i	$0.0536040\pi$
$984$	−159.512	+	385.096i	−0.162106	+	0.391358i
$985$			8.54155i			0.00867162i
$986$		0			0
$987$	−1116.46			−1.13117
$988$	−356.378	−	147.617i	−0.360707	−	0.149410i
$989$	−0.962475	−	4.83869i	−0.000973180	−	0.00489251i
$990$	38.2508	+	38.2508i	0.0386371	+	0.0386371i
$991$	186.370	+	124.529i	0.188063	+	0.125659i	0.646037	−	0.763306i	$-0.276425\pi$
$991$	186.370	+	124.529i	0.188063	+	0.125659i	−0.457975	+	0.888965i	$0.651425\pi$
$992$	92.0435	−	462.734i	0.0927857	−	0.466465i
$993$	−118.937	+	79.4709i	−0.119775	+	0.0800311i
$994$	−34.3746	−	82.9877i	−0.0345821	−	0.0834886i
$995$	20.6346	−	8.54714i	0.0207383	−	0.00859009i
$996$	402.710	+	602.699i	0.404328	+	0.605119i
$997$	1024.04	+	203.694i	1.02712	+	0.204306i	0.679767	−	0.733429i	$-0.262081\pi$
$997$	1024.04	+	203.694i	1.02712	+	0.204306i	0.347351	+	0.937735i	$0.387081\pi$
$998$	447.110	−	669.148i	0.448006	−	0.670489i
$999$	−2744.95	+	2744.95i	−2.74769	+	2.74769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.3.e.q.249.3	yes	48
17.2	even	8	inner	289.3.e.q.214.3	yes	48
17.3	odd	16	inner	289.3.e.q.65.4	yes	48
17.4	even	4	inner	289.3.e.q.40.3	✓	48
17.5	odd	16	inner	289.3.e.q.224.4	yes	48
17.6	odd	16	inner	289.3.e.q.158.3	yes	48
17.7	odd	16	inner	289.3.e.q.131.3	yes	48
17.8	even	8	inner	289.3.e.q.75.3	yes	48
17.9	even	8	inner	289.3.e.q.75.4	yes	48
17.10	odd	16	inner	289.3.e.q.131.4	yes	48
17.11	odd	16	inner	289.3.e.q.158.4	yes	48
17.12	odd	16	inner	289.3.e.q.224.3	yes	48
17.13	even	4	inner	289.3.e.q.40.4	yes	48
17.14	odd	16	inner	289.3.e.q.65.3	yes	48
17.15	even	8	inner	289.3.e.q.214.4	yes	48
17.16	even	2	inner	289.3.e.q.249.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.3.e.q.40.3	✓	48	17.4	even	4	inner
289.3.e.q.40.4	yes	48	17.13	even	4	inner
289.3.e.q.65.3	yes	48	17.14	odd	16	inner
289.3.e.q.65.4	yes	48	17.3	odd	16	inner
289.3.e.q.75.3	yes	48	17.8	even	8	inner
289.3.e.q.75.4	yes	48	17.9	even	8	inner
289.3.e.q.131.3	yes	48	17.7	odd	16	inner
289.3.e.q.131.4	yes	48	17.10	odd	16	inner
289.3.e.q.158.3	yes	48	17.6	odd	16	inner
289.3.e.q.158.4	yes	48	17.11	odd	16	inner
289.3.e.q.214.3	yes	48	17.2	even	8	inner
289.3.e.q.214.4	yes	48	17.15	even	8	inner
289.3.e.q.224.3	yes	48	17.12	odd	16	inner
289.3.e.q.224.4	yes	48	17.5	odd	16	inner
289.3.e.q.249.3	yes	48	1.1	even	1	trivial
289.3.e.q.249.4	yes	48	17.16	even	2	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	289.e (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09461 - 0.453400i) q^{2} +(-1.09032 - 5.48139i) q^{3} +(-1.83584 - 1.83584i) q^{4} +(0.173703 + 0.116065i) q^{5} +(-1.29180 + 6.49431i) q^{6} +(-3.34395 + 2.23436i) q^{7} +(2.99075 + 7.22031i) q^{8} +(-20.5419 + 8.50875i) q^{9} +O(q^{10})\)	\(q+(-1.09461 - 0.453400i) q^{2} +(-1.09032 - 5.48139i) q^{3} +(-1.83584 - 1.83584i) q^{4} +(0.173703 + 