LMFDB - Embedded newform 220.3.i.a.43.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(43,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("220.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.i (of order $4$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.20
Character	$\chi$	$=$	220.43
Dual form			220.3.i.a.87.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.17390 - 1.61925i) q^{2} +(-2.04929 + 2.04929i) q^{3} +(-1.24394 + 3.80166i) q^{4} +(-1.54252 + 4.75612i) q^{5} +(5.72396 + 0.912660i) q^{6} +(-0.191923 + 0.191923i) q^{7} +(7.61609 - 2.44850i) q^{8} +0.600827i q^{9} +(9.51209 - 3.08546i) q^{10} +(2.04378 - 10.8085i) q^{11} +(-5.24151 - 10.3399i) q^{12} +(-11.7111 + 11.7111i) q^{13} +(0.536069 + 0.0854739i) q^{14} +(-6.58560 - 12.9077i) q^{15} +(-12.9052 - 9.45807i) q^{16} +(-3.02352 - 3.02352i) q^{17} +(0.972889 - 0.705308i) q^{18} -29.9372i q^{19} +(-16.1623 - 11.7804i) q^{20} -0.786612i q^{21} +(-19.9008 + 9.37862i) q^{22} +(-16.8498 + 16.8498i) q^{23} +(-10.5899 + 20.6253i) q^{24} +(-20.2413 - 14.6728i) q^{25} +(32.7108 + 5.21560i) q^{26} +(-19.6749 - 19.6749i) q^{27} +(-0.490885 - 0.968367i) q^{28} +11.2003 q^{29} +(-13.1700 + 25.8160i) q^{30} +12.8505i q^{31} +(-0.165600 + 31.9996i) q^{32} +(17.9614 + 26.3380i) q^{33} +(-1.34654 + 8.44512i) q^{34} +(-0.616764 - 1.20885i) q^{35} +(-2.28414 - 0.747393i) q^{36} +(9.72307 - 9.72307i) q^{37} +(-48.4758 + 35.1431i) q^{38} -47.9989i q^{39} +(-0.102599 + 39.9999i) q^{40} -23.8309i q^{41} +(-1.27372 + 0.923400i) q^{42} +(-49.2420 - 49.2420i) q^{43} +(38.5478 + 21.2148i) q^{44} +(-2.85760 - 0.926786i) q^{45} +(47.0640 + 7.50415i) q^{46} +(4.51450 + 4.51450i) q^{47} +(45.8289 - 7.06421i) q^{48} +48.9263i q^{49} +(0.00225408 + 50.0000i) q^{50} +12.3921 q^{51} +(-29.9537 - 59.0895i) q^{52} +(-23.7927 - 23.7927i) q^{53} +(-8.76230 + 54.9548i) q^{54} +(48.2538 + 26.3927i) q^{55} +(-0.991780 + 1.93163i) q^{56} +(61.3500 + 61.3500i) q^{57} +(-13.1480 - 18.1361i) q^{58} +14.6598 q^{59} +(57.2628 - 8.97976i) q^{60} -66.0194i q^{61} +(20.8082 - 15.0852i) q^{62} +(-0.115313 - 0.115313i) q^{63} +(52.0097 - 37.2960i) q^{64} +(-37.6348 - 73.7640i) q^{65} +(21.5630 - 60.0020i) q^{66} +(-35.2878 - 35.2878i) q^{67} +(15.2555 - 7.73331i) q^{68} -69.0604i q^{69} +(-1.23342 + 2.41776i) q^{70} +107.125i q^{71} +(1.47113 + 4.57595i) q^{72} +(-52.4871 + 52.4871i) q^{73} +(-27.1579 - 4.33021i) q^{74} +(71.5490 - 11.4115i) q^{75} +(113.811 + 37.2401i) q^{76} +(1.68215 + 2.46664i) q^{77} +(-77.7222 + 56.3457i) q^{78} -122.830i q^{79} +(64.8902 - 46.7895i) q^{80} +75.2316 q^{81} +(-38.5882 + 27.9750i) q^{82} +(81.9671 + 81.9671i) q^{83} +(2.99043 + 0.978498i) q^{84} +(19.0440 - 9.71638i) q^{85} +(-21.9302 + 137.540i) q^{86} +(-22.9526 + 22.9526i) q^{87} +(-10.8989 - 87.3225i) q^{88} -24.0688i q^{89} +(1.85383 + 5.71512i) q^{90} -4.49526i q^{91} +(-43.0972 - 85.0175i) q^{92} +(-26.3344 - 26.3344i) q^{93} +(2.01056 - 12.6097i) q^{94} +(142.385 + 46.1786i) q^{95} +(-65.2370 - 65.9157i) q^{96} +(-36.5473 + 36.5473i) q^{97} +(79.2240 - 57.4344i) q^{98} +(6.49402 + 1.22796i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) $ 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.17390	−	1.61925i	−0.586948	−	0.809625i
$2$	−1.17390	−	1.61925i	−0.586948	−	0.809625i
$3$	−2.04929	+	2.04929i	−0.683096	+	0.683096i	−0.960697	−	0.277600i	$-0.910461\pi$
$3$	−2.04929	+	2.04929i	−0.683096	+	0.683096i	0.277600	+	0.960697i	$0.410461\pi$
$4$	−1.24394	+	3.80166i	−0.310985	+	0.950415i
$5$	−1.54252	+	4.75612i	−0.308503	+	0.951223i
$5$	−1.54252	+	4.75612i	−0.308503	+	0.951223i
$6$	5.72396	+	0.912660i	0.953994	+	0.152110i
$7$	−0.191923	+	0.191923i	−0.0274176	+	0.0274176i	−0.720683	−	0.693265i	$-0.756172\pi$
$7$	−0.191923	+	0.191923i	−0.0274176	+	0.0274176i	0.693265	+	0.720683i	$0.256172\pi$
$8$	7.61609	−	2.44850i	0.952011	−	0.306062i
$9$			0.600827i			0.0667586i
$10$	9.51209	−	3.08546i	0.951209	−	0.308546i
$11$	2.04378	−	10.8085i	0.185798	−	0.982588i
$11$	2.04378	−	10.8085i	0.185798	−	0.982588i
$12$	−5.24151	−	10.3399i	−0.436792	−	0.861658i
$13$	−11.7111	+	11.7111i	−0.900854	+	0.900854i	−0.995510	−	0.0946558i	$-0.969825\pi$
$13$	−11.7111	+	11.7111i	−0.900854	+	0.900854i	0.0946558	+	0.995510i	$0.469825\pi$
$14$	0.536069	+	0.0854739i	0.0382907	+	0.00610528i
$15$	−6.58560	−	12.9077i	−0.439040	−	0.860515i
$16$	−12.9052	−	9.45807i	−0.806577	−	0.591130i
$17$	−3.02352	−	3.02352i	−0.177854	−	0.177854i	0.612566	−	0.790420i	$-0.290137\pi$
$17$	−3.02352	−	3.02352i	−0.177854	−	0.177854i	−0.790420	+	0.612566i	$0.790137\pi$
$18$	0.972889	−	0.705308i	0.0540494	−	0.0391838i
$19$		−	29.9372i		−	1.57564i	−0.615904	−	0.787821i	$-0.711209\pi$
$19$		−	29.9372i		−	1.57564i	0.615904	−	0.787821i	$-0.288791\pi$
$20$	−16.1623	−	11.7804i	−0.808117	−	0.589022i
$21$		−	0.786612i		−	0.0374577i
$22$	−19.9008	+	9.37862i	−0.904581	+	0.426301i
$23$	−16.8498	+	16.8498i	−0.732602	+	0.732602i	−0.971134	−	0.238533i	$-0.923334\pi$
$23$	−16.8498	+	16.8498i	−0.732602	+	0.732602i	0.238533	+	0.971134i	$0.423334\pi$
$24$	−10.5899	+	20.6253i	−0.441245	+	0.859386i
$25$	−20.2413	−	14.6728i	−0.809651	−	0.586911i
$26$	32.7108	+	5.21560i	1.25811	+	0.200600i
$27$	−19.6749	−	19.6749i	−0.728699	−	0.728699i
$28$	−0.490885	−	0.968367i	−0.0175316	−	0.0345845i
$29$	11.2003			0.386217			0.193109	−	0.981177i	$-0.438143\pi$
$29$	11.2003			0.386217			0.193109	+	0.981177i	$0.438143\pi$
$30$	−13.1700	+	25.8160i	−0.439001	+	0.860535i
$31$			12.8505i			0.414533i	0.978285	+	0.207267i	$0.0664567\pi$
$31$			12.8505i			0.414533i	−0.978285	+	0.207267i	$0.933543\pi$
$32$	−0.165600	+	31.9996i	−0.00517502	+	0.999987i
$33$	17.9614	+	26.3380i	0.544284	+	0.798120i
$34$	−1.34654	+	8.44512i	−0.0396041	+	0.248386i
$35$	−0.616764	−	1.20885i	−0.0176218	−	0.0345387i
$36$	−2.28414	−	0.747393i	−0.0634483	−	0.0207609i
$37$	9.72307	−	9.72307i	0.262786	−	0.262786i	−0.563399	−	0.826185i	$-0.690507\pi$
$37$	9.72307	−	9.72307i	0.262786	−	0.262786i	0.826185	+	0.563399i	$0.190507\pi$
$38$	−48.4758	+	35.1431i	−1.27568	+	0.924820i
$39$		−	47.9989i		−	1.23074i
$40$	−0.102599	+	39.9999i	−0.00256498	+	0.999997i
$41$		−	23.8309i		−	0.581242i	−0.956838	−	0.290621i	$-0.906138\pi$
$41$		−	23.8309i		−	0.581242i	0.956838	−	0.290621i	$-0.0938619\pi$
$42$	−1.27372	+	0.923400i	−0.0303267	+	0.0219857i
$43$	−49.2420	−	49.2420i	−1.14516	−	1.14516i	−0.987492	−	0.157671i	$-0.949601\pi$
$43$	−49.2420	−	49.2420i	−1.14516	−	1.14516i	−0.157671	−	0.987492i	$-0.550399\pi$
$44$	38.5478	+	21.2148i	0.876086	+	0.482156i
$45$	−2.85760	−	0.926786i	−0.0635023	−	0.0205952i
$46$	47.0640	+	7.50415i	1.02313	+	0.163134i
$47$	4.51450	+	4.51450i	0.0960533	+	0.0960533i	0.753501	−	0.657447i	$-0.228364\pi$
$47$	4.51450	+	4.51450i	0.0960533	+	0.0960533i	−0.657447	+	0.753501i	$0.728364\pi$
$48$	45.8289	−	7.06421i	0.954768	−	0.147171i
$49$			48.9263i			0.998497i
$50$	0.00225408	+	50.0000i	4.50817e−5	+	1.00000i
$51$	12.3921			0.242983
