LMFDB - Embedded newform 220.3.i.a.43.15

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			43.15
Character	$\chi$	$=$	220.43
Dual form			220.3.i.a.87.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.61925 - 1.17390i) 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} +(2.44850 - 7.61609i) q^{8} +0.600827i q^{9} +(8.08090 - 5.89059i) q^{10} +(-2.04378 + 10.8085i) q^{11} +(10.3399 + 5.24151i) 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} +(0.705308 - 0.972889i) q^{18} +29.9372i q^{19} +(-19.9999 + 0.0522011i) q^{20} -0.786612i q^{21} +(15.9974 - 15.1024i) 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} +(0.968367 + 0.490885i) q^{28} +11.2003 q^{29} +(4.48859 - 28.6316i) q^{30} -12.8505i q^{31} +(31.9996 - 0.165600i) 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} +(35.1431 - 48.4758i) q^{38} +47.9989i q^{39} +(32.4462 + 23.3933i) q^{40} -23.8309i q^{41} +(-0.923400 + 1.27372i) q^{42} +(49.2420 + 49.2420i) q^{43} +(-43.6324 + 5.67533i) q^{44} +(-2.85760 - 0.926786i) q^{45} +(-47.0640 + 7.50415i) q^{46} +(-4.51450 - 4.51450i) q^{47} +(-7.06421 + 45.8289i) q^{48} +48.9263i q^{49} +(15.5514 + 47.5200i) q^{50} -12.3921 q^{51} +(-59.0895 - 29.9537i) 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} +(-18.1361 - 13.1480i) q^{58} -14.6598 q^{59} +(-40.8787 + 41.0926i) q^{60} -66.0194i q^{61} +(-15.0852 + 20.8082i) q^{62} +(0.115313 + 0.115313i) q^{63} +(-52.0097 - 37.2960i) q^{64} +(-37.6348 - 73.7640i) q^{65} +(1.83406 - 63.7325i) q^{66} +(35.2878 + 35.2878i) q^{67} +(7.73331 - 15.2555i) q^{68} -69.0604i q^{69} +(0.420372 - 2.68145i) q^{70} -107.125i q^{71} +(4.57595 + 1.47113i) 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} +(56.3457 - 77.7222i) q^{78} +122.830i q^{79} +(-25.0772 - 75.9680i) q^{80} +75.2316 q^{81} +(-27.9750 + 38.5882i) 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} +(77.3141 + 42.0301i) q^{88} -24.0688i q^{89} +(3.53923 + 4.85523i) q^{90} +4.49526i q^{91} +(85.0175 + 43.0972i) 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} +(57.4344 - 79.2240i) 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 $

$2$	−1.61925	−	1.17390i	−0.809625	−	0.586948i
$2$	−1.61925	−	1.17390i	−0.809625	−	0.586948i
$3$	2.04929	−	2.04929i	0.683096	−	0.683096i	−0.277600	−	0.960697i	$-0.589539\pi$
$3$	2.04929	−	2.04929i	0.683096	−	0.683096i	0.960697	+	0.277600i	$0.0895391\pi$
$4$	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	−0.693265	−	0.720683i	$-0.743828\pi$
$7$	0.191923	−	0.191923i	0.0274176	−	0.0274176i	0.720683	+	0.693265i	$0.243828\pi$
$8$	2.44850	−	7.61609i	0.306062	−	0.952011i
$9$			0.600827i			0.0667586i
$10$	8.08090	−	5.89059i	0.808090	−	0.589059i
$11$	−2.04378	+	10.8085i	−0.185798	+	0.982588i
$11$	−2.04378	+	10.8085i	−0.185798	+	0.982588i
$12$	10.3399	+	5.24151i	0.861658	+	0.436792i
$13$	−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	$0.790137\pi$
$18$	0.705308	−	0.972889i	0.0391838	−	0.0540494i
$19$			29.9372i			1.57564i	0.615904	+	0.787821i	$0.288791\pi$
$19$			29.9372i			1.57564i	−0.615904	+	0.787821i	$0.711209\pi$
$20$	−19.9999	+	0.0522011i	−0.999997	+	0.00261006i
$21$		−	0.786612i		−	0.0374577i
$22$	15.9974	−	15.1024i	0.727154	−	0.686474i
$23$	16.8498	−	16.8498i	0.732602	−	0.732602i	−0.238533	−	0.971134i	$-0.576666\pi$
$23$	16.8498	−	16.8498i	0.732602	−	0.732602i	0.971134	+	0.238533i	$0.0766664\pi$
$24$	−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
$28$	0.968367	+	0.490885i	0.0345845	+	0.0175316i
$29$	11.2003			0.386217			0.193109	−	0.981177i	$-0.438143\pi$
$29$	11.2003			0.386217			0.193109	+	0.981177i	$0.438143\pi$
$30$	4.48859	−	28.6316i	0.149620	−	0.954387i
$31$		−	12.8505i		−	0.414533i	−0.978285	−	0.207267i	$-0.933543\pi$
$31$		−	12.8505i		−	0.414533i	0.978285	−	0.207267i	$-0.0664567\pi$
$32$	31.9996	−	0.165600i	0.999987	−	0.00517502i
$33$	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	$0.190507\pi$
$38$	35.1431	−	48.4758i	0.924820	−	1.27568i
$39$			47.9989i			1.23074i
$40$	32.4462	+	23.3933i	0.811154	+	0.584832i
$41$		−	23.8309i		−	0.581242i	−0.956838	−	0.290621i	$-0.906138\pi$
$41$		−	23.8309i		−	0.581242i	0.956838	−	0.290621i	$-0.0938619\pi$
$42$	−0.923400	+	1.27372i	−0.0219857	+	0.0303267i
$43$	49.2420	+	49.2420i	1.14516	+	1.14516i	0.987492	+	0.157671i	$0.0503987\pi$
$43$	49.2420	+	49.2420i	1.14516	+	1.14516i	0.157671	+	0.987492i	$0.449601\pi$
$44$	−43.6324	+	5.67533i	−0.991647	+	0.128985i
$45$	−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	0.657447	−	0.753501i	$-0.271636\pi$
$47$	−4.51450	−	4.51450i	−0.0960533	−	0.0960533i	−0.753501	+	0.657447i	$0.771636\pi$
$48$	−7.06421	+	45.8289i	−0.147171	+	0.954768i
$49$			48.9263i			0.998497i
$50$	15.5514	+	47.5200i	0.311028	+	0.950401i
$51$	−12.3921			−0.242983