0.116065i) q^{5} +(-1.29180 + 6.49431i) q^{6} +(-3.34395 + 2.23436i) q^{7} +(2.99075 + 7.22031i) q^{8} +(-20.5419 + 8.50875i) q^{9} +(-0.137513 - 0.205802i) q^{10} +(9.64051 + 1.91762i) q^{11} +(-8.06130 + 12.0646i) q^{12} +(-6.06272 + 6.06272i) q^{13} +(4.67337 - 0.929590i) q^{14} +(0.446804 - 1.07868i) q^{15} +1.12567i q^{16} +26.3432 q^{18} +(-16.0096 - 6.63138i) q^{19} +(-0.105815 - 0.531967i) q^{20} +(15.8933 + 15.8933i) q^{21} +(-9.68310 - 6.47004i) q^{22} +(2.94549 - 14.8080i) q^{23} +(36.3165 - 24.2659i) q^{24} +(-9.55038 - 23.0567i) q^{25} +(9.38512 - 3.88745i) q^{26} +(41.0923 + 61.4990i) q^{27} +(10.2409 + 2.03704i) q^{28} +(-9.52069 + 14.2487i) q^{29} +(-0.978149 + 0.978149i) q^{30} +(14.1967 - 2.82389i) q^{31} +(12.4734 - 30.1134i) q^{32} -54.9342i q^{33} -0.840185 q^{35} +(53.3323 + 22.0910i) q^{36} +(10.2391 + 51.4755i) q^{37} +(14.5175 + 14.5175i) q^{38} +(39.8424 + 26.6218i) q^{39} +(-0.318520 + 1.60131i) q^{40} +(-7.93493 + 5.30195i) q^{41} +(-10.1909 - 24.6030i) q^{42} +(0.301889 - 0.125047i) q^{43} +(-14.1780 - 21.2188i) q^{44} +(-4.55576 - 0.906197i) q^{45} +(-9.93809 + 14.8734i) q^{46} +(-35.1236 + 35.1236i) q^{47} +(6.17022 - 1.22733i) q^{48} +(-12.5618 + 30.3269i) q^{49} +29.5681i q^{50} +22.2603 q^{52} +(-66.5792 - 27.5780i) q^{53} +(-17.0962 - 85.9484i) q^{54} +(1.45202 + 1.45202i) q^{55} +(-26.1337 - 17.4620i) q^{56} +(-18.8937 + 94.9850i) q^{57} +(16.8818 - 11.2800i) q^{58} +(26.9981 + 65.1792i) q^{59} +(-2.80054 + 1.16002i) q^{60} +(-43.5673 - 65.2030i) q^{61} +(-16.8201 - 3.34573i) q^{62} +(49.6796 - 74.3508i) q^{63} +(-24.1230 + 24.1230i) q^{64} +(-1.75678 + 0.349445i) q^{65} +(-24.9072 + 60.1313i) q^{66} +84.8560i q^{67} -84.3798 q^{69} +(0.919671 + 0.380940i) q^{70} +(-3.67771 - 18.4891i) q^{71} +(-122.872 - 122.872i) q^{72} +(16.6405 + 11.1188i) q^{73} +(12.1312 - 60.9878i) q^{74} +(-115.970 + 77.4884i) q^{75} +(17.2168 + 41.5651i) q^{76} +(-36.5220 + 15.1279i) q^{77} +(-31.5414 - 47.2050i) q^{78} +(86.0035 + 17.1072i) q^{79} +(-0.130650 + 0.195532i) q^{80} +(150.797 - 150.797i) q^{81} +(11.0895 - 2.20584i) q^{82} +(19.1173 - 46.1534i) q^{83} -58.3552i q^{84} -0.387146 q^{86} +(88.4834 + 36.6510i) q^{87} +(14.9866 + 75.3426i) q^{88} +(37.5364 + 37.5364i) q^{89} +(4.57589 + 3.05751i) q^{90} +(6.72716 - 33.8197i) q^{91} +(-32.5925 + 21.7776i) q^{92} +(-30.9577 - 74.7386i) q^{93} +(54.3716 - 22.5214i) q^{94} +(-2.01124 - 3.01004i) q^{95} +(-178.663 - 35.5383i) q^{96} +(15.3846 - 23.0248i) q^{97} +(27.5005 - 27.5005i) q^{98} +(-214.351 + 42.6371i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 432 q^{18} + 144 q^{35} - 720 q^{52} - 432 q^{69}+O(q^{100}) \) 48 * q + 432 * q^18 + 144 * q^35 - 720 * q^52 - 432 * q^69

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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