$52$	−29.9537	−	59.0895i	−0.576033	−	1.13634i
$53$	−23.7927	−	23.7927i	−0.448918	−	0.448918i	0.446076	−	0.894995i	$-0.352821\pi$
$53$	−23.7927	−	23.7927i	−0.448918	−	0.448918i	−0.894995	+	0.446076i	$0.852821\pi$
$54$	−8.76230	+	54.9548i	−0.162265	+	1.01768i
$55$	48.2538	+	26.3927i	0.877341	+	0.479867i
$56$	−0.991780	+	1.93163i	−0.0177104	+	0.0344934i
$57$	61.3500	+	61.3500i	1.07632	+	1.07632i
$58$	−13.1480	−	18.1361i	−0.226689	−	0.312691i
$59$	14.6598			0.248471			0.124235	−	0.992253i	$-0.460352\pi$
$59$	14.6598			0.248471			0.124235	+	0.992253i	$0.460352\pi$
$60$	57.2628	−	8.97976i	0.954381	−	0.149663i
$61$		−	66.0194i		−	1.08228i	−0.840931	−	0.541142i	$-0.817992\pi$
$61$		−	66.0194i		−	1.08228i	0.840931	−	0.541142i	$-0.182008\pi$
$62$	20.8082	−	15.0852i	0.335616	−	0.243309i
$63$	−0.115313	−	0.115313i	−0.00183036	−	0.00183036i
$64$	52.0097	−	37.2960i	0.812652	−	0.582750i
$65$	−37.6348	−	73.7640i	−0.578997	−	1.13483i
$66$	21.5630	−	60.0020i	0.326712	−	0.909121i
$67$	−35.2878	−	35.2878i	−0.526684	−	0.526684i	0.392898	−	0.919582i	$-0.371473\pi$
$67$	−35.2878	−	35.2878i	−0.526684	−	0.526684i	−0.919582	+	0.392898i	$0.871473\pi$
$68$	15.2555	−	7.73331i	0.224345	−	0.113725i
$69$		−	69.0604i		−	1.00088i
$70$	−1.23342	+	2.41776i	−0.0176203	+	0.0345395i
$71$			107.125i			1.50881i	0.656410	+	0.754404i	$0.272074\pi$
$71$			107.125i			1.50881i	−0.656410	+	0.754404i	$0.727926\pi$
$72$	1.47113	+	4.57595i	0.0204323	+	0.0635549i
$73$	−52.4871	+	52.4871i	−0.719001	+	0.719001i	−0.968401	−	0.249399i	$-0.919767\pi$
$73$	−52.4871	+	52.4871i	−0.719001	+	0.719001i	0.249399	+	0.968401i	$0.419767\pi$
$74$	−27.1579	−	4.33021i	−0.366999	−	0.0585164i
$75$	71.5490	−	11.4115i	0.953987	−	0.152153i
$76$	113.811	+	37.2401i	1.49751	+	0.490001i
$77$	1.68215	+	2.46664i	0.0218461	+	0.0320343i
$78$	−77.7222	+	56.3457i	−0.996438	+	0.722380i
$79$		−	122.830i		−	1.55480i	−0.629004	−	0.777402i	$-0.716537\pi$
$79$		−	122.830i		−	1.55480i	0.629004	−	0.777402i	$-0.283463\pi$
$80$	64.8902	−	46.7895i	0.811128	−	0.584869i
$81$	75.2316			0.928785
$82$	−38.5882	+	27.9750i	−0.470588	+	0.341159i
$83$	81.9671	+	81.9671i	0.987556	+	0.987556i	0.999924	−	0.0123677i	$-0.00393686\pi$
$83$	81.9671	+	81.9671i	0.987556	+	0.987556i	−0.0123677	+	0.999924i	$0.503937\pi$
$84$	2.99043	+	0.978498i	0.0356004	+	0.0116488i
$85$	19.0440	−	9.71638i	0.224047	−	0.114310i
$86$	−21.9302	+	137.540i	−0.255002	+	1.59930i
$87$	−22.9526	+	22.9526i	−0.263824	+	0.263824i
$88$	−10.8989	−	87.3225i	−0.123851	−	0.992301i
$89$		−	24.0688i		−	0.270435i	−0.990816	−	0.135218i	$-0.956827\pi$
$89$		−	24.0688i		−	0.270435i	0.990816	−	0.135218i	$-0.0431734\pi$
$90$	1.85383	+	5.71512i	0.0205981	+	0.0635014i
$91$		−	4.49526i		−	0.0493985i
$92$	−43.0972	−	85.0175i	−0.468447	−	0.924104i
$93$	−26.3344	−	26.3344i	−0.283166	−	0.283166i
$94$	2.01056	−	12.6097i	0.0213889	−	0.134145i
$95$	142.385	+	46.1786i	1.49879	+	0.486091i
$96$	−65.2370	−	65.9157i	−0.679552	−	0.686622i
$97$	−36.5473	+	36.5473i	−0.376777	+	0.376777i	−0.869938	−	0.493161i	$-0.835841\pi$
$97$	−36.5473	+	36.5473i	−0.376777	+	0.376777i	0.493161	+	0.869938i	$0.335841\pi$
$98$	79.2240	−	57.4344i	0.808408	−	0.586065i
$99$	6.49402	+	1.22796i	0.0655962	+	0.0124036i
$100$	80.9598	−	58.6984i	0.809598	−	0.586984i
$101$			147.722i			1.46260i	0.682057	+	0.731299i	$0.261086\pi$
$101$			147.722i			1.46260i	−0.682057	+	0.731299i	$0.738914\pi$
$102$	−14.5471	−	20.0659i	−0.142618	−	0.196725i
$103$	−15.3839	+	15.3839i	−0.149358	+	0.149358i	−0.777831	−	0.628473i	$-0.783680\pi$
$103$	−15.3839	+	15.3839i	−0.149358	+	0.149358i	0.628473	+	0.777831i	$0.283680\pi$
$104$	−60.5182	+	117.867i	−0.581906	+	1.13334i
$105$	3.74122	+	1.21336i	0.0356306	+	0.0115558i
$106$	−10.5962	+	66.4564i	−0.0999640	+	0.626947i
$107$	−66.6257	+	66.6257i	−0.622670	+	0.622670i	−0.946213	−	0.323543i	$-0.895126\pi$
$107$	−66.6257	+	66.6257i	−0.622670	+	0.622670i	0.323543	+	0.946213i	$0.395126\pi$
$108$	99.2715	−	50.3228i	0.919181	−	0.465952i
$109$	−147.808			−1.35604			−0.678018	−	0.735045i	$-0.737161\pi$
$109$	−147.808			−1.35604			−0.678018	+	0.735045i	$0.737161\pi$
$110$	−13.9085	−	109.117i	−0.126441	−	0.991974i
$111$			39.8508i			0.359016i
$112$	4.29203	−	0.661588i	0.0383217	−	0.00590704i
$113$	101.361	+	101.361i	0.896998	+	0.896998i	0.995170	−	0.0981712i	$-0.0312993\pi$
$113$	101.361	+	101.361i	0.896998	+	0.896998i	−0.0981712	+	0.995170i	$0.531299\pi$
$114$	27.3225	−	171.359i	0.239671	−	1.50315i
$115$	−54.1486	−	106.131i	−0.470858	−	0.922878i
$116$	−13.9325	+	42.5797i	−0.120108	+	0.367066i
$117$	−7.03635	−	7.03635i	−0.0601397	−	0.0601397i
$118$	−17.2090	−	23.7378i	−0.145839	−	0.201168i
$119$	1.16057			0.00975266
$120$	−81.7610	−	82.1816i	−0.681342	−	0.684846i
$121$	−112.646	−	44.1803i	−0.930958	−	0.365126i
$122$	−106.902	+	77.4998i	−0.876245	+	0.635244i
$123$	48.8364	+	48.8364i	0.397044	+	0.397044i
$124$	−48.8533	−	15.9853i	−0.393978	−	0.128914i
$125$	101.008	−	73.6369i	0.808064	−	0.589095i
$126$	−0.0513550	+	0.322085i	−0.000407579	+	0.00255623i
$127$	−128.689	+	128.689i	−1.01330	+	1.01330i	−0.0133851	+	0.999910i	$0.504261\pi$
$127$	−128.689	+	128.689i	−1.01330	+	1.01330i	−0.999910	+	0.0133851i	$0.995739\pi$
$128$	−121.445	−	40.4351i	−0.948793	−	0.315899i
$129$	201.822			1.56451
$130$	−75.2630	+	147.531i	−0.578946	+	1.13486i
$131$	−122.974			−0.938730			−0.469365	−	0.883004i	$-0.655517\pi$
$131$	−122.974			−0.938730			−0.469365	+	0.883004i	$0.655517\pi$
$132$	−122.471	+	35.5202i	−0.927810	+	0.269092i
$133$	5.74564	+	5.74564i	0.0432003	+	0.0432003i
$134$	−15.7156	+	98.5640i	−0.117281	+	0.735552i
$135$	123.925	−	63.2272i	0.917961	−	0.468349i
$136$	−30.4305	−	15.6243i	−0.223753	−	0.114885i
$137$	−158.269	+	158.269i	−1.15525	+	1.15525i	−0.169766	+	0.985484i	$0.554301\pi$
$137$	−158.269	+	158.269i	−1.15525	+	1.15525i	−0.985484	+	0.169766i	$0.945699\pi$
$138$	−111.826	+	81.0697i	−0.810333	+	0.587461i
$139$			101.883i			0.732970i	0.930424	+	0.366485i	$0.119439\pi$
$139$			101.883i			0.732970i	−0.930424	+	0.366485i	$0.880561\pi$
$140$	5.36287	−	0.840986i	0.0383062	−	0.00600704i
$141$	−18.5030			−0.131227
$142$	173.463	−	125.754i	1.22157	−	0.885591i
$143$	102.644	+	150.514i	0.717791	+	1.05255i
$144$	5.68267	−	7.75381i	0.0394630	−	0.0538459i
$145$	−17.2766	+	53.2699i	−0.119149	+	0.367379i
$146$	146.604	+	23.3754i	1.00414	+	0.160105i
$147$	−100.264	−	100.264i	−0.682069	−	0.682069i
$148$	24.8689	+	49.0587i	0.168033	+	0.331478i
$149$	87.1478			0.584885			0.292442	−	0.956283i	$-0.405532\pi$
$149$	87.1478			0.584885			0.292442	+	0.956283i	$0.405532\pi$
$150$	−102.469	−	102.460i	−0.683127	−	0.683066i
$151$	−192.284			−1.27340			−0.636701	−	0.771111i	$-0.719701\pi$
$151$	−192.284			−1.27340			−0.636701	+	0.771111i	$0.719701\pi$
$152$	−73.3012	−	228.005i	−0.482245	−	1.50003i
$153$	1.81661	−	1.81661i	0.0118733	−	0.0118733i
$154$	2.01945	−	5.61940i	0.0131133	−	0.0364896i
$155$	−61.1186	−	19.8222i	−0.394314	−	0.127885i
