LMFDB - Embedded newform 220.3.i.a.43.12

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			43.12
Character	$\chi$	$=$	220.43
Dual form			220.3.i.a.87.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.71305 + 1.03221i) q^{2} +(-2.84767 + 2.84767i) q^{3} +(1.86907 - 3.53646i) q^{4} +(-4.99552 + 0.211543i) q^{5} +(1.93880 - 7.81761i) q^{6} +(-7.03107 + 7.03107i) q^{7} +(0.448578 + 7.98741i) q^{8} -7.21849i q^{9} +(8.33922 - 5.51883i) q^{10} +(-5.03383 - 9.78062i) q^{11} +(4.74819 + 15.3932i) q^{12} +(-1.58388 + 1.58388i) q^{13} +(4.78700 - 19.3021i) q^{14} +(13.6232 - 14.8280i) q^{15} +(-9.01315 - 13.2198i) q^{16} +(-0.925270 - 0.925270i) q^{17} +(7.45103 + 12.3656i) q^{18} +22.8764i q^{19} +(-8.58887 + 18.0619i) q^{20} -40.0444i q^{21} +(18.7189 + 11.5587i) q^{22} +(19.2468 - 19.2468i) q^{23} +(-24.0230 - 21.4681i) q^{24} +(24.9105 - 2.11354i) q^{25} +(1.07836 - 4.34817i) q^{26} +(-5.07315 - 5.07315i) q^{27} +(11.7236 + 38.0067i) q^{28} +41.7404 q^{29} +(-8.03154 + 39.4632i) q^{30} +35.7503i q^{31} +(29.0856 + 13.3427i) q^{32} +(42.1867 + 13.5173i) q^{33} +(2.54011 + 0.629956i) q^{34} +(33.6365 - 36.6113i) q^{35} +(-25.5279 - 13.4919i) q^{36} +(0.765756 - 0.765756i) q^{37} +(-23.6133 - 39.1884i) q^{38} -9.02075i q^{39} +(-3.93057 - 39.8064i) q^{40} -27.8390i q^{41} +(41.3344 + 68.5980i) q^{42} +(-48.0507 - 48.0507i) q^{43} +(-43.9974 - 0.478692i) q^{44} +(1.52702 + 36.0601i) q^{45} +(-13.1039 + 52.8375i) q^{46} +(14.5319 + 14.5319i) q^{47} +(63.3122 + 11.9792i) q^{48} -49.8720i q^{49} +(-40.4913 + 29.3335i) q^{50} +5.26974 q^{51} +(2.64095 + 8.56172i) q^{52} +(-33.3564 - 33.3564i) q^{53} +(13.9271 + 3.45398i) q^{54} +(27.2157 + 47.7944i) q^{55} +(-59.3141 - 53.0061i) q^{56} +(-65.1445 - 65.1445i) q^{57} +(-71.5033 + 43.0850i) q^{58} -74.0986 q^{59} +(-26.9760 - 75.8926i) q^{60} -24.4634i q^{61} +(-36.9019 - 61.2419i) q^{62} +(50.7538 + 50.7538i) q^{63} +(-63.5976 + 7.16596i) q^{64} +(7.57725 - 8.24737i) q^{65} +(-86.2207 + 20.3899i) q^{66} +(23.1532 + 23.1532i) q^{67} +(-5.00158 + 1.54279i) q^{68} +109.617i q^{69} +(-19.8303 + 97.4369i) q^{70} -126.669i q^{71} +(57.6571 - 3.23806i) q^{72} +(-70.6214 + 70.6214i) q^{73} +(-0.521353 + 2.10220i) q^{74} +(-64.9183 + 76.9556i) q^{75} +(80.9016 + 42.7576i) q^{76} +(104.162 + 33.3750i) q^{77} +(9.31134 + 15.4530i) q^{78} +6.19455i q^{79} +(47.8220 + 