$52$	−59.0895	−	29.9537i	−1.13634	−	0.576033i
$53$	−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
$58$	−18.1361	−	13.1480i	−0.312691	−	0.226689i
$59$	−14.6598			−0.248471			−0.124235	−	0.992253i	$-0.539648\pi$
$59$	−14.6598			−0.248471			−0.124235	+	0.992253i	$0.539648\pi$
$60$	−40.8787	+	41.0926i	−0.681311	+	0.684877i
$61$		−	66.0194i		−	1.08228i	−0.840931	−	0.541142i	$-0.817992\pi$
$61$		−	66.0194i		−	1.08228i	0.840931	−	0.541142i	$-0.182008\pi$
$62$	−15.0852	+	20.8082i	−0.243309	+	0.335616i
$63$	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
$66$	1.83406	−	63.7325i	0.0277888	−	0.965644i
$67$	35.2878	+	35.2878i	0.526684	+	0.526684i	0.919582	−	0.392898i	$-0.128527\pi$
$67$	35.2878	+	35.2878i	0.526684	+	0.526684i	−0.392898	+	0.919582i	$0.628527\pi$
$68$	7.73331	−	15.2555i	0.113725	−	0.224345i
$69$		−	69.0604i		−	1.00088i
$70$	0.420372	−	2.68145i	0.00600531	−	0.0383065i
$71$		−	107.125i		−	1.50881i	−0.656410	−	0.754404i	$-0.727926\pi$
$71$		−	107.125i		−	1.50881i	0.656410	−	0.754404i	$-0.272074\pi$
$72$	4.57595	+	1.47113i	0.0635549	+	0.0204323i
$73$	−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
$78$	56.3457	−	77.7222i	0.722380	−	0.996438i
$79$			122.830i			1.55480i	0.629004	+	0.777402i	$0.283463\pi$
$79$			122.830i			1.55480i	−0.629004	+	0.777402i	$0.716537\pi$
$80$	−25.0772	−	75.9680i	−0.313465	−	0.949600i
$81$	75.2316			0.928785
$82$	−27.9750	+	38.5882i	−0.341159	+	0.470588i
$83$	−81.9671	−	81.9671i	−0.987556	−	0.987556i	0.0123677	−	0.999924i	$-0.496063\pi$
$83$	−81.9671	−	81.9671i	−0.987556	−	0.987556i	−0.999924	+	0.0123677i	$0.996063\pi$
$84$	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
$88$	77.3141	+	42.0301i	0.878569	+	0.477615i
$89$		−	24.0688i		−	0.270435i	−0.990816	−	0.135218i	$-0.956827\pi$
$89$		−	24.0688i		−	0.270435i	0.990816	−	0.135218i	$-0.0431734\pi$
$90$	3.53923	+	4.85523i	0.0393247	+	0.0539470i
$91$			4.49526i			0.0493985i
$92$	85.0175	+	43.0972i	0.924104	+	0.468447i
$93$	−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	$0.335841\pi$
$98$	57.4344	−	79.2240i	0.586065	−	0.808408i
$99$	−6.49402	−	1.22796i	−0.0655962	−	0.0124036i
$100$	30.6020	−	95.2025i	0.306020	−	0.952025i
$101$			147.722i			1.46260i	0.682057	+	0.731299i	$0.261086\pi$
$101$			147.722i			1.46260i	−0.682057	+	0.731299i	$0.738914\pi$
$102$	20.0659	+	14.5471i	0.196725	+	0.142618i
$103$	15.3839	−	15.3839i	0.149358	−	0.149358i	−0.628473	−	0.777831i	$-0.716320\pi$
$103$	15.3839	−	15.3839i	0.149358	−	0.149358i	0.777831	+	0.628473i	$0.216320\pi$
$104$	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	−0.323543	−	0.946213i	$-0.604874\pi$
$107$	66.6257	−	66.6257i	0.622670	−	0.622670i	0.946213	+	0.323543i	$0.104874\pi$
$108$	−50.3228	+	99.2715i	−0.465952	+	0.919181i
$109$	−147.808			−1.35604			−0.678018	−	0.735045i	$-0.737161\pi$
$109$	−147.808			−1.35604			−0.678018	+	0.735045i	$0.737161\pi$
$110$	47.1526	+	99.3812i	0.428660	+	0.903466i
$111$		−	39.8508i		−	0.359016i
$112$	−0.661588	+	4.29203i	−0.00590704	+	0.0383217i
$113$	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
$118$	23.7378	+	17.2090i	0.201168	+	0.145839i
$119$	−1.16057			−0.00975266
$120$	114.431	−	18.5519i	0.953593	−	0.154600i
$121$	−112.646	−	44.1803i	−0.930958	−	0.365126i
$122$	−77.4998	+	106.902i	−0.635244	+	0.876245i
$123$	−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	$-0.495739\pi$
$127$	128.689	−	128.689i	1.01330	−	1.01330i	0.999910	−	0.0133851i	$-0.00426073\pi$
$128$	40.4351	+	121.445i	0.315899	+	0.948793i
$129$	201.822			1.56451
$130$	−25.6510	+	163.622i	−0.197315	+	1.25863i
$131$	122.974			0.938730			0.469365	−	0.883004i	$-0.344483\pi$
$131$	122.974			0.938730			0.469365	+	0.883004i	$0.344483\pi$
$132$	−77.7851	+	101.046i	−0.589281	+	0.765499i
$133$	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	$0.945699\pi$
$138$	−81.0697	+	111.826i	−0.587461	+	0.810333i
$139$		−	101.883i		−	0.732970i	−0.930424	−	0.366485i	$-0.880561\pi$
$139$		−	101.883i		−	0.732970i	0.930424	−	0.366485i	$-0.119439\pi$
$140$	−3.82843	+	3.84847i	−0.0273459	+	0.0274891i
$141$	−18.5030			−0.131227
$142$	−125.754	+	173.463i	−0.885591	+	1.22157i
$143$	−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
$148$	49.0587	+	24.8689i	0.331478	+	0.168033i
$149$	87.1478			0.584885			0.292442	−	0.956283i	$-0.405532\pi$
$149$	87.1478			0.584885			0.292442	+	0.956283i	$0.405532\pi$
$150$	129.252	+	65.5130i	0.861677	+	0.436753i
$151$	192.284			1.27340			0.636701	−	0.771111i	$-0.280299\pi$
$151$	192.284			1.27340			0.636701	+	0.771111i	$0.280299\pi$
$152$	228.005	+	73.3012i	1.50003	+	0.482245i
$153$	1.81661	−	1.81661i	0.0118733	−	0.0118733i
$154$	0.171766	−	5.96878i	0.00111536	−	0.0387583i
$155$	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	$0.0140332\pi$