$156$	182.475	+	59.7077i	1.16971	+	0.382742i
$157$	149.928	−	149.928i	0.954956	−	0.954956i	−0.0440723	−	0.999028i	$-0.514033\pi$
$157$	149.928	−	149.928i	0.954956	−	0.954956i	0.999028	+	0.0440723i	$0.0140332\pi$
$158$	−198.892	+	144.189i	−1.25881	+	0.912588i
$159$	97.5162			0.613309
$160$	−151.938	−	50.1475i	−0.949614	−	0.313422i
$161$		−	6.46775i		−	0.0401723i
$162$	−88.3140	−	121.819i	−0.545148	−	0.751967i
$163$	−20.1712	+	20.1712i	−0.123750	+	0.123750i	−0.766269	−	0.642520i	$-0.777889\pi$
$163$	−20.1712	+	20.1712i	−0.123750	+	0.123750i	0.642520	+	0.766269i	$0.277889\pi$
$164$	90.5970	+	29.6442i	0.552421	+	0.180758i
$165$	−152.972	+	44.7996i	−0.927104	+	0.271513i
$166$	36.5044	−	228.946i	0.219906	−	1.37919i
$167$	−56.4559	+	56.4559i	−0.338059	+	0.338059i	−0.855636	−	0.517577i	$-0.826834\pi$
$167$	−56.4559	+	56.4559i	−0.338059	+	0.338059i	0.517577	+	0.855636i	$0.326834\pi$
$168$	−1.92602	−	5.99091i	−0.0114644	−	0.0356602i
$169$		−	105.300i		−	0.623077i
$170$	−38.0889	−	19.4310i	−0.224053	−	0.114300i
$171$	17.9871			0.105188
$172$	248.455	−	125.947i	1.44451	−	0.732251i
$173$	128.028	−	128.028i	0.740047	−	0.740047i	−0.232540	−	0.972587i	$-0.574704\pi$
$173$	128.028	−	128.028i	0.740047	−	0.740047i	0.972587	+	0.232540i	$0.0747037\pi$
$174$	64.1101	+	10.2221i	0.368449	+	0.0587475i
$175$	6.70082	−	1.06873i	0.0382904	−	0.00610700i
$176$	−128.603	+	120.155i	−0.730697	+	0.682702i
$177$	−30.0421	+	30.0421i	−0.169729	+	0.169729i
$178$	−38.9733	+	28.2542i	−0.218951	+	0.158731i
$179$	−326.200			−1.82234			−0.911172	−	0.412025i	$-0.864821\pi$
$179$	−326.200			−1.82234			−0.911172	+	0.412025i	$0.864821\pi$
$180$	7.07801	−	9.71077i	0.0393223	−	0.0539487i
$181$	−7.65453			−0.0422902			−0.0211451	−	0.999776i	$-0.506731\pi$
$181$	−7.65453			−0.0422902			−0.0211451	+	0.999776i	$0.506731\pi$
$182$	−7.27896	+	5.27697i	−0.0399943	+	0.0289943i
$183$	135.293	+	135.293i	0.739305	+	0.739305i
$184$	−87.0731	+	169.587i	−0.473223	+	0.921667i
$185$	31.2461	+	61.2421i	0.168898	+	0.331038i
$186$	−11.7282	+	73.5559i	−0.0630547	+	0.395462i
$187$	−38.8590	+	26.5002i	−0.207802	+	0.141712i
$188$	−22.7784	+	11.5468i	−0.121162	+	0.0614193i
$189$	7.55213			0.0399583
$190$	−92.3701	−	284.766i	−0.486159	−	1.49877i
$191$			28.8142i			0.150860i	0.997151	+	0.0754299i	$0.0240329\pi$
$191$			28.8142i			0.150860i	−0.997151	+	0.0754299i	$0.975967\pi$
$192$	−30.1526	+	183.013i	−0.157045	+	0.953194i
$193$	124.886	−	124.886i	0.647078	−	0.647078i	−0.305208	−	0.952286i	$-0.598726\pi$
$193$	124.886	−	124.886i	0.647078	−	0.647078i	0.952286	+	0.305208i	$0.0987260\pi$
$194$	102.082	+	16.2765i	0.526196	+	0.0838996i
$195$	228.288	+	74.0391i	1.17071	+	0.379688i
$196$	−186.001	−	60.8614i	−0.948986	−	0.310517i
$197$	−159.965	−	159.965i	−0.812005	−	0.812005i	0.172930	−	0.984934i	$-0.444677\pi$
$197$	−159.965	−	159.965i	−0.812005	−	0.812005i	−0.984934	+	0.172930i	$0.944677\pi$
$198$	−5.63493	−	11.9569i	−0.0284592	−	0.0603886i
$199$	246.680			1.23960			0.619800	−	0.784760i	$-0.287214\pi$
$199$	246.680			1.23960			0.619800	+	0.784760i	$0.287214\pi$
$200$	−190.086	−	62.1884i	−0.950429	−	0.310942i
$201$	144.630			0.719552
$202$	239.199	−	173.411i	1.18416	−	0.858468i
$203$	−2.14960	+	2.14960i	−0.0105891	+	0.0105891i
$204$	−15.4151	+	47.1106i	−0.0755640	+	0.230934i
$205$	113.343	+	36.7596i	0.552891	+	0.179315i
$206$	42.9694	+	6.85127i	0.208589	+	0.0332586i
$207$	−10.1238	−	10.1238i	−0.0489074	−	0.0489074i
$208$	261.899	−	40.3700i	1.25913	−	0.194086i
$209$	−323.575	−	61.1851i	−1.54821	−	0.292752i
$210$	−2.42706	−	7.48233i	−0.0115574	−	0.0356301i
$211$	−154.668			−0.733025			−0.366512	−	0.930413i	$-0.619448\pi$
$211$	−154.668			−0.733025			−0.366512	+	0.930413i	$0.619448\pi$
$212$	120.048	−	60.8550i	0.566266	−	0.287052i
$213$	−219.531	−	219.531i	−1.03066	−	1.03066i
$214$	186.095	+	29.6721i	0.869604	+	0.138655i
$215$	310.157	−	158.244i	1.44259	−	0.736019i
$216$	−198.020	−	101.672i	−0.916757	−	0.470702i
$217$	−2.46631	−	2.46631i	−0.0113655	−	0.0113655i
$218$	173.511	+	239.338i	0.795922	+	1.09788i
$219$		−	215.123i		−	0.982295i
$220$	−160.361	+	150.613i	−0.728913	+	0.684606i
$221$	70.8175			0.320441
$222$	64.5284	−	46.7806i	0.290668	−	0.210724i
$223$	104.480	−	104.480i	0.468519	−	0.468519i	−0.432916	−	0.901434i	$-0.642515\pi$
$223$	104.480	−	104.480i	0.468519	−	0.468519i	0.901434	+	0.432916i	$0.142515\pi$
$224$	−6.10968	−	6.17324i	−0.0272753	−	0.0275591i
$225$	8.81580	−	12.1615i	0.0391813	−	0.0540512i
$226$	45.1415	−	283.115i	0.199741	−	1.25272i
$227$	56.0911	−	56.0911i	0.247097	−	0.247097i	−0.572681	−	0.819778i	$-0.694097\pi$
$227$	56.0911	−	56.0911i	0.247097	−	0.247097i	0.819778	+	0.572681i	$0.194097\pi$
$228$	−309.548	+	156.916i	−1.35766	+	0.688228i
$229$			295.729i			1.29139i	0.763595	+	0.645696i	$0.223433\pi$
$229$			295.729i			1.29139i	−0.763595	+	0.645696i	$0.776567\pi$
$230$	−108.288	+	212.267i	−0.470816	+	0.922899i
$231$	−8.50207	−	1.60766i	−0.0368055	−	0.00695958i
$232$	85.3025	−	27.4239i	0.367683	−	0.118207i
$233$	138.848	−	138.848i	0.595913	−	0.595913i	−0.343309	−	0.939222i	$-0.611548\pi$
$233$	138.848	−	138.848i	0.595913	−	0.595913i	0.939222	+	0.343309i	$0.111548\pi$
$234$	−3.13367	+	19.6535i	−0.0133918	+	0.0839895i
$235$	−28.4352	+	14.5078i	−0.121001	+	0.0617354i
$236$	−18.2359	+	55.7314i	−0.0772706	+	0.236150i
$237$	251.713	+	251.713i	1.06208	+	1.06208i
$238$	−1.36238	−	1.87925i	−0.00572430	−	0.00789599i
$239$		−	330.896i		−	1.38450i	−0.721656	−	0.692251i	$-0.756619\pi$
$239$		−	330.896i		−	1.38450i	0.721656	−	0.692251i	$-0.243381\pi$
$240$	−37.0936	+	228.864i	−0.154557	+	0.953600i
$241$			353.916i			1.46853i	0.678863	+	0.734265i	$0.262473\pi$
$241$			353.916i			1.46853i	−0.678863	+	0.734265i	$0.737527\pi$
$242$	60.6956	+	234.265i	0.250808	+	0.968037i
$243$	22.9026	−	22.9026i	0.0942494	−	0.0942494i
$244$	250.983	+	82.1241i	1.02862	+	0.336574i
$245$	−232.699	−	75.4697i	−0.949793	−	0.308040i
$246$	21.7495	−	136.407i	0.0884128	−	0.554501i
$247$	350.598	+	350.598i	1.41942	+	1.41942i
$248$	31.4645	+	97.8708i	0.126873	+	0.394640i
$249$	−335.949			−1.34919
$250$	−237.809	−	77.1151i	−0.951237	−	0.308460i
$251$			15.6105i			0.0621931i	0.999516	+	0.0310965i	$0.00989993\pi$
$251$			15.6105i			0.0621931i	−0.999516	+	0.0310965i	$0.990100\pi$
$252$	0.581821	−	0.294937i	0.00230881	−	0.00117039i
$253$	147.684	+	216.558i	0.583729	+	0.855962i
$254$	359.446	+	57.3120i	1.41514	+	0.225638i
$255$	−19.1151	+	58.9384i	−0.0749610	+	0.231131i
$256$	77.0897	+	244.117i	0.301132	+	0.953583i
$257$	276.648	−	276.648i	1.07645	−	1.07645i	0.0796260	−	0.996825i	$-0.474627\pi$
$257$	276.648	−	276.648i	1.07645	−	1.07645i	0.996825	−	0.0796260i	$-0.0253726\pi$
$258$	−236.918	−	326.801i	−0.918287	−	1.26667i
$259$			3.73216i			0.0144099i
$260$	327.241	−	51.3168i	1.25862	−	0.197372i
$261$			6.72944i			0.0257833i
$262$	144.358	+	199.125i	0.550986	+	0.760020i
$263$	−85.2580	−	85.2580i	−0.324175	−	0.324175i	0.526191	−	0.850366i	$-0.323620\pi$