64.1331i) q^{80} +93.8598 q^{81} +(28.7358 + 47.6896i) q^{82} +(-56.4297 - 56.4297i) q^{83} +(-141.616 - 74.8458i) q^{84} +(4.81794 + 4.42648i) q^{85} +(131.912 + 32.7146i) q^{86} +(-118.863 + 118.863i) q^{87} +(75.8638 - 44.5947i) q^{88} +107.129i q^{89} +(-39.8376 - 60.1966i) q^{90} -22.2728i q^{91} +(-32.0920 - 104.039i) q^{92} +(-101.805 - 101.805i) q^{93} +(-39.8937 - 9.89379i) q^{94} +(-4.83934 - 114.280i) q^{95} +(-120.822 + 44.8308i) q^{96} +(54.6816 - 54.6816i) q^{97} +(51.4786 + 85.4332i) q^{98} +(-70.6013 + 36.3367i) 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 $

$2$	−1.71305	+	1.03221i	−0.856524	+	0.516107i
$2$	−1.71305	+	1.03221i	−0.856524	+	0.516107i
$3$	−2.84767	+	2.84767i	−0.949225	+	0.949225i	−0.998772	−	0.0495472i	$-0.984222\pi$
$3$	−2.84767	+	2.84767i	−0.949225	+	0.949225i	0.0495472	+	0.998772i	$0.484222\pi$
$4$	1.86907	−	3.53646i	0.467268	−	0.884116i
$5$	−4.99552	+	0.211543i	−0.999105	+	0.0423086i
$5$	−4.99552	+	0.211543i	−0.999105	+	0.0423086i
$6$	1.93880	−	7.81761i	0.323133	−	1.30294i
$7$	−7.03107	+	7.03107i	−1.00444	+	1.00444i	−0.00444905	+	0.999990i	$0.501416\pi$
$7$	−7.03107	+	7.03107i	−1.00444	+	1.00444i	−0.999990	+	0.00444905i	$0.998584\pi$
$8$	0.448578	+	7.98741i	0.0560723	+	0.998427i
$9$		−	7.21849i		−	0.802055i
$10$	8.33922	−	5.51883i	0.833922	−	0.551883i
$11$	−5.03383	−	9.78062i	−0.457621	−	0.889147i
$11$	−5.03383	−	9.78062i	−0.457621	−	0.889147i
$12$	4.74819	+	15.3932i	0.395683	+	1.28277i
$13$	−1.58388	+	1.58388i	−0.121837	+	0.121837i	−0.765396	−	0.643559i	$-0.777457\pi$
$13$	−1.58388	+	1.58388i	−0.121837	+	0.121837i	0.643559	+	0.765396i	$0.277457\pi$
$14$	4.78700	−	19.3021i	0.341929	−	1.37872i
$15$	13.6232	−	14.8280i	0.908214	−	0.988535i
$16$	−9.01315	−	13.2198i	−0.563322	−	0.826237i
$17$	−0.925270	−	0.925270i	−0.0544277	−	0.0544277i	0.679369	−	0.733797i	$-0.262254\pi$
$17$	−0.925270	−	0.925270i	−0.0544277	−	0.0544277i	−0.733797	+	0.679369i	$0.762254\pi$
$18$	7.45103	+	12.3656i	0.413946	+	0.686979i
$19$			22.8764i			1.20402i	0.798488	+	0.602011i	$0.205633\pi$
$19$			22.8764i			1.20402i	−0.798488	+	0.602011i	$0.794367\pi$
$20$	−8.58887	+	18.0619i	−0.429443	+	0.903094i
$21$		−	40.0444i		−	1.90688i
$22$	18.7189	+	11.5587i	0.850859	+	0.525395i
$23$	19.2468	−	19.2468i	0.836817	−	0.836817i	−0.151621	−	0.988439i	$-0.548449\pi$
$23$	19.2468	−	19.2468i	0.836817	−	0.836817i	0.988439	+	0.151621i	$0.0484494\pi$