$158$	144.189	−	198.892i	0.912588	−	1.25881i
$159$	−97.5162			−0.613309
$160$	−48.5723	+	152.449i	−0.303577	+	0.952807i
$161$		−	6.46775i		−	0.0401723i
$162$	−121.819	−	88.3140i	−0.751967	−	0.545148i
$163$	20.1712	−	20.1712i	0.123750	−	0.123750i	−0.642520	−	0.766269i	$-0.722111\pi$
$163$	20.1712	−	20.1712i	0.123750	−	0.123750i	0.766269	+	0.642520i	$0.222111\pi$
$164$	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	−0.517577	−	0.855636i	$-0.673166\pi$
$167$	56.4559	−	56.4559i	0.338059	−	0.338059i	0.855636	+	0.517577i	$0.173166\pi$
$168$	−5.99091	−	1.92602i	−0.0356602	−	0.0114644i
$169$		−	105.300i		−	0.623077i
$170$	−42.2430	−	6.62245i	−0.248489	−	0.0389556i
$171$	−17.9871			−0.105188
$172$	−125.947	+	248.455i	−0.732251	+	1.44451i
$173$	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
$176$	−75.8518	−	158.816i	−0.430976	−	0.902363i
$177$	−30.0421	+	30.0421i	−0.169729	+	0.169729i
$178$	−28.2542	+	38.9733i	−0.158731	+	0.218951i
$179$	326.200			1.82234			0.911172	−	0.412025i	$-0.135179\pi$
$179$	326.200			1.82234			0.911172	+	0.412025i	$0.135179\pi$
$180$	−0.0313639	−	12.0165i	−0.000174244	−	0.0667583i
$181$	−7.65453			−0.0422902			−0.0211451	−	0.999776i	$-0.506731\pi$
$181$	−7.65453			−0.0422902			−0.0211451	+	0.999776i	$0.506731\pi$
$182$	5.27697	−	7.27896i	0.0289943	−	0.0399943i
$183$	−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
$188$	11.5468	−	22.7784i	0.0614193	−	0.121162i
$189$	7.55213			0.0399583
$190$	176.348	+	241.920i	0.928146	+	1.27326i
$191$		−	28.8142i		−	0.150860i	−0.997151	−	0.0754299i	$-0.975967\pi$
$191$		−	28.8142i		−	0.150860i	0.997151	−	0.0754299i	$-0.0240329\pi$
$192$	−183.013	+	30.1526i	−0.953194	+	0.157045i
$193$	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	$0.944677\pi$
$198$	9.07395	+	9.61167i	0.0458280	+	0.0485438i
$199$	−246.680			−1.23960			−0.619800	−	0.784760i	$-0.712786\pi$
$199$	−246.680			−1.23960			−0.619800	+	0.784760i	$0.712786\pi$
$200$	−161.310	+	118.233i	−0.806550	+	0.591166i
$201$	144.630			0.719552
$202$	173.411	−	239.199i	0.858468	−	1.18416i
$203$	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
$208$	40.3700	−	261.899i	0.194086	−	1.25913i
$209$	−323.575	−	61.1851i	−1.54821	−	0.292752i
$210$	−4.63361	−	6.35653i	−0.0220648	−	0.0302692i
$211$	154.668			0.733025			0.366512	−	0.930413i	$-0.380552\pi$
$211$	154.668			0.733025			0.366512	+	0.930413i	$0.380552\pi$
$212$	60.8550	−	120.048i	0.287052	−	0.566266i
$213$	−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
$218$	239.338	+	173.511i	1.09788	+	0.795922i
$219$			215.123i			0.982295i
$220$	40.3113	−	216.275i	0.183233	−	0.983070i
$221$	70.8175			0.320441
$222$	−46.7806	+	64.5284i	−0.210724	+	0.290668i
$223$	−104.480	+	104.480i	−0.468519	+	0.468519i	−0.901434	−	0.432916i	$-0.857485\pi$
$223$	−104.480	+	104.480i	−0.468519	+	0.468519i	0.432916	+	0.901434i	$0.357485\pi$
$224$	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	−0.819778	−	0.572681i	$-0.805903\pi$
$227$	−56.0911	+	56.0911i	−0.247097	+	0.247097i	0.572681	+	0.819778i	$0.305903\pi$
$228$	−156.916	+	309.548i	−0.688228	+	1.35766i
$229$			295.729i			1.29139i	0.763595	+	0.645696i	$0.223433\pi$
$229$			295.729i			1.29139i	−0.763595	+	0.645696i	$0.776567\pi$
$230$	36.9064	−	235.417i	0.160463	−	1.02355i
$231$	8.50207	+	1.60766i	0.0368055	+	0.00695958i
$232$	27.4239	−	85.3025i	0.118207	−	0.367683i
$233$	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
$238$	1.87925	+	1.36238i	0.00789599	+	0.00572430i
$239$			330.896i			1.38450i	0.721656	+	0.692251i	$0.243381\pi$
$239$			330.896i			1.38450i	−0.721656	+	0.692251i	$0.756619\pi$
$240$	−207.071	−	104.290i	−0.862795	−	0.434542i
$241$			353.916i			1.46853i	0.678863	+	0.734265i	$0.262473\pi$
$241$			353.916i			1.46853i	−0.678863	+	0.734265i	$0.737527\pi$
$242$	130.539	+	203.773i	0.539417	+	0.842039i
$243$	−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
$248$	−97.8708	−	31.4645i	−0.394640	−	0.126873i
$249$	−335.949			−1.34919
$250$	−249.999	+	0.663785i	−0.999996	+	0.00265514i
$251$		−	15.6105i		−	0.0621931i	−0.999516	−	0.0310965i	$-0.990100\pi$
$251$		−	15.6105i		−	0.0621931i	0.999516	−	0.0310965i	$-0.00989993\pi$
$252$	−0.294937	+	0.581821i	−0.00117039	+	0.00230881i
$253$	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	$-0.0253726\pi$
$258$	−326.801	−	236.918i	−1.26667	−	0.918287i
$259$		−	3.73216i		−	0.0144099i
$260$	233.610	−	234.833i	0.898500	−	0.903202i
$261$			6.72944i			0.0257833i
$262$	−199.125	−	144.358i	−0.760020	−	0.550986i
$263$	85.2580	+	85.2580i	0.324175	+	0.324175i	0.850366	−	0.526191i	$-0.176380\pi$
$263$	85.2580	+	85.2580i	0.324175	+	0.324175i	−0.526191	+	0.850366i	$0.676380\pi$
$264$	244.571	−	72.3070i	0.926405	−	0.273890i