$263$	−85.2580	−	85.2580i	−0.324175	−	0.324175i	−0.850366	+	0.526191i	$0.823620\pi$
$264$	201.284	+	156.614i	0.762439	+	0.593235i
$265$	149.861	−	76.4601i	0.565515	−	0.288529i
$266$	2.55885	−	16.0484i	0.00961973	−	0.0603324i
$267$	49.3238	+	49.3238i	0.184733	+	0.184733i
$268$	178.048	−	90.2564i	0.664359	−	0.336777i
$269$			426.434i			1.58526i	0.609705	+	0.792628i	$0.291288\pi$
$269$			426.434i			1.58526i	−0.609705	+	0.792628i	$0.708712\pi$
$270$	−247.855	−	126.443i	−0.917983	−	0.468308i
$271$	−268.779			−0.991806			−0.495903	−	0.868378i	$-0.665163\pi$
$271$	−268.779			−0.991806			−0.495903	+	0.868378i	$0.665163\pi$
$272$	10.4225	+	67.6158i	0.0383181	+	0.248588i
$273$	9.21210	+	9.21210i	0.0337439	+	0.0337439i
$274$	442.069	+	70.4860i	1.61339	+	0.257248i
$275$	−199.959	+	188.789i	−0.727124	+	0.686507i
$276$	262.544	+	85.9070i	0.951247	+	0.311257i
$277$	−191.192	−	191.192i	−0.690225	−	0.690225i	0.272057	−	0.962281i	$-0.412296\pi$
$277$	−191.192	−	191.192i	−0.690225	−	0.690225i	−0.962281	+	0.272057i	$0.912296\pi$
$278$	164.974	−	119.600i	0.593430	−	0.430215i
$279$	−7.72095			−0.0276736
$280$	−7.65721	−	7.69659i	−0.0273472	−	0.0274878i
$281$			109.574i			0.389944i	0.980809	+	0.194972i	$0.0624616\pi$
$281$			109.574i			0.389944i	−0.980809	+	0.194972i	$0.937538\pi$
$282$	21.7206	+	29.9611i	0.0770235	+	0.106245i
$283$	−25.6303	−	25.6303i	−0.0905664	−	0.0905664i	0.660372	−	0.750939i	$-0.270399\pi$
$283$	−25.6303	−	25.6303i	−0.0905664	−	0.0905664i	−0.750939	+	0.660372i	$0.770399\pi$
$284$	−407.254	−	133.258i	−1.43399	−	0.469217i
$285$	−386.421	+	197.154i	−1.35586	+	0.691770i
$286$	123.226	−	342.894i	0.430861	−	1.19893i
$287$	4.57370	+	4.57370i	0.0159363	+	0.0159363i
$288$	−19.2262	−	0.0994973i	−0.0667577	−	0.000345477i
$289$		−	270.717i		−	0.936736i
$290$	106.538	−	34.5581i	0.367373	−	0.119166i
$291$		−	149.792i		−	0.514749i
$292$	−134.247	−	264.829i	−0.459751	−	0.906948i
$293$	−143.187	+	143.187i	−0.488691	+	0.488691i	−0.907893	−	0.419202i	$-0.862310\pi$
$293$	−143.187	+	143.187i	−0.488691	+	0.488691i	0.419202	+	0.907893i	$0.362310\pi$
$294$	−44.6531	+	280.052i	−0.151881	+	0.952559i
$295$	−22.6129	+	69.7236i	−0.0766540	+	0.236351i
$296$	50.2449	−	97.8587i	0.169746	−	0.330604i
$297$	−252.866	+	172.444i	−0.851402	+	0.580620i
$298$	−102.302	−	141.114i	−0.343297	−	0.473537i
$299$		−	394.660i		−	1.31993i
$300$	−45.6201	+	286.200i	−0.152067	+	0.954001i
$301$	18.9014			0.0627952
$302$	225.721	+	311.355i	0.747420	+	1.03098i
$303$	−302.726	−	302.726i	−0.999095	−	0.999095i
$304$	−283.148	+	386.346i	−0.931409	+	1.27088i
$305$	313.996	+	101.836i	1.02949	+	0.333888i
$306$	−5.07406	−	0.809036i	−0.0165819	−	0.00264391i
$307$	−302.068	+	302.068i	−0.983936	+	0.983936i	−0.999873	−	0.0159367i	$-0.994927\pi$
$307$	−302.068	+	302.068i	−0.983936	+	0.983936i	0.0159367	+	0.999873i	$0.494927\pi$
$308$	−11.4698	+	3.32659i	−0.0372397	+	0.0108006i
$309$		−	63.0520i		−	0.204052i
$310$	39.6498	+	122.235i	0.127903	+	0.394308i
$311$			245.922i			0.790745i	0.918521	+	0.395373i	$0.129385\pi$
$311$			245.922i			0.790745i	−0.918521	+	0.395373i	$0.870615\pi$
$312$	−117.525	−	365.564i	−0.376683	−	1.17168i
$313$	−265.176	−	265.176i	−0.847207	−	0.847207i	0.142576	−	0.989784i	$-0.454461\pi$
$313$	−265.176	−	265.176i	−0.847207	−	0.847207i	−0.989784	+	0.142576i	$0.954461\pi$
$314$	−418.771	−	66.7712i	−1.33367	−	0.212647i
$315$	0.726312	−	0.370569i	0.00230575	−	0.00117641i
$316$	466.956	+	152.793i	1.47771	+	0.483521i
$317$	161.326	−	161.326i	0.508916	−	0.508916i	−0.405278	−	0.914194i	$-0.632825\pi$
$317$	161.326	−	161.326i	0.508916	−	0.508916i	0.914194	+	0.405278i	$0.132825\pi$
$318$	−114.474	−	157.903i	−0.359980	−	0.496550i
$319$	22.8909	−	121.058i	0.0717584	−	0.379492i
$320$	97.1583	+	304.894i	0.303620	+	0.952793i
$321$		−	273.071i		−	0.850688i
$322$	−10.4729	+	7.59246i	−0.0325245	+	0.0235791i
$323$	−90.5157	+	90.5157i	−0.280234	+	0.280234i
$324$	−93.5836	+	286.005i	−0.288838	+	0.882731i
$325$	408.882	−	65.2134i	1.25810	−	0.200657i
$326$	56.3410	+	8.98333i	0.172825	+	0.0275562i
$327$	302.901	−	302.901i	0.926303	−	0.926303i
$328$	−58.3500	−	181.498i	−0.177896	−	0.553349i
$329$	−1.73288			−0.00526710
$330$	252.115	+	195.110i	0.763985	+	0.591243i
$331$		−	447.273i		−	1.35128i	−0.737232	−	0.675639i	$-0.763868\pi$
$331$		−	447.273i		−	1.35128i	0.737232	−	0.675639i	$-0.236132\pi$
$332$	−413.573	+	209.649i	−1.24570	+	0.631473i
$333$	5.84189	+	5.84189i	0.0175432	+	0.0175432i
$334$	157.690	+	25.1429i	0.472124	+	0.0752781i
$335$	222.265	−	113.401i	0.663478	−	0.338510i
$336$	−7.43983	+	10.1514i	−0.0221424	+	0.0302125i
$337$	−151.689	−	151.689i	−0.450115	−	0.450115i	0.445278	−	0.895393i	$-0.353105\pi$
$337$	−151.689	−	151.689i	−0.450115	−	0.450115i	−0.895393	+	0.445278i	$0.853105\pi$
$338$	−170.507	+	123.611i	−0.504458	+	0.365713i
$339$	−415.435			−1.22547
$340$	13.2487	+	84.4855i	0.0389668	+	0.248487i
$341$	138.895	+	26.2637i	0.407315	+	0.0770195i
$342$	−21.1150	−	29.1256i	−0.0617396	−	0.0851625i
$343$	−18.7943	−	18.7943i	−0.0547940	−	0.0547940i
$344$	−495.601	−	254.463i	−1.44070	−	0.739717i
$345$	328.459	+	106.527i	0.952056	+	0.308773i
$346$	−357.601	−	57.0179i	−1.03353	−	0.164792i
$347$	−1.95387	+	1.95387i	−0.00563075	+	0.00563075i	−0.709917	−	0.704286i	$-0.751267\pi$
$347$	−1.95387	+	1.95387i	−0.00563075	+	0.00563075i	0.704286	+	0.709917i	$0.251267\pi$
$348$	−58.7064	−	115.810i	−0.168697	−	0.332787i
$349$	507.289			1.45355			0.726774	−	0.686876i	$-0.241019\pi$
$349$	507.289			1.45355			0.726774	+	0.686876i	$0.241019\pi$
$350$	−9.59659	−	9.59572i	−0.0274188	−	0.0274164i
$351$	460.829			1.31290
$352$	345.528	+	67.1900i	0.981613	+	0.190881i
$353$	−20.6594	−	20.6594i	−0.0585252	−	0.0585252i	0.677238	−	0.735764i	$-0.263177\pi$
$353$	−20.6594	−	20.6594i	−0.0585252	−	0.0585252i	−0.735764	+	0.677238i	$0.763177\pi$
$354$	83.9120	+	13.3794i	0.237039	+	0.0377949i
$355$	−509.501	−	165.243i	−1.43521	−	0.465472i
$356$	91.5012	+	29.9401i	0.257026	+	0.0841014i
$357$	−2.37834	+	2.37834i	−0.00666200	+	0.00666200i
$358$	382.924	+	528.199i	1.06962	+	1.47542i
$359$		−	286.206i		−	0.797231i	−0.917118	−	0.398615i	$-0.869491\pi$
$359$		−	286.206i		−	0.797231i	0.917118	−	0.398615i	$-0.130509\pi$
$360$	−24.0330	−	0.0616443i	−0.0667584	−	0.000171234i
$361$	−535.236			−1.48265
$362$	8.98562	+	12.3946i	0.0248222	+	0.0342392i
$363$	321.382	−	140.306i	0.885350	−	0.386518i
$364$	17.0895	+	5.59184i	0.0469491	+	0.0153622i
$365$	−168.673	−	330.597i	−0.462117	−	0.905745i
$366$	60.2533	−	377.892i	0.164626	−	1.03249i
$367$	107.002	+	107.002i	0.291558	+	0.291558i	0.837696	−	0.546138i	$-0.183902\pi$
$367$	107.002	+	107.002i	0.291558	+	0.291558i	−0.546138	+	0.837696i	$0.683902\pi$
$368$	376.818	−	58.0840i	1.02396	−	0.157837i
$369$	14.3183			0.0388029
$370$	62.4866	−	122.487i	0.168883	−	0.331046i
$371$	9.13273			0.0246165
$372$	132.873	−	67.3561i	0.357186	−	0.181065i