$24$	−24.0230	−	21.4681i	−1.00096	−	0.894506i
$25$	24.9105	−	2.11354i	0.996420	−	0.0845415i
$26$	1.07836	−	4.34817i	0.0414754	−	0.167237i
$27$	−5.07315	−	5.07315i	−0.187894	−	0.187894i
$28$	11.7236	+	38.0067i	0.418699	+	1.35738i
$29$	41.7404			1.43932			0.719662	−	0.694324i	$-0.244297\pi$
$29$	41.7404			1.43932			0.719662	+	0.694324i	$0.244297\pi$
$30$	−8.03154	+	39.4632i	−0.267718	+	1.31544i
$31$			35.7503i			1.15323i	0.817015	+	0.576617i	$0.195628\pi$
$31$			35.7503i			1.15323i	−0.817015	+	0.576617i	$0.804372\pi$
$32$	29.0856	+	13.3427i	0.908926	+	0.416958i
$33$	42.1867	+	13.5173i	1.27839	+	0.409615i
$34$	2.54011	+	0.629956i	0.0747091	+	0.0185281i
$35$	33.6365	−	36.6113i	0.961043	−	1.04604i
$36$	−25.5279	−	13.4919i	−0.709109	−	0.374774i
$37$	0.765756	−	0.765756i	0.0206961	−	0.0206961i	−0.696683	−	0.717379i	$-0.745342\pi$
$37$	0.765756	−	0.765756i	0.0206961	−	0.0206961i	0.717379	+	0.696683i	$0.245342\pi$
$38$	−23.6133	−	39.1884i	−0.621403	−	1.03127i
$39$		−	9.02075i		−	0.231301i
$40$	−3.93057	−	39.8064i	−0.0982641	−	0.995160i
$41$		−	27.8390i		−	0.679000i	−0.940606	−	0.339500i	$-0.889742\pi$
$41$		−	27.8390i		−	0.679000i	0.940606	−	0.339500i	$-0.110258\pi$
$42$	41.3344	+	68.5980i	0.984152	+	1.63329i
$43$	−48.0507	−	48.0507i	−1.11746	−	1.11746i	−0.992113	−	0.125345i	$-0.959996\pi$
$43$	−48.0507	−	48.0507i	−1.11746	−	1.11746i	−0.125345	−	0.992113i	$-0.540004\pi$
$44$	−43.9974	−	0.478692i	−0.999941	−	0.0108794i
$45$	1.52702	+	36.0601i	0.0339338	+	0.801337i
$46$	−13.1039	+	52.8375i	−0.284867	+	1.14864i
$47$	14.5319	+	14.5319i	0.309188	+	0.309188i	0.844595	−	0.535406i	$-0.179841\pi$
$47$	14.5319	+	14.5319i	0.309188	+	0.309188i	−0.535406	+	0.844595i	$0.679841\pi$
$48$	63.3122	+	11.9792i	1.31900	+	0.249566i
$49$		−	49.8720i		−	1.01780i
$50$	−40.4913	+	29.3335i	−0.809825	+	0.586671i
$51$	5.26974			0.103328
$52$	2.64095	+	8.56172i	0.0507876	+	0.164648i
$53$	−33.3564	−	33.3564i	−0.629365	−	0.629365i	0.318543	−	0.947908i	$-0.396806\pi$
$53$	−33.3564	−	33.3564i	−0.629365	−	0.629365i	−0.947908	+	0.318543i	$0.896806\pi$
$54$	13.9271	+	3.45398i	0.257910	+	0.0639626i
$55$	27.2157	+	47.7944i	0.494830	+	0.868990i
$56$	−59.3141	−	53.0061i	−1.05918	−	0.946538i
$57$	−65.1445	−	65.1445i	−1.14289	−	1.14289i
$58$	−71.5033	+	43.0850i	−1.23282	+	0.742845i