$265$	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
$268$	−90.2564	+	178.048i	−0.336777	+	0.664359i
$269$			426.434i			1.58526i	0.609705	+	0.792628i	$0.291288\pi$
$269$			426.434i			1.58526i	−0.609705	+	0.792628i	$0.708712\pi$
$270$	274.887	+	43.0942i	1.01810	+	0.159608i
$271$	268.779			0.991806			0.495903	−	0.868378i	$-0.334837\pi$
$271$	268.779			0.991806			0.495903	+	0.868378i	$0.334837\pi$
$272$	67.6158	+	10.4225i	0.248588	+	0.0383181i
$273$	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	$0.912296\pi$
$278$	−119.600	+	164.974i	−0.430215	+	0.593430i
$279$	7.72095			0.0276736
$280$	10.7169	−	1.73745i	0.0382746	−	0.00620520i
$281$			109.574i			0.389944i	0.980809	+	0.194972i	$0.0624616\pi$
$281$			109.574i			0.389944i	−0.980809	+	0.194972i	$0.937538\pi$
$282$	29.9611	+	21.7206i	0.106245	+	0.0770235i
$283$	25.6303	+	25.6303i	0.0905664	+	0.0905664i	0.750939	−	0.660372i	$-0.229601\pi$
$283$	25.6303	+	25.6303i	0.0905664	+	0.0905664i	−0.660372	+	0.750939i	$0.729601\pi$
$284$	407.254	−	133.258i	1.43399	−	0.469217i
$285$	−386.421	+	197.154i	−1.35586	+	0.691770i
$286$	−10.4811	+	364.213i	−0.0366473	+	1.27347i
$287$	−4.57370	−	4.57370i	−0.0159363	−	0.0159363i
$288$	0.0994973	+	19.2262i	0.000345477	+	0.0667577i
$289$		−	270.717i		−	0.936736i
$290$	90.5085	−	65.9763i	0.312098	−	0.227505i
$291$			149.792i			0.514749i
$292$	−264.829	−	134.247i	−0.906948	−	0.459751i
$293$	−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
$298$	−141.114	−	102.302i	−0.473537	−	0.343297i
$299$			394.660i			1.31993i
$300$	−132.385	−	257.810i	−0.441284	−	0.859366i
$301$	18.9014			0.0627952
$302$	−311.355	−	225.721i	−1.03098	−	0.747420i
$303$	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	−0.0159367	−	0.999873i	$-0.505073\pi$
$307$	302.068	−	302.068i	0.983936	−	0.983936i	0.999873	+	0.0159367i	$0.00507304\pi$
$308$	−7.28485	+	9.46330i	−0.0236521	+	0.0307250i
$309$		−	63.0520i		−	0.204052i
$310$	−75.6972	−	103.844i	−0.244184	−	0.334980i
$311$		−	245.922i		−	0.790745i	−0.918521	−	0.395373i	$-0.870615\pi$
$311$		−	245.922i		−	0.790745i	0.918521	−	0.395373i	$-0.129385\pi$
$312$	365.564	+	117.525i	1.17168	+	0.376683i
$313$	−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	$0.132825\pi$
$318$	157.903	+	114.474i	0.496550	+	0.359980i
$319$	−22.8909	+	121.058i	−0.0717584	+	0.379492i
$320$	257.610	−	189.834i	0.805031	−	0.593233i
$321$		−	273.071i		−	0.850688i
$322$	−7.59246	+	10.4729i	−0.0235791	+	0.0325245i
$323$	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
$328$	−181.498	−	58.3500i	−0.553349	−	0.177896i
$329$	−1.73288			−0.00526710
$330$	300.290	+	107.032i	0.909971	+	0.324338i
$331$			447.273i			1.35128i	0.737232	+	0.675639i	$0.236132\pi$
$331$			447.273i			1.35128i	−0.737232	+	0.675639i	$0.763868\pi$
$332$	209.649	−	413.573i	0.631473	−	1.24570i
$333$	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	$0.853105\pi$
$338$	−123.611	+	170.507i	−0.365713	+	0.504458i
$339$	415.435			1.22547
$340$	60.6280	+	60.3123i	0.178318	+	0.177389i
$341$	138.895	+	26.2637i	0.407315	+	0.0770195i
$342$	29.1256	+	21.1150i	0.0851625	+	0.0617396i
$343$	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	−0.704286	−	0.709917i	$-0.748733\pi$
$347$	1.95387	−	1.95387i	0.00563075	−	0.00563075i	0.709917	+	0.704286i	$0.248733\pi$
$348$	115.810	+	58.7064i	0.332787	+	0.168697i
$349$	507.289			1.45355			0.726774	−	0.686876i	$-0.241019\pi$
$349$	507.289			1.45355			0.726774	+	0.686876i	$0.241019\pi$
$350$	12.1049	+	6.13552i	0.0345853	+	0.0175301i
$351$	−460.829			−1.31290
$352$	−63.6102	+	346.205i	−0.180711	+	0.983536i
$353$	−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
$358$	−528.199	−	382.924i	−1.47542	−	1.06962i
$359$			286.206i			0.797231i	0.917118	+	0.398615i	$0.130509\pi$
$359$			286.206i			0.797231i	−0.917118	+	0.398615i	$0.869491\pi$
$360$	−14.0553	+	19.4945i	−0.0390426	+	0.0541515i
$361$	−535.236			−1.48265
$362$	12.3946	+	8.98562i	0.0342392	+	0.0248222i
$363$	−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	0.546138	−	0.837696i	$-0.316098\pi$
$367$	−107.002	−	107.002i	−0.291558	−	0.291558i	−0.837696	+	0.546138i	$0.816098\pi$
$368$	−58.0840	+	376.818i	−0.157837	+	1.02396i
$369$	14.3183			0.0388029
$370$	21.2966	−	135.846i	0.0575583	−	0.367151i
$371$	−9.13273			−0.0246165
$372$	67.3561	−	132.873i	0.181065	−	0.357186i
$373$	−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	$0.486887\pi$
$374$	−94.0309	−	2.70597i	−0.251419	−	0.00723521i
$375$	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
$378$	−12.2288	−	8.86540i	−0.0323513	−	0.0234534i
$379$	454.313			1.19872			0.599358	−	0.800481i	$-0.295423\pi$
$379$	454.313			1.19872			0.599358	+	0.800481i	$0.295423\pi$
$380$	−1.56276	−	598.742i	−0.00411252	−	1.57564i