$373$	−357.322	+	357.322i	−0.957967	+	0.957967i	−0.999152	−	0.0411849i	$-0.986887\pi$
$373$	−357.322	+	357.322i	−0.957967	+	0.957967i	0.0411849	+	0.999152i	$0.486887\pi$
$374$	88.5268	+	31.8140i	0.236703	+	0.0850641i
$375$	−56.0912	+	357.898i	−0.149577	+	0.954394i
$376$	45.4366	+	23.3291i	0.120842	+	0.0620455i
$377$	−131.168	+	131.168i	−0.347925	+	0.347925i
$378$	−8.86540	−	12.2288i	−0.0234534	−	0.0323513i
$379$	−454.313			−1.19872			−0.599358	−	0.800481i	$-0.704577\pi$
$379$	−454.313			−1.19872			−0.599358	+	0.800481i	$0.704577\pi$
$380$	−352.674	+	483.855i	−0.928089	+	1.27330i
$381$		−	527.440i		−	1.38436i
$382$	46.6574	−	33.8249i	0.122140	−	0.0885468i
$383$	228.002	−	228.002i	0.595306	−	0.595306i	−0.343754	−	0.939060i	$-0.611698\pi$
$383$	228.002	−	228.002i	0.595306	−	0.595306i	0.939060	+	0.343754i	$0.111698\pi$
$384$	331.740	−	166.014i	0.863907	−	0.432327i
$385$	−14.3264	+	4.19564i	−0.0372114	+	0.0108978i
$386$	−348.825	−	55.6186i	−0.903691	−	0.144090i
$387$	29.5859	−	29.5859i	0.0764495	−	0.0764495i
$388$	−93.4778	−	184.403i	−0.240922	−	0.475266i
$389$			109.473i			0.281421i	0.990051	+	0.140711i	$0.0449387\pi$
$389$			109.473i			0.281421i	−0.990051	+	0.140711i	$0.955061\pi$
$390$	−148.099	−	456.570i	−0.379740	−	1.17069i
$391$	101.892			0.260592
$392$	119.796	+	372.627i	0.305602	+	0.950580i
$393$	252.009	−	252.009i	0.641243	−	0.641243i
$394$	−71.2411	+	446.805i	−0.180815	+	1.13402i
$395$	584.191	+	189.467i	1.47897	+	0.479662i
$396$	−12.7465	+	23.1605i	−0.0321880	+	0.0584862i
$397$	−107.593	+	107.593i	−0.271016	+	0.271016i	−0.829509	−	0.558493i	$-0.811380\pi$
$397$	−107.593	+	107.593i	−0.271016	+	0.271016i	0.558493	+	0.829509i	$0.311380\pi$
$398$	−289.577	−	399.437i	−0.727580	−	1.00361i
$399$	−23.5490			−0.0590200
$400$	122.442	+	380.799i	0.306105	+	0.951998i
$401$	−213.669			−0.532841			−0.266421	−	0.963857i	$-0.585841\pi$
$401$	−213.669			−0.532841			−0.266421	+	0.963857i	$0.585841\pi$
$402$	−169.780	−	234.192i	−0.422339	−	0.582567i
$403$	−150.494	−	150.494i	−0.373434	−	0.373434i
$404$	−561.590	−	183.758i	−1.39007	−	0.454846i
$405$	−116.046	+	357.810i	−0.286533	+	0.883482i
$406$	6.00413	+	0.957333i	0.0147885	+	0.00235796i
$407$	−85.2197	−	124.963i	−0.209385	−	0.307035i
$408$	94.3796	−	30.3421i	0.231322	−	0.0743679i
$409$	165.802			0.405385			0.202692	−	0.979242i	$-0.435031\pi$
$409$	165.802			0.405385			0.202692	+	0.979242i	$0.435031\pi$
$410$	−73.5294	−	226.682i	−0.179340	−	0.552883i
$411$		−	648.679i		−	1.57830i
$412$	−39.3476	−	77.6208i	−0.0955039	−	0.188400i
$413$	−2.81355	+	2.81355i	−0.00681247	+	0.00681247i
$414$	−4.50870	+	28.2774i	−0.0108906	+	0.0683028i
$415$	−516.281	+	263.410i	−1.24405	+	0.634722i
$416$	−372.811	−	376.690i	−0.896180	−	0.905504i
$417$	−208.787	−	208.787i	−0.500689	−	0.500689i
$418$	280.770	+	595.774i	0.671698	+	1.42530i
$419$	−53.5275			−0.127751			−0.0638753	−	0.997958i	$-0.520346\pi$
$419$	−53.5275			−0.127751			−0.0638753	+	0.997958i	$0.520346\pi$
$420$	−9.26664	+	12.7135i	−0.0220634	+	0.0302702i
$421$	226.307			0.537546			0.268773	−	0.963203i	$-0.413382\pi$
$421$	226.307			0.537546			0.268773	+	0.963203i	$0.413382\pi$
$422$	181.564	+	250.446i	0.430247	+	0.593475i
$423$	−2.71244	+	2.71244i	−0.00641238	+	0.00641238i
$424$	−239.464	−	122.951i	−0.564773	−	0.289978i
$425$	16.8365	+	105.563i	0.0396152	+	0.248384i
$426$	−97.7691	+	613.182i	−0.229505	+	1.43939i
$427$	12.6706	+	12.6706i	0.0296736	+	0.0296736i
$428$	−170.410	−	336.167i	−0.398154	−	0.785436i
$429$	−518.794	−	98.0992i	−1.20931	−	0.228669i
$430$	−620.329	−	316.460i	−1.44263	−	0.735954i
$431$	184.190			0.427354			0.213677	−	0.976904i	$-0.431456\pi$
$431$	184.190			0.427354			0.213677	+	0.976904i	$0.431456\pi$
$432$	67.8223	+	439.995i	0.156996	+	1.01851i
$433$	355.695	+	355.695i	0.821467	+	0.821467i	0.986318	−	0.164851i	$-0.0527143\pi$
$433$	355.695	+	355.695i	0.821467	+	0.821467i	−0.164851	+	0.986318i	$0.552714\pi$
$434$	−1.09838	+	6.88877i	−0.00253084	+	0.0158727i
$435$	−73.7606	−	144.570i	−0.169565	−	0.332346i
$436$	183.864	−	561.915i	0.421707	−	1.28880i
$437$	504.437	+	504.437i	1.15432	+	1.15432i
$438$	−348.337	+	252.531i	−0.795290	+	0.576555i
$439$			444.731i			1.01305i	0.862224	+	0.506527i	$0.169071\pi$
$439$			444.731i			1.01305i	−0.862224	+	0.506527i	$0.830929\pi$
$440$	432.128	+	82.8599i	0.982108	+	0.188318i
$441$	−29.3963			−0.0666582
$442$	−83.1323	−	114.671i	−0.188082	−	0.259437i
$443$	335.016	−	335.016i	0.756244	−	0.756244i	−0.219393	−	0.975637i	$-0.570408\pi$
$443$	335.016	−	335.016i	0.756244	−	0.756244i	0.975637	+	0.219393i	$0.0704077\pi$
$444$	−151.499	−	49.5720i	−0.341214	−	0.111649i
$445$	114.474	+	37.1265i	0.257244	+	0.0834302i
$446$	−291.827	−	46.5305i	−0.654321	−	0.104329i
$447$	−178.591	+	178.591i	−0.399533	+	0.399533i
$448$	−2.82390	+	17.1398i	−0.00630335	+	0.0382585i
$449$		−	503.174i		−	1.12066i	−0.828271	−	0.560328i	$-0.810675\pi$
$449$		−	503.174i		−	1.12066i	0.828271	−	0.560328i	$-0.189325\pi$
$450$	−30.0414	+	0.00135431i	−0.0667586	+	3.00959e-6i
$451$	−257.576	−	48.7052i	−0.571121	−	0.107994i
$452$	−511.426	+	259.253i	−1.13147	+	0.573567i
$453$	394.045	−	394.045i	0.869856	−	0.869856i
$454$	−156.671	−	24.9804i	−0.345090	−	0.0550230i
$455$	21.3800	+	6.93402i	0.0469890	+	0.0152396i
$456$	617.463	+	317.032i	1.35408	+	0.695245i
$457$	537.579	+	537.579i	1.17632	+	1.17632i	0.980674	+	0.195648i	$0.0626809\pi$
$457$	537.579	+	537.579i	1.17632	+	1.17632i	0.195648	+	0.980674i	$0.437319\pi$
$458$	478.859	−	347.155i	1.04554	−	0.757980i
$459$			118.975i			0.259204i
$460$	470.831	−	73.8341i	1.02355	−	0.160509i
$461$			95.1876i			0.206481i	0.994656	+	0.103240i	$0.0329211\pi$
$461$			95.1876i			0.206481i	−0.994656	+	0.103240i	$0.967079\pi$
$462$	7.37733	+	15.6542i	0.0159683	+	0.0338836i
$463$	−494.077	+	494.077i	−1.06712	+	1.06712i	−0.0695422	+	0.997579i	$0.522154\pi$
$463$	−494.077	+	494.077i	−1.06712	+	1.06712i	−0.997579	+	0.0695422i	$0.977846\pi$
$464$	−144.542	−	105.933i	−0.311514	−	0.228304i
$465$	165.871	−	84.6284i	0.356712	−	0.181996i
$466$	−387.822	−	61.8365i	−0.832236	−	0.132696i
$467$	−34.3502	−	34.3502i	−0.0735550	−	0.0735550i	0.669372	−	0.742927i	$-0.266563\pi$
$467$	−34.3502	−	34.3502i	−0.0735550	−	0.0735550i	−0.742927	+	0.669372i	$0.766563\pi$
$468$	35.5026	−	17.9970i	0.0758603	−	0.0384551i
$469$	13.5451			0.0288808
$470$	56.8717	+	29.0131i	0.121004	+	0.0617299i
$471$			614.492i			1.30465i
$472$	111.650	−	35.8944i	0.236547	−	0.0760475i
$473$	−632.870	+	431.591i	−1.33799	+	0.912454i
$474$	112.102	−	703.072i	0.236501	−	1.48327i
$475$	−439.262	+	605.968i	−0.924762	+	1.27572i
$476$	−1.44367	+	4.41208i	−0.00303293	+	0.00926907i
$477$	14.2953	−	14.2953i	0.0299692	−	0.0299692i
$478$	−535.804	+	388.437i	−1.12093	+	0.812631i
$479$			687.002i			1.43424i	0.696949	+	0.717121i	$0.254540\pi$
$479$			687.002i			1.43424i	−0.696949	+	0.717121i	$0.745460\pi$
$480$	414.132	−	208.599i	0.862775	−	0.434581i
$481$			227.736i			0.473463i