$381$		−	527.440i		−	1.38436i
$382$	−33.8249	+	46.6574i	−0.0885468	+	0.122140i
$383$	−228.002	+	228.002i	−0.595306	+	0.595306i	−0.939060	−	0.343754i	$-0.888302\pi$
$383$	−228.002	+	228.002i	−0.595306	+	0.595306i	0.343754	+	0.939060i	$0.388302\pi$
$384$	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
$388$	−184.403	−	93.4778i	−0.475266	−	0.240922i
$389$			109.473i			0.281421i	0.990051	+	0.140711i	$0.0449387\pi$
$389$			109.473i			0.281421i	−0.990051	+	0.140711i	$0.955061\pi$
$390$	282.742	+	387.874i	0.724979	+	0.994549i
$391$	−101.892			−0.260592
$392$	372.627	+	119.796i	0.950580	+	0.305602i
$393$	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
$396$	−3.40989	−	26.2156i	−0.00861084	−	0.0662009i
$397$	−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	$0.311380\pi$
$398$	399.437	+	289.577i	1.00361	+	0.727580i
$399$	23.5490			0.0590200
$400$	399.995	−	2.08804i	0.999986	−	0.00522010i
$401$	−213.669			−0.532841			−0.266421	−	0.963857i	$-0.585841\pi$
$401$	−213.669			−0.532841			−0.266421	+	0.963857i	$0.585841\pi$
$402$	−234.192	−	169.780i	−0.582567	−	0.422339i
$403$	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
$408$	−30.3421	+	94.3796i	−0.0743679	+	0.231322i
$409$	165.802			0.405385			0.202692	−	0.979242i	$-0.435031\pi$
$409$	165.802			0.405385			0.202692	+	0.979242i	$0.435031\pi$
$410$	−140.378	−	192.575i	−0.342386	−	0.469696i
$411$			648.679i			1.57830i
$412$	77.6208	+	39.3476i	0.188400	+	0.0955039i
$413$	−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
$418$	452.124	+	478.917i	1.08164	+	1.14574i
$419$	53.5275			0.127751			0.0638753	−	0.997958i	$-0.479654\pi$
$419$	53.5275			0.127751			0.0638753	+	0.997958i	$0.479654\pi$
$420$	0.0410620	+	15.7322i	9.77668e−5	+	0.0374576i
$421$	226.307			0.537546			0.268773	−	0.963203i	$-0.413382\pi$
$421$	226.307			0.537546			0.268773	+	0.963203i	$0.413382\pi$
$422$	−250.446	−	181.564i	−0.593475	−	0.430247i
$423$	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
$428$	336.167	+	170.410i	0.785436	+	0.398154i
$429$	−518.794	−	98.0992i	−1.20931	−	0.228669i
$430$	687.984	+	107.855i	1.59996	+	0.250827i
$431$	−184.190			−0.427354			−0.213677	−	0.976904i	$-0.568544\pi$
$431$	−184.190			−0.427354			−0.213677	+	0.976904i	$0.568544\pi$
$432$	−439.995	−	67.8223i	−1.01851	−	0.156996i
$433$	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
$438$	252.531	−	348.337i	0.576555	−	0.795290i
$439$		−	444.731i		−	1.01305i	−0.862224	−	0.506527i	$-0.830929\pi$
$439$		−	444.731i		−	1.01305i	0.862224	−	0.506527i	$-0.169071\pi$
$440$	−319.159	+	302.883i	−0.725360	+	0.688369i
$441$	−29.3963			−0.0666582
$442$	−114.671	−	83.1323i	−0.259437	−	0.188082i
$443$	−335.016	+	335.016i	−0.756244	+	0.756244i	−0.975637	−	0.219393i	$-0.929592\pi$
$443$	−335.016	+	335.016i	−0.756244	+	0.756244i	0.219393	+	0.975637i	$0.429592\pi$
$444$	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
$448$	−17.1398	+	2.82390i	−0.0382585	+	0.00630335i
$449$		−	503.174i		−	1.12066i	−0.828271	−	0.560328i	$-0.810675\pi$
$449$		−	503.174i		−	1.12066i	0.828271	−	0.560328i	$-0.189325\pi$
$450$	−28.5513	+	9.34370i	−0.0634474	+	0.0207638i
$451$	257.576	+	48.7052i	0.571121	+	0.107994i
$452$	−259.253	+	511.426i	−0.573567	+	1.13147i
$453$	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	$0.437319\pi$
$458$	347.155	−	478.859i	0.757980	−	1.04554i
$459$		−	118.975i		−	0.259204i
$460$	−336.116	+	337.875i	−0.730687	+	0.734511i
$461$			95.1876i			0.206481i	0.994656	+	0.103240i	$0.0329211\pi$
$461$			95.1876i			0.206481i	−0.994656	+	0.103240i	$0.967079\pi$
$462$	−11.8797	−	12.5837i	−0.0257137	−	0.0272375i
$463$	494.077	−	494.077i	1.06712	−	1.06712i	0.0695422	−	0.997579i	$-0.477846\pi$
$463$	494.077	−	494.077i	1.06712	−	1.06712i	0.997579	−	0.0695422i	$-0.0221539\pi$
$464$	−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	0.742927	−	0.669372i	$-0.233437\pi$
$467$	34.3502	+	34.3502i	0.0735550	+	0.0735550i	−0.669372	+	0.742927i	$0.733437\pi$
$468$	17.9970	−	35.5026i	0.0384551	−	0.0758603i
$469$	13.5451			0.0288808
$470$	−63.0743	−	9.88818i	−0.134201	−	0.0210387i
$471$		−	614.492i		−	1.30465i
$472$	−35.8944	+	111.650i	−0.0760475	+	0.236547i
$473$	−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
$478$	388.437	−	535.804i	0.812631	−	1.12093i
$479$		−	687.002i		−	1.43424i	−0.696949	−	0.717121i	$-0.745460\pi$
$479$		−	687.002i		−	1.43424i	0.696949	−	0.717121i	$-0.254540\pi$
$480$	212.874	+	411.951i	0.443487	+	0.858231i
$481$			227.736i			0.473463i
$482$	415.460	−	573.078i	0.861950	−	1.18896i
$483$	−13.2543	−	13.2543i	−0.0274416	−	0.0274416i
$484$	27.8335	−	483.199i	0.0575073	−	0.998345i
$485$	−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	0.157424	−	0.987531i	$-0.449681\pi$
$487$	−404.262	−	404.262i	−0.830107	−	0.830107i	−0.987531	+	0.157424i	$0.949681\pi$
$488$	−502.810	−	161.648i	−1.03035	−	0.331247i
$489$		−	82.6732i		−	0.169066i
$490$	288.205	+	395.369i	0.588173	+	0.806875i
$491$	274.934			0.559946			0.279973	−	0.960008i	$-0.409674\pi$
$491$	274.934			0.559946			0.279973	+	0.960008i	$0.409674\pi$
$492$	124.910	−	246.409i	0.253882	−	0.500832i
$493$	−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
$498$	543.985	+	394.369i	1.09234	+	0.791905i
$499$	−181.398			−0.363524			−0.181762	−	0.983343i	$-0.558180\pi$
$499$	−181.398			−0.363524			−0.181762	+	0.983343i	$0.558180\pi$
$500$	405.590	+	292.398i	0.811180	+	0.584796i
$501$		−	231.389i		−	0.461854i
$502$	−18.3250	+	25.2772i	−0.0365041	+	0.0503531i
$503$	−523.663	−	523.663i	−1.04108	−	1.04108i	−0.999119	−	0.0419598i	$-0.986640\pi$
$503$	−523.663	−	523.663i	−1.04108	−	1.04108i	−0.0419598	−	0.999119i	$-0.513360\pi$
$504$	1.16057	−	0.595889i	0.00230273	−	0.00118232i
$505$	−702.585	−	227.864i	−1.39126	−	0.451216i
$506$	15.0802	−	524.027i	0.0298027	−	1.03563i
$507$	−215.790	−	215.790i	−0.425621	−	0.425621i
$508$	649.311	+	329.149i	1.27817	+	0.647931i
$509$			273.380i			0.537093i	0.963267	+	0.268546i	$0.0865433\pi$
$509$			273.380i			0.537093i	−0.963267	+	0.268546i	$0.913457\pi$
$510$	−100.140	+	72.9969i	−0.196352	+	0.143131i
$511$			20.1470i			0.0394266i
$512$	−411.395	+	304.791i	−0.803507	+	0.595296i
$513$	−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
$518$	−4.38117	+	6.04331i	−0.00845786	+	0.0116666i
$519$		−	524.733i		−	1.01105i
$520$	−653.942	+	106.019i	−1.25758	+	0.203883i
$521$	−381.228			−0.731723			−0.365861	−	0.930669i	$-0.619226\pi$
$521$	−381.228			−0.731723			−0.365861	+	0.930669i	$0.619226\pi$
$522$	7.89966	−	10.8966i	0.0151334	−	0.0208748i
$523$	450.960	+	450.960i	0.862256	+	0.862256i	0.991600	−	0.129344i	$-0.0412872\pi$
$523$	450.960	+	450.960i	0.862256	+	0.862256i	−0.129344	+	0.991600i	$0.541287\pi$
$524$	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
$528$	−480.902	−	170.017i	−0.910799	−	0.322003i
$529$		−	38.8341i		−	0.0734105i
$530$	−332.419	−	52.1134i	−0.627206	−	0.0983273i
$531$		−	8.80799i		−	0.0165875i
$532$	−14.6957	+	28.9902i	−0.0276236	+	0.0544929i
$533$	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
$538$	500.589	−	690.503i	0.930463	−	1.28346i
$539$	−528.819	−	99.9947i	−0.981111	−	0.185519i
$540$	−394.523	−	392.469i	−0.730598	−	0.726795i
$541$			684.932i			1.26605i	0.774132	+	0.633024i	$0.218187\pi$
$541$			684.932i			1.26605i	−0.774132	+	0.633024i	$0.781813\pi$
$542$	−435.221	−	315.519i	−0.802991	−	0.582138i
$543$	−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	−0.715024	−	0.699100i	$-0.753584\pi$
$547$	−8.71058	+	8.71058i	−0.0159243	+	0.0159243i	0.699100	+	0.715024i	$0.253584\pi$
$548$	−798.564	−	404.809i	−1.45723	−	0.738702i
$549$	39.6662			0.0722518
$550$	−545.402	+	70.9662i	−0.991641	+	0.129029i
$551$			335.306i			0.608540i
$552$	−525.970	−	169.094i	−0.952845	−	0.306330i
$553$	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	$0.835614\pi$
$558$	−12.5021	−	9.06358i	−0.0224053	−	0.0162430i
$559$	−1153.36			−2.06325
$560$	−19.3929	−	9.76713i	−0.0346302	−	0.0174413i
$561$	25.3268	−	133.940i	0.0451458	−	0.238752i
$562$	128.629	−	177.428i	0.228877	−	0.315708i
$563$	−704.567	−	704.567i	−1.25145	−	1.25145i	−0.955069	−	0.296382i	$-0.904220\pi$
$563$	−704.567	−	704.567i	−1.25145	−	1.25145i	−0.296382	−	0.955069i	$-0.595780\pi$
$564$	−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
$568$	−815.877	−	262.296i	−1.43640	−	0.461789i
$569$	886.554			1.55809			0.779045	−	0.626967i	$-0.215704\pi$
$569$	886.554			1.55809			0.779045	+	0.626967i	$0.215704\pi$
$570$	857.151	+	134.376i	1.50377	+	0.235747i
$571$	−737.017			−1.29075			−0.645374	−	0.763867i	$-0.723298\pi$
$571$	−737.017			−1.29075			−0.645374	+	0.763867i	$0.723298\pi$
$572$	444.520	−	577.449i	0.777133	−	1.00953i
$573$	−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	$0.100167\pi$
$578$	−317.793	+	438.358i	−0.549815	+	0.758405i
$579$		−	511.855i		−	0.884033i
$580$	−224.005	+	0.584668i	−0.386216	+	0.00100805i
$581$	−31.4628			−0.0541528
$582$	175.840	−	242.551i	0.302131	−	0.416754i
$583$	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	0.815363	−	0.578950i	$-0.196537\pi$
$587$	138.774	+	138.774i	0.236413	+	0.236413i	−0.578950	+	0.815363i	$0.696537\pi$
$588$	−256.448	+	505.893i	−0.436135	+	0.860362i
$589$	384.709			0.653156
$590$	−118.464	+	86.3546i	−0.200787	+	0.146364i
$591$	−655.629			−1.10935
$592$	−33.5169	+	217.440i	−0.0566164	+	0.367297i
$593$	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	$0.215682\pi$
$594$	611.885	+	17.6085i	1.03011	+	0.0296439i
$595$	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