$482$	573.078	−	415.460i	1.18896	−	0.861950i
$483$	13.2543	+	13.2543i	0.0274416	+	0.0274416i
$484$	308.083	−	373.284i	0.636535	−	0.771248i
$485$	−117.448	−	230.198i	−0.242162	−	0.474635i
$486$	−63.9703	−	10.1998i	−0.131626	−	0.0209872i
$487$	404.262	+	404.262i	0.830107	+	0.830107i	0.987531	−	0.157424i	$-0.0503189\pi$
$487$	404.262	+	404.262i	0.830107	+	0.830107i	−0.157424	+	0.987531i	$0.550319\pi$
$488$	−161.648	−	502.810i	−0.331247	−	1.03035i
$489$		−	82.6732i		−	0.169066i
$490$	150.960	+	465.392i	0.308082	+	0.949779i
$491$	−274.934			−0.559946			−0.279973	−	0.960008i	$-0.590326\pi$
$491$	−274.934			−0.559946			−0.279973	+	0.960008i	$0.590326\pi$
$492$	−246.409	+	124.910i	−0.500832	+	0.253882i
$493$	−33.8643	−	33.8643i	−0.0686903	−	0.0686903i
$494$	156.140	−	979.270i	0.316074	−	1.98233i
$495$	−15.8575	+	28.9922i	−0.0320353	+	0.0585700i
$496$	121.541	−	165.839i	0.245043	−	0.334353i
$497$	−20.5598	−	20.5598i	−0.0413679	−	0.0413679i
$498$	394.369	+	543.985i	0.791905	+	1.09234i
$499$	181.398			0.363524			0.181762	−	0.983343i	$-0.441820\pi$
$499$	181.398			0.363524			0.181762	+	0.983343i	$0.441820\pi$
$500$	154.295	+	475.598i	0.308589	+	0.951195i
$501$		−	231.389i		−	0.461854i
$502$	25.2772	−	18.3250i	0.0503531	−	0.0365041i
$503$	523.663	+	523.663i	1.04108	+	1.04108i	0.999119	+	0.0419598i	$0.0133602\pi$
$503$	523.663	+	523.663i	1.04108	+	1.04108i	0.0419598	+	0.999119i	$0.486640\pi$
$504$	−1.16057	−	0.595889i	−0.00230273	−	0.00118232i
$505$	−702.585	−	227.864i	−1.39126	−	0.451216i
$506$	177.297	−	493.353i	0.350389	−	0.975007i
$507$	215.790	+	215.790i	0.425621	+	0.425621i
$508$	−329.149	−	649.311i	−0.647931	−	1.27817i
$509$			273.380i			0.537093i	0.963267	+	0.268546i	$0.0865433\pi$
$509$			273.380i			0.537093i	−0.963267	+	0.268546i	$0.913457\pi$
$510$	117.875	−	38.2354i	0.231128	−	0.0749714i
$511$		−	20.1470i		−	0.0394266i
$512$	304.791	−	411.395i	0.595296	−	0.803507i
$513$	−589.011	+	589.011i	−1.14817	+	1.14817i
$514$	−772.718	−	123.206i	−1.50334	−	0.239701i
$515$	−49.4376	−	96.8973i	−0.0959953	−	0.188150i
$516$	−251.055	+	767.259i	−0.486540	+	1.48694i
$517$	58.0215	−	39.5682i	0.112227	−	0.0765343i
$518$	6.04331	−	4.38117i	0.0116666	−	0.00845786i
$519$			524.733i			1.01105i
$520$	−467.241	−	469.644i	−0.898541	−	0.903162i
$521$	−381.228			−0.731723			−0.365861	−	0.930669i	$-0.619226\pi$
$521$	−381.228			−0.731723			−0.365861	+	0.930669i	$0.619226\pi$
$522$	10.8966	−	7.89966i	0.0208748	−	0.0151334i
$523$	−450.960	−	450.960i	−0.862256	−	0.862256i	0.129344	−	0.991600i	$-0.458713\pi$
$523$	−450.960	−	450.960i	−0.862256	−	0.862256i	−0.991600	+	0.129344i	$0.958713\pi$
$524$	152.972	−	467.504i	0.291931	−	0.892183i
$525$	−11.5418	+	15.9220i	−0.0219843	+	0.0303277i
$526$	−37.9701	+	238.138i	−0.0721864	+	0.452734i
$527$	38.8538	−	38.8538i	0.0737264	−	0.0737264i
$528$	17.3108	−	509.778i	0.0327856	−	0.965488i
$529$		−	38.8341i		−	0.0734105i
$530$	−299.730	−	152.907i	−0.565528	−	0.288503i
$531$			8.80799i			0.0165875i
$532$	−28.9902	+	14.6957i	−0.0544929	+	0.0276236i
$533$	279.086	+	279.086i	0.523614	+	0.523614i
$534$	21.9666	−	137.769i	0.0411360	−	0.257994i
$535$	−214.108	−	419.651i	−0.400203	−	0.784394i
$536$	−355.158	−	182.353i	−0.662607	−	0.340211i
$537$	668.478	−	668.478i	1.24484	−	1.24484i
$538$	690.503	−	500.589i	1.28346	−	0.930463i
$539$	528.819	+	99.9947i	0.981111	+	0.185519i
$540$	86.2131	+	549.771i	0.159654	+	1.01809i
$541$			684.932i			1.26605i	0.774132	+	0.633024i	$0.218187\pi$
$541$			684.932i			1.26605i	−0.774132	+	0.633024i	$0.781813\pi$
$542$	315.519	+	435.221i	0.582138	+	0.802991i
$543$	15.6864	−	15.6864i	0.0288883	−	0.0288883i
$544$	97.2520	−	96.2506i	0.178772	−	0.176931i
$545$	227.996	−	702.992i	0.418342	−	1.28989i
$546$	4.10265	−	25.7307i	0.00751401	−	0.0471259i
$547$	8.71058	−	8.71058i	0.0159243	−	0.0159243i	−0.699100	−	0.715024i	$-0.746416\pi$
$547$	8.71058	−	8.71058i	0.0159243	−	0.0159243i	0.715024	+	0.699100i	$0.246416\pi$
$548$	−404.809	−	798.564i	−0.738702	−	1.45723i
$549$	39.6662			0.0722518
$550$	540.428	+	102.165i	0.982596	+	0.185754i
$551$		−	335.306i		−	0.608540i
$552$	−169.094	−	525.970i	−0.306330	−	0.952845i
$553$	23.5738	+	23.5738i	0.0426290	+	0.0426290i
$554$	−85.1483	+	534.028i	−0.153697	+	0.963949i
$555$	−189.535	−	61.4705i	−0.341504	−	0.110758i
$556$	−387.324	−	126.736i	−0.696625	−	0.227943i
$557$	−209.323	−	209.323i	−0.375805	−	0.375805i	0.493781	−	0.869586i	$-0.335614\pi$
$557$	−209.323	−	209.323i	−0.375805	−	0.375805i	−0.869586	+	0.493781i	$0.835614\pi$
$558$	9.06358	+	12.5021i	0.0162430	+	0.0224053i
$559$	1153.36			2.06325
$560$	−3.47394	+	21.4339i	−0.00620347	+	0.0382749i
$561$	25.3268	−	133.940i	0.0451458	−	0.238752i
$562$	177.428	−	128.629i	0.315708	−	0.228877i
$563$	704.567	+	704.567i	1.25145	+	1.25145i	0.955069	+	0.296382i	$0.0957802\pi$
$563$	704.567	+	704.567i	1.25145	+	1.25145i	0.296382	+	0.955069i	$0.404220\pi$
$564$	23.0167	−	70.3423i	0.0408097	−	0.124720i
$565$	−638.435	+	325.733i	−1.12997	+	0.576519i
$566$	−11.4146	+	71.5891i	−0.0201671	+	0.126482i
$567$	−14.4387	+	14.4387i	−0.0254650	+	0.0254650i
$568$	262.296	+	815.877i	0.461789	+	1.43640i
$569$	886.554			1.55809			0.779045	−	0.626967i	$-0.215704\pi$
$569$	886.554			1.55809			0.779045	+	0.626967i	$0.215704\pi$
$570$	772.860	+	394.274i	1.35589	+	0.691708i
$571$	737.017			1.29075			0.645374	−	0.763867i	$-0.276702\pi$
$571$	737.017			1.29075			0.645374	+	0.763867i	$0.276702\pi$
$572$	−699.886	+	202.988i	−1.22358	+	0.354874i
$573$	−59.0487	−	59.0487i	−0.103052	−	0.103052i
$574$	2.03692	−	12.7750i	0.00354864	−	0.0222561i
$575$	588.296	−	93.8284i	1.02312	−	0.163180i
$576$	22.4084	+	31.2488i	0.0389036	+	0.0542515i
$577$	370.075	−	370.075i	0.641378	−	0.641378i	−0.309516	−	0.950894i	$-0.600167\pi$
$577$	370.075	−	370.075i	0.641378	−	0.641378i	0.950894	+	0.309516i	$0.100167\pi$
$578$	−438.358	+	317.793i	−0.758405	+	0.549815i
$579$			511.855i			0.884033i
$580$	−181.023	−	131.944i	−0.312109	−	0.227491i
$581$	−31.4628			−0.0541528
$582$	−242.551	+	175.840i	−0.416754	+	0.302131i
$583$	−305.789	+	208.535i	−0.524510	+	0.357694i
$584$	−271.232	+	528.261i	−0.464438	+	0.904557i
$585$	44.3194	−	22.6120i	0.0757596	−	0.0386530i
$586$	399.941	+	63.7688i	0.682493	+	0.108820i
$587$	−138.774	−	138.774i	−0.236413	−	0.236413i	0.578950	−	0.815363i	$-0.303463\pi$
$587$	−138.774	−	138.774i	−0.236413	−	0.236413i	−0.815363	+	0.578950i	$0.803463\pi$
$588$	505.893	−	256.448i	0.860362	−	0.436135i
$589$	384.709			0.653156
$590$	139.445	−	45.2322i	0.236348	−	0.0766647i
$591$	655.629			1.10935
$592$	−217.440	+	33.5169i	−0.367297	+	0.0566164i
$593$	90.2407	−	90.2407i	0.152177	−	0.152177i	−0.626913	−	0.779089i	$-0.715682\pi$
$593$	90.2407	−	90.2407i	0.152177	−	0.152177i	0.779089	+	0.626913i	$0.215682\pi$
$594$	576.069	+	207.022i	0.969813	+	0.348523i
$595$	−1.79019	+	5.51979i	−0.00300873	+	0.00927695i
$596$	−108.407	+	331.306i	−0.181890	+	0.555883i