$598$	463.290	−	639.054i	0.774732	−	1.06865i
$599$	−34.1675			−0.0570408			−0.0285204	−	0.999593i	$-0.509080\pi$
$599$	−34.1675			−0.0570408			−0.0285204	+	0.999593i	$0.509080\pi$
$600$	−88.2768	+	572.865i	−0.147128	+	0.954775i
$601$		−	912.806i		−	1.51881i	−0.650617	−	0.759406i	$-0.725490\pi$
$601$		−	912.806i		−	1.51881i	0.650617	−	0.759406i	$-0.274510\pi$
$602$	−30.6060	−	22.1882i	−0.0508406	−	0.0368575i
$603$	−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	−0.994905	−	0.100815i	$-0.967855\pi$
$607$	−542.713	+	542.713i	−0.894090	+	0.894090i	0.100815	+	0.994905i	$0.467855\pi$
$608$	4.95762	+	957.978i	0.00815397	+	1.57562i
$609$		−	8.81029i		−	0.0144668i
$610$	−388.893	−	533.496i	−0.637529	−	0.874584i
$611$	105.740			0.173060
$612$	9.16589	+	4.64638i	0.0149770	+	0.00759213i
$613$	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
$616$	22.9049	−	6.77180i	0.0371833	−	0.0109932i
$617$	−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	$0.499362\pi$
$618$	−74.0164	+	102.097i	−0.119768	+	0.165205i
$619$	368.464			0.595257			0.297628	−	0.954682i	$-0.403804\pi$
$619$	368.464			0.595257			0.297628	+	0.954682i	$0.403804\pi$
$620$	0.670812	+	257.010i	0.00108196	+	0.414532i
$621$	663.037			1.06769
$622$	−288.686	+	398.209i	−0.464126	+	0.640207i
$623$	−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
$628$	756.477	+	383.474i	1.20458	+	0.610627i
$629$	−58.7958			−0.0934750
$630$	1.61109	+	0.252571i	0.00255728	+	0.000400906i
$631$		−	1158.33i		−	1.83571i	−0.396916	−	0.917855i	$-0.629920\pi$
$631$		−	1158.33i		−	1.83571i	0.396916	−	0.917855i	$-0.370080\pi$
$632$	935.481	+	300.748i	1.48019	+	0.475867i
$633$	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
$638$	179.176	−	169.152i	0.280840	−	0.265128i
$639$	64.3638			0.100726
$640$	−639.981	+	4.98241i	−0.999970	+	0.00778502i
$641$	460.419			0.718283			0.359142	−	0.933283i	$-0.383070\pi$
$641$	460.419			0.718283			0.359142	+	0.933283i	$0.383070\pi$
$642$	−320.556	+	442.170i	−0.499309	+	0.688738i
$643$	423.311	−	423.311i	0.658338	−	0.658338i	−0.296649	−	0.954987i	$-0.595869\pi$
$643$	423.311	−	423.311i	0.658338	−	0.658338i	0.954987	+	0.296649i	$0.0958691\pi$
$644$	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	$0.0166400\pi$
$647$	679.923	+	679.923i	1.05089	+	1.05089i	0.0522523	+	0.998634i	$0.483360\pi$
$648$	184.204	−	572.970i	0.284266	−	0.884214i
$649$	29.9613	−	158.450i	0.0461654	−	0.244144i
$650$	−738.636	−	374.388i	−1.13636	−	0.575982i
$651$	−10.1084			−0.0155275
$652$	101.776	+	51.5922i	0.156098	+	0.0791292i
$653$	−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
$658$	2.80596	+	2.03421i	0.00426437	+	0.00309151i
$659$		−	1044.69i		−	1.58526i	−0.609703	−	0.792630i	$-0.708711\pi$
$659$		−	1044.69i		−	1.58526i	0.609703	−	0.792630i	$-0.291289\pi$
$660$	−360.601	−	525.820i	−0.546365	−	0.796697i
$661$	476.865			0.721429			0.360715	−	0.932676i	$-0.382533\pi$
$661$	476.865			0.721429			0.360715	+	0.932676i	$0.382533\pi$
$662$	525.052	−	724.247i	0.793130	−	1.09403i
$663$	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
$668$	284.854	+	144.398i	0.426428	+	0.216165i
$669$			428.218i			0.640087i
$670$	493.024	+	77.2914i	0.735856	+	0.115360i
$671$	713.568	+	134.929i	1.06344	+	0.201087i
$672$	−0.130263	−	25.1712i	−0.000193844	−	0.0374572i
$673$	−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	$0.901792\pi$
$678$	−672.693	−	487.677i	−0.992173	−	0.719288i
$679$			14.0286i			0.0206606i
$680$	−27.3715	−	168.832i	−0.0402522	−	0.248282i
$681$			229.894i			0.337583i
$682$	−194.074	−	205.575i	−0.284566	−	0.301430i
$683$	−623.294	+	623.294i	−0.912583	+	0.912583i	−0.996475	−	0.0838919i	$-0.973265\pi$
$683$	−623.294	+	623.294i	−0.912583	+	0.912583i	0.0838919	+	0.996475i	$0.473265\pi$
$684$	−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
$688$	−1101.21	−	169.745i	−1.60060	−	0.246722i
$689$	557.277			0.808820
$690$	−406.806	−	558.070i	−0.589574	−	0.808797i
$691$			549.965i			0.795897i	0.917408	+	0.397948i	$0.130278\pi$
$691$			549.965i			0.795897i	−0.917408	+	0.397948i	$0.869722\pi$
$692$	645.979	+	327.460i	0.933495	+	0.473208i
$693$	−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
$698$	−821.427	−	595.504i	−1.17683	−	0.853157i
$699$		−	569.078i		−	0.814132i
$700$	−12.3983	−	24.1448i	−0.0177119	−	0.0344926i
$701$		−	546.768i		−	0.779982i	−0.920819	−	0.389991i	$-0.872478\pi$
$701$		−	546.768i		−	0.779982i	0.920819	−	0.389991i	$-0.127522\pi$
$702$	746.197	+	540.965i	1.06296	+	0.770605i
$703$	291.082	+	291.082i	0.414056	+	0.414056i
$704$	509.409	−	485.920i	0.723592	−	0.690228i
$705$	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
$708$	−151.580	−	76.8393i	−0.214097	−	0.108530i
$709$		−	514.197i		−	0.725242i	−0.931937	−	0.362621i	$-0.881882\pi$
$709$		−	514.197i		−	0.725242i	0.931937	−	0.362621i	$-0.118118\pi$
$710$	−631.031	−	865.670i	−0.888777	−	1.21925i
$711$	−73.7993			−0.103797
$712$	−183.310	−	58.9323i	−0.257458	−	0.0827701i
$713$	−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
$718$	335.976	−	463.439i	0.467933	−	0.645458i
$719$	−189.750			−0.263908			−0.131954	−	0.991256i	$-0.542125\pi$
$719$	−189.750			−0.263908			−0.131954	+	0.991256i	$0.542125\pi$
$720$	45.6436	−	15.0670i	0.0633939	−	0.0209265i
$721$		−	5.90504i		−	0.00819007i
$722$	866.681	+	628.311i	1.20039	+	0.870237i
$723$	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
$726$	685.103	+	150.079i	0.943667	+	0.206720i
$727$	927.043	+	927.043i	1.27516	+	1.27516i	0.943343	+	0.331819i	$0.107662\pi$
$727$	927.043	+	927.043i	1.27516	+	1.27516i	0.331819	+	0.943343i	$0.392338\pi$
$728$	34.2363	+	11.0067i	0.0470279	+	0.0151190i
$729$			770.952i			1.05755i
$730$	−114.963	+	733.323i	−0.157484	+	1.00455i
$731$		−	297.768i		−	0.407344i
$732$	346.041	−	682.633i	0.472734	−	0.932559i
$733$	−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
$738$	−23.1848	−	16.8081i	−0.0314158	−	0.0227753i
$739$			694.401i			0.939650i	0.882760	+	0.469825i	$0.155683\pi$
$739$			694.401i			0.939650i	−0.882760	+	0.469825i	$0.844317\pi$
$740$	−193.953	+	194.968i	−0.262099	+	0.263471i
$741$	−1436.95			−1.93921
$742$	14.7882	+	10.7209i	0.0199302	+	0.0144486i
$743$	641.222	+	641.222i	0.863018	+	0.863018i	0.991687	−	0.128670i	$-0.0410708\pi$
$743$	641.222	+	641.222i	0.863018	+	0.863018i	−0.128670	+	0.991687i	$0.541071\pi$
$744$	−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
$748$	149.083	+	114.764i	0.199309	+	0.153428i
$749$		−	25.5740i		−	0.0341442i
$750$	−510.960	+	513.681i	−0.681280	+	0.684908i
$751$			530.192i			0.705982i	0.935627	+	0.352991i	$0.114835\pi$
$751$			530.192i			0.705982i	−0.935627	+	0.352991i	$0.885165\pi$
$752$	100.959	+	15.5622i	0.134254	+	0.0206944i
$753$	−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	$0.0753866\pi$
$758$	−735.646	−	533.316i	−0.970510	−	0.703583i
$759$	746.437	+	141.144i	0.983448	+	0.185961i
$760$	−700.330	+	971.348i	−0.921487	+	1.27809i
$761$			1419.91i			1.86584i	0.360080	+	0.932921i	$0.382749\pi$
$761$			1419.91i			1.86584i	−0.360080	+	0.932921i	$0.617251\pi$
$762$	−619.159	+	854.057i	−0.812545	+	1.12081i
$763$	−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
$768$	−342.288	−	658.246i	−0.445687	−	0.857091i
$769$	−746.894			−0.971254			−0.485627	−	0.874166i	$-0.661409\pi$
$769$	−746.894			−0.971254			−0.485627	+	0.874166i	$0.661409\pi$
$770$	28.1232	+	10.0239i	0.0365237	+	0.0130180i
$771$		−	1133.86i		−	1.47064i
$772$	630.125	+	319.423i	0.816224	+	0.413761i

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+(-1.61925 - 1.17390i) 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} +(2.44850 - 7.61609i) q^{8} +0.600827i q^{9} +(8.08090 - 5.89059i) q^{10} +(-2.04378 + 10.8085i) q^{11} +(10.3399 + 5.24151i) 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} +(0.705308 - 0.972889i) q^{18} +29.9372i q^{19} +(-19.9999 + 0.0522011i) q^{20} -0.786612i q^{21} +(15.9974 - 15.1024i) 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} +(0.968367 + 0.490885i) q^{28} +11.2003 q^{29} +(4.48859 - 28.6316i) q^{30} -12.8505i q^{31} +(31.9996 - 0.165600i) 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} +(35.1431 - 48.4758i) q^{38} +47.9989i q^{39} +(32.4462 + 23.3933i) q^{40} -23.8309i q^{41} +(-0.923400 + 1.27372i) q^{42} +(49.2420 + 49.2420i) q^{43} +(-43.6324 + 5.67533i) q^{44} +(-2.85760 - 0.926786i) q^{45} +(-47.0640 + 7.50415i) q^{46} +(-4.51450 - 4.51450i) q^{47} +(-7.06421 + 45.8289i) q^{48} +48.9263i q^{49} +(15.5514 + 47.5200i) q^{50} -12.3921 q^{51} +(-59.0895 - 29.9537i) 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} +(-18.1361 - 13.1480i) q^{58} -14.6598 q^{59} +(-40.8787 + 41.0926i) q^{60} -66.0194i q^{61} +(-15.0852 + 20.8082i) q^{62} +(0.115313 + 0.115313i) q^{63} +(-52.0097 - 37.2960i) q^{64} +(-37.6348 - 73.7640i) q^{65} +(1.83406 - 63.7325i) q^{66} +(35.2878 + 35.2878i) q^{67} +(7.73331 - 15.2555i) q^{68} -69.0604i q^{69} +(0.420372 - 2.68145i) q^{70} -107.125i q^{71} +(4.57595 + 1.47113i) 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} +(56.3457 - 77.7222i) q^{78} +122.830i q^{79} +(-25.0772 - 75.9680i) q^{80} +75.2316 q^{81} +(-27.9750 + 38.5882i) 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} +(77.3141 + 42.0301i) q^{88} -24.0688i q^{89} +(3.53923 + 4.85523i) q^{90} +4.49526i q^{91} +(85.0175 + 43.0972i) 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} +(57.4344 - 79.2240i) 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

Properties

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