$597$	−505.520	+	505.520i	−0.846766	+	0.846766i
$598$	−639.054	+	463.290i	−1.06865	+	0.774732i
$599$	34.1675			0.0570408			0.0285204	−	0.999593i	$-0.490920\pi$
$599$	34.1675			0.0570408			0.0285204	+	0.999593i	$0.490920\pi$
$600$	516.983	−	262.099i	0.861638	−	0.436831i
$601$		−	912.806i		−	1.51881i	−0.650617	−	0.759406i	$-0.725490\pi$
$601$		−	912.806i		−	1.51881i	0.650617	−	0.759406i	$-0.274510\pi$
$602$	−22.1882	−	30.6060i	−0.0368575	−	0.0508406i
$603$	21.2019	−	21.2019i	0.0351607	−	0.0351607i
$604$	239.189	−	730.997i	0.396009	−	1.21026i
$605$	383.885	−	467.608i	0.634520	−	0.772906i
$606$	−134.820	+	845.557i	−0.222476	+	1.39531i
$607$	542.713	−	542.713i	0.894090	−	0.894090i	−0.100815	−	0.994905i	$-0.532145\pi$
$607$	542.713	−	542.713i	0.894090	−	0.894090i	0.994905	+	0.100815i	$0.0321451\pi$
$608$	957.978	+	4.95762i	1.57562	+	0.00815397i
$609$		−	8.81029i		−	0.0144668i
$610$	−203.700	−	627.982i	−0.333935	−	1.02948i
$611$	−105.740			−0.173060
$612$	4.64638	+	9.16589i	0.00759213	+	0.0149770i
$613$	265.278	−	265.278i	0.432754	−	0.432754i	−0.456810	−	0.889564i	$-0.651008\pi$
$613$	265.278	−	265.278i	0.432754	−	0.432754i	0.889564	+	0.456810i	$0.151008\pi$
$614$	843.721	+	134.528i	1.37414	+	0.219100i
$615$	−307.603	+	156.941i	−0.500167	+	0.255188i
$616$	18.8510	+	14.6674i	0.0306022	+	0.0238108i
$617$	−615.762	+	615.762i	−0.997994	+	0.997994i	−0.999998	−	0.00200418i	$-0.999362\pi$
$617$	−615.762	+	615.762i	−0.997994	+	0.997994i	0.00200418	+	0.999998i	$0.499362\pi$
$618$	−102.097	+	74.0164i	−0.165205	+	0.119768i
$619$	−368.464			−0.595257			−0.297628	−	0.954682i	$-0.596196\pi$
$619$	−368.464			−0.595257			−0.297628	+	0.954682i	$0.596196\pi$
$620$	151.385	−	207.695i	0.244169	−	0.334991i
$621$	663.037			1.06769
$622$	398.209	−	288.686i	0.640207	−	0.464126i
$623$	4.61935	+	4.61935i	0.00741469	+	0.00741469i
$624$	−453.977	+	619.436i	−0.727527	+	0.992687i
$625$	194.419	+	593.992i	0.311071	+	0.950387i
$626$	−118.097	+	740.675i	−0.188654	+	1.18319i
$627$	788.485	−	537.714i	1.25755	−	0.857597i
$628$	383.474	+	756.477i	0.610627	+	1.20458i
$629$	−58.7958			−0.0934750
$630$	−1.45266	−	0.741072i	−0.00230581	−	0.00117630i
$631$			1158.33i			1.83571i	0.396916	+	0.917855i	$0.370080\pi$
$631$			1158.33i			1.83571i	−0.396916	+	0.917855i	$0.629920\pi$
$632$	−300.748	−	935.481i	−0.475867	−	1.48019i
$633$	316.960	−	316.960i	0.500727	−	0.500727i
$634$	−450.608	−	71.8474i	−0.710737	−	0.113324i
$635$	−413.553	−	810.562i	−0.651265	−	1.27648i
$636$	−121.304	+	370.723i	−0.190730	+	0.582898i
$637$	−572.981	−	572.981i	−0.899500	−	0.899500i
$638$	−222.895	+	105.043i	−0.349365	+	0.164645i
$639$	−64.3638			−0.100726
$640$	379.646	−	515.237i	0.593196	−	0.805058i
$641$	460.419			0.718283			0.359142	−	0.933283i	$-0.383070\pi$
$641$	460.419			0.718283			0.359142	+	0.933283i	$0.383070\pi$
$642$	−442.170	+	320.556i	−0.688738	+	0.499309i
$643$	−423.311	+	423.311i	−0.658338	+	0.658338i	−0.954987	−	0.296649i	$-0.904131\pi$
$643$	−423.311	+	423.311i	−0.658338	+	0.658338i	0.296649	+	0.954987i	$0.404131\pi$
$644$	24.5882	+	8.04549i	0.0381804	+	0.0124930i
$645$	−311.314	+	959.890i	−0.482658	+	1.48820i
$646$	252.823	+	40.3116i	0.391368	+	0.0624018i
$647$	−679.923	−	679.923i	−1.05089	−	1.05089i	−0.998634	−	0.0522523i	$-0.983360\pi$
$647$	−679.923	−	679.923i	−1.05089	−	1.05089i	−0.0522523	−	0.998634i	$-0.516640\pi$
$648$	572.970	−	184.204i	0.884214	−	0.284266i
$649$	29.9613	−	158.450i	0.0461654	−	0.244144i
$650$	−585.582	−	585.529i	−0.900895	−	0.900814i
$651$	10.1084			0.0155275
$652$	−51.5922	−	101.776i	−0.0791292	−	0.156098i
$653$	−441.796	−	441.796i	−0.676564	−	0.676564i	0.282657	−	0.959221i	$-0.408784\pi$
$653$	−441.796	−	441.796i	−0.676564	−	0.676564i	−0.959221	+	0.282657i	$0.908784\pi$
$654$	−846.047	−	134.898i	−1.29365	−	0.206267i
$655$	189.689	−	584.877i	0.289601	−	0.892942i
$656$	−225.395	+	307.543i	−0.343589	+	0.468816i
$657$	−31.5357	−	31.5357i	−0.0479995	−	0.0479995i
$658$	2.03421	+	2.80596i	0.00309151	+	0.00426437i
$659$			1044.69i			1.58526i	0.609703	+	0.792630i	$0.291289\pi$
$659$			1044.69i			1.58526i	−0.609703	+	0.792630i	$0.708711\pi$
$660$	19.9753	−	637.276i	0.0302656	−	0.965570i
$661$	476.865			0.721429			0.360715	−	0.932676i	$-0.382533\pi$
$661$	476.865			0.721429			0.360715	+	0.932676i	$0.382533\pi$
$662$	−724.247	+	525.052i	−1.09403	+	0.793130i
$663$	−145.125	+	145.125i	−0.218892	+	0.218892i
$664$	824.966	+	423.573i	1.24242	+	0.637911i
$665$	−36.1897	+	18.4642i	−0.0544206	+	0.0277657i
$666$	2.60171	−	16.3172i	0.00390647	−	0.0245004i
$667$	−188.723	+	188.723i	−0.282943	+	0.282943i
$668$	−144.398	−	284.854i	−0.216165	−	0.426428i
$669$			428.218i			0.640087i
$670$	−444.540	−	226.782i	−0.663493	−	0.338480i
$671$	−713.568	−	134.929i	−1.06344	−	0.201087i
$672$	25.1712	+	0.130263i	0.0374572	+	0.000193844i
$673$	−25.1247	+	25.1247i	−0.0373324	+	0.0373324i	−0.725527	−	0.688194i	$-0.758404\pi$
$673$	−25.1247	+	25.1247i	−0.0373324	+	0.0373324i	0.688194	+	0.725527i	$0.258404\pi$
$674$	−67.5553	+	423.689i	−0.100230	+	0.628618i
$675$	109.560	+	686.930i	0.162311	+	1.01767i
$676$	400.315	+	130.987i	0.592181	+	0.193768i
$677$	−439.457	−	439.457i	−0.649125	−	0.649125i	0.303657	−	0.952781i	$-0.401792\pi$
$677$	−439.457	−	439.457i	−0.649125	−	0.649125i	−0.952781	+	0.303657i	$0.901792\pi$
$678$	487.677	+	672.693i	0.719288	+	0.992173i
$679$		−	14.0286i		−	0.0206606i
$680$	121.251	−	120.630i	0.178310	−	0.177397i
$681$			229.894i			0.337583i
$682$	−120.520	−	255.736i	−0.176716	−	0.374979i
$683$	623.294	−	623.294i	0.912583	−	0.912583i	−0.0838919	−	0.996475i	$-0.526735\pi$
$683$	623.294	−	623.294i	0.912583	−	0.912583i	0.996475	+	0.0838919i	$0.0267350\pi$
$684$	−22.3749	+	68.3808i	−0.0327118	+	0.0999719i
$685$	−508.614	−	996.880i	−0.742503	−	1.45530i
$686$	−8.37014	+	52.4953i	−0.0122014	+	0.0765237i
$687$	−606.034	−	606.034i	−0.882145	−	0.882145i
$688$	169.745	+	1101.21i	0.246722	+	1.60060i
$689$	557.277			0.808820
$690$	−213.083	−	656.909i	−0.308816	−	0.952042i
$691$		−	549.965i		−	0.795897i	−0.917408	−	0.397948i	$-0.869722\pi$
$691$		−	549.965i		−	0.795897i	0.917408	−	0.397948i	$-0.130278\pi$
$692$	327.460	+	645.979i	0.473208	+	0.933495i
$693$	−1.48203	+	1.01068i	−0.00213857	+	0.00145841i
$694$	5.45744	+	0.870165i	0.00786375	+	0.00125384i
$695$	−484.566	−	157.156i	−0.697218	−	0.226124i
$696$	−118.610	+	231.009i	−0.170417	+	0.331909i
$697$	−72.0532	+	72.0532i	−0.103376	+	0.103376i
$698$	−595.504	−	821.427i	−0.853157	−	1.17683i
$699$			569.078i			0.814132i
$700$	−4.27248	+	26.8036i	−0.00610355	+	0.0382909i
$701$		−	546.768i		−	0.779982i	−0.920819	−	0.389991i	$-0.872478\pi$
$701$		−	546.768i		−	0.779982i	0.920819	−	0.389991i	$-0.127522\pi$
$702$	−540.965	−	746.197i	−0.770605	−	1.06296i
$703$	−291.082	−	291.082i	−0.414056	−	0.414056i
$704$	−296.816	−	638.370i	−0.421614	−	0.906775i
$705$	28.5413	−	88.0026i	0.0404841	−	0.124826i
$706$	−9.20075	+	57.7047i	−0.0130322	+	0.0817347i
$707$	−28.3513	−	28.3513i	−0.0401009	−	0.0401009i
$708$	−76.8393	−	151.580i	−0.108530	−	0.214097i
$709$		−	514.197i		−	0.725242i	−0.931937	−	0.362621i	$-0.881882\pi$
$709$		−	514.197i		−	0.725242i	0.931937	−	0.362621i	$-0.118118\pi$
$710$	330.531	+	1018.99i	0.465537	+	1.43519i
$711$	73.7993			0.103797
$712$	−58.9323	−	183.310i	−0.0827701	−	0.257458i
$713$	−216.529	−	216.529i	−0.303688	−	0.303688i
$714$	6.64304	+	1.05920i	0.00930397	+	0.00148348i
$715$	−874.193	+	256.017i	−1.22265	+	0.358066i
$716$	405.773	−	1240.10i	0.566722	−	1.73198i
$717$	678.102	+	678.102i	0.945749	+	0.945749i
$718$	−463.439	+	335.976i	−0.645458	+	0.467933i
$719$	189.750			0.263908			0.131954	−	0.991256i	$-0.457875\pi$
$719$	189.750			0.263908			0.131954	+	0.991256i	$0.457875\pi$
$720$	28.1124	+	38.9878i	0.0390450	+	0.0541497i
$721$		−	5.90504i		−	0.00819007i
$722$	628.311	+	866.681i	0.870237	+	1.20039i
$723$	−725.276	−	725.276i	−1.00315	−	1.00315i
$724$	9.52178	−	29.0999i	0.0131516	−	0.0401933i
$725$	−226.708	−	164.339i	−0.312701	−	0.226675i
$726$	−604.459	−	355.694i	−0.832589	−	0.489936i
$727$	−927.043	−	927.043i	−1.27516	−	1.27516i	−0.943343	−	0.331819i	$-0.892338\pi$
$727$	−927.043	−	927.043i	−1.27516	−	1.27516i	−0.331819	−	0.943343i	$-0.607662\pi$
$728$	−11.0067	−	34.2363i	−0.0151190	−	0.0470279i
$729$			770.952i			1.05755i
$730$	−337.315	+	661.209i	−0.462076	+	0.905766i
$731$			297.768i			0.407344i
$732$	−682.633	+	346.041i	−0.932559	+	0.472734i
$733$	−416.046	+	416.046i	−0.567594	+	0.567594i	−0.931454	−	0.363860i	$-0.881459\pi$
$733$	−416.046	+	416.046i	−0.567594	+	0.567594i	0.363860	+	0.931454i	$0.381459\pi$
$734$	47.6537	−	298.872i	0.0649234	−	0.407182i
$735$	631.527	−	322.209i	0.859221	−	0.438380i
$736$	−536.397	−	541.978i	−0.728801	−	0.736383i
$737$	−453.528	+	309.287i	−0.615370	+	0.419656i
$738$	−16.8081	−	23.1848i	−0.0227753	−	0.0314158i
$739$		−	694.401i		−	0.939650i	−0.882760	−	0.469825i	$-0.844317\pi$
$739$		−	694.401i		−	0.939650i	0.882760	−	0.469825i	$-0.155683\pi$
$740$	−271.690	+	42.6054i	−0.367148	+	0.0575749i
$741$	−1436.95			−1.93921
$742$	−10.7209	−	14.7882i	−0.0144486	−	0.0199302i
$743$	−641.222	−	641.222i	−0.863018	−	0.863018i	0.128670	−	0.991687i	$-0.458929\pi$
$743$	−641.222	−	641.222i	−0.863018	−	0.863018i	−0.991687	+	0.128670i	$0.958929\pi$
$744$	−265.045	−	136.086i	−0.356244	−	0.182911i
$745$	−134.427	+	414.485i	−0.180439	+	0.556356i
$746$	998.051	+	159.135i	1.33787	+	0.213317i
$747$	−49.2481	+	49.2481i	−0.0659278	+	0.0659278i
$748$	−52.4064	−	180.693i	−0.0700620	−	0.241569i
$749$		−	25.5740i		−	0.0341442i
$750$	645.371	−	329.309i	0.860495	−	0.439078i
$751$		−	530.192i		−	0.705982i	−0.935627	−	0.352991i	$-0.885165\pi$
$751$		−	530.192i		−	0.705982i	0.935627	−	0.352991i	$-0.114835\pi$
$752$	−15.5622	−	100.959i	−0.0206944	−	0.134254i
$753$	−31.9904	−	31.9904i	−0.0424839	−	0.0424839i
$754$	366.371	+	58.4162i	0.485903	+	0.0774751i
$755$	296.601	−	914.523i	0.392849	−	1.21129i
$756$	−9.39439	+	28.7106i	−0.0124264	+	0.0379770i
$757$	558.257	−	558.257i	0.737459	−	0.737459i	−0.234626	−	0.972086i	$-0.575387\pi$
$757$	558.257	−	558.257i	0.737459	−	0.737459i	0.972086	+	0.234626i	$0.0753866\pi$
$758$	533.316	+	735.646i	0.703583	+	0.970510i
$759$	−746.437	−	141.144i	−0.983448	−	0.185961i
$760$	1197.48	+	3.07153i	1.57564	+	0.00404148i
$761$			1419.91i			1.86584i	0.360080	+	0.932921i	$0.382749\pi$
$761$			1419.91i			1.86584i	−0.360080	+	0.932921i	$0.617251\pi$
$762$	−854.057	+	619.159i	−1.12081	+	0.812545i
$763$	28.3678	−	28.3678i	0.0371792	−	0.0371792i
$764$	−109.542	−	35.8432i	−0.143379	−	0.0469151i
$765$	5.83786	+	11.4422i	0.00763119	+	0.0149571i
$766$	−636.844	−	101.542i	−0.831388	−	0.132561i
$767$	−171.682	+	171.682i	−0.223836	+	0.223836i
$768$	−658.246	−	342.288i	−0.857091	−	0.445687i
$769$	−746.894			−0.971254			−0.485627	−	0.874166i	$-0.661409\pi$
$769$	−746.894			−0.971254			−0.485627	+	0.874166i	$0.661409\pi$
$770$	23.6115	+	18.2727i	0.0306642	+	0.0237308i
$771$			1133.86i			1.47064i
$772$

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17390 - 1.61925i) q^{2} +(-2.04929 + 2.04929i) q^{3} +(-1.24394 + 3.80166i) q^{4} +(-1.54252 + 4.75612i) q^{5} +(5.72396 + 0.912660i) q^{6} +(-0.191923 + 0.191923i) q^{7} +(7.61609 - 2.44850i) q^{8} +0.600827i q^{9} +(9.51209 - 3.08546i) q^{10} +(2.04378 - 10.8085i) q^{11} +(-5.24151 - 10.3399i) q^{12} +(-11.7111 + 11.7111i) q^{13} +(0.536069 + 0.0854739i) q^{14} +(-6.58560 - 12.9077i) q^{15} +(-12.9052 - 9.45807i) q^{16} +(-3.02352 - 3.02352i) q^{17} +(0.972889 - 0.705308i) q^{18} -29.9372i q^{19} +(-16.1623 - 11.7804i) q^{20} -0.786612i q^{21} +(-19.9008 + 9.37862i) q^{22} +(-16.8498 + 16.8498i) q^{23} +(-10.5899 + 20.6253i) q^{24} +(-20.2413 - 14.6728i) q^{25} +(32.7108 + 5.21560i) q^{26} +(-19.6749 - 19.6749i) q^{27} +(-0.490885 - 0.968367i) q^{28} +11.2003 q^{29} +(-13.1700 + 25.8160i) q^{30} +12.8505i q^{31} +(-0.165600 + 31.9996i) q^{32} +(17.9614 + 26.3380i) q^{33} +(-1.34654 + 8.44512i) q^{34} +(-0.616764 - 1.20885i) q^{35} +(-2.28414 - 0.747393i) q^{36} +(9.72307 - 9.72307i) q^{37} +(-48.4758 + 35.1431i) q^{38} -47.9989i q^{39} +(-0.102599 + 39.9999i) q^{40} -23.8309i q^{41} +(-1.27372 + 0.923400i) q^{42} +(-49.2420 - 49.2420i) q^{43} +(38.5478 + 21.2148i) q^{44} +(-2.85760 - 0.926786i) q^{45} +(47.0640 + 7.50415i) q^{46} +(4.51450 + 4.51450i) q^{47} +(45.8289 - 7.06421i) q^{48} +48.9263i q^{49} +(0.00225408 + 50.0000i) q^{50} +12.3921 q^{51} +(-29.9537 - 59.0895i) q^{52} +(-23.7927 - 23.7927i) q^{53} +(-8.76230 + 54.9548i) q^{54} +(48.2538 + 26.3927i) q^{55} +(-0.991780 + 1.93163i) q^{56} +(61.3500 + 61.3500i) q^{57} +(-13.1480 - 18.1361i) q^{58} +14.6598 q^{59} +(57.2628 - 8.97976i) q^{60} -66.0194i q^{61} +(20.8082 - 15.0852i) q^{62} +(-0.115313 - 0.115313i) q^{63} +(52.0097 - 37.2960i) q^{64} +(-37.6348 - 73.7640i) q^{65} +(21.5630 - 60.0020i) q^{66} +(-35.2878 - 35.2878i) q^{67} +(15.2555 - 7.73331i) q^{68} -69.0604i q^{69} +(-1.23342 + 2.41776i) q^{70} +107.125i q^{71} +(1.47113 + 4.57595i) q^{72} +(-52.4871 + 52.4871i) q^{73} +(-27.1579 - 4.33021i) q^{74} +(71.5490 - 11.4115i) q^{75} +(113.811 + 37.2401i) q^{76} +(1.68215 + 2.46664i) q^{77} +(-77.7222 + 56.3457i) q^{78} -122.830i q^{79} +(64.8902 - 46.7895i) q^{80} +75.2316 q^{81} +(-38.5882 + 27.9750i) q^{82} +(81.9671 + 81.9671i) q^{83} +(2.99043 + 0.978498i) q^{84} +(19.0440 - 9.71638i) q^{85} +(-21.9302 + 137.540i) q^{86} +(-22.9526 + 22.9526i) q^{87} +(-10.8989 - 87.3225i) q^{88} -24.0688i q^{89} +(1.85383 + 5.71512i) q^{90} -4.49526i q^{91} +(-43.0972 - 85.0175i) q^{92} +(-26.3344 - 26.3344i) q^{93} +(2.01056 - 12.6097i) q^{94} +(142.385 + 46.1786i) q^{95} +(-65.2370 - 65.9157i) q^{96} +(-36.5473 + 36.5473i) q^{97} +(79.2240 - 57.4344i) q^{98} +(6.49402 + 1.22796i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) \) 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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