$59$	−74.0986			−1.25591			−0.627954	−	0.778250i	$-0.716107\pi$
$59$	−74.0986			−1.25591			−0.627954	+	0.778250i	$0.716107\pi$
$60$	−26.9760	−	75.8926i	−0.449601	−	1.26488i
$61$		−	24.4634i		−	0.401039i	−0.979690	−	0.200520i	$-0.935737\pi$
$61$		−	24.4634i		−	0.401039i	0.979690	−	0.200520i	$-0.0642630\pi$
$62$	−36.9019	−	61.2419i	−0.595192	−	0.987773i
$63$	50.7538	+	50.7538i	0.805615	+	0.805615i
$64$	−63.5976	+	7.16596i	−0.993712	+	0.111968i
$65$	7.57725	−	8.24737i	0.116573	−	0.126883i
$66$	−86.2207	+	20.3899i	−1.30637	+	0.308938i
$67$	23.1532	+	23.1532i	0.345571	+	0.345571i	0.858457	−	0.512886i	$-0.171424\pi$
$67$	23.1532	+	23.1532i	0.345571	+	0.345571i	−0.512886	+	0.858457i	$0.671424\pi$
$68$	−5.00158	+	1.54279i	−0.0735527	+	0.0226881i
$69$			109.617i			1.58866i
$70$	−19.8303	+	97.4369i	−0.283291	+	1.39196i
$71$		−	126.669i		−	1.78407i	−0.451962	−	0.892037i	$-0.649276\pi$
$71$		−	126.669i		−	1.78407i	0.451962	−	0.892037i	$-0.350724\pi$
$72$	57.6571	−	3.23806i	0.800793	−	0.0449731i
$73$	−70.6214	+	70.6214i	−0.967416	+	0.967416i	−0.999486	−	0.0320692i	$-0.989790\pi$
$73$	−70.6214	+	70.6214i	−0.967416	+	0.967416i	0.0320692	+	0.999486i	$0.489790\pi$
$74$	−0.521353	+	2.10220i	−0.00704531	+	0.0284081i
$75$	−64.9183	+	76.9556i	−0.865578	+	1.02608i
$76$	80.9016	+	42.7576i	1.06449	+	0.562600i
$77$	104.162	+	33.3750i	1.35275	+	0.433442i
$78$	9.31134	+	15.4530i	0.119376	+	0.198115i
$79$			6.19455i			0.0784120i	0.999231	+	0.0392060i	$0.0124829\pi$
$79$			6.19455i			0.0784120i	−0.999231	+	0.0392060i	$0.987517\pi$
$80$	47.8220	+	64.1331i	0.597775	+	0.801664i
$81$	93.8598			1.15876
$82$	28.7358	+	47.6896i	0.350437	+	0.581580i
$83$	−56.4297	−	56.4297i	−0.679876	−	0.679876i	0.280096	−	0.959972i	$-0.409634\pi$
$83$	−56.4297	−	56.4297i	−0.679876	−	0.679876i	−0.959972	+	0.280096i	$0.909634\pi$
$84$	−141.616	−	74.8458i	−1.68590	−	0.891022i
$85$	4.81794	+	4.42648i	0.0566817	+	0.0520762i
$86$	131.912	+	32.7146i	1.53386	+	0.380402i
$87$	−118.863	+	118.863i	−1.36624	+	1.36624i
$88$	75.8638	−	44.5947i	0.862088	−	0.506758i
$89$			107.129i			1.20370i	0.798609	+	0.601850i	$0.205570\pi$
$89$			107.129i			1.20370i	−0.798609	+	0.601850i	$0.794430\pi$
$90$	−39.8376	−	60.1966i	−0.442640	−	0.668851i
$91$		−	22.2728i		−	0.244756i
$92$	−32.0920	−	104.039i	−0.348826	−	1.13086i
$93$	−101.805	−	101.805i	−1.09468	−	1.09468i
$94$	−39.8937	−	9.89379i	−0.424402	−	0.105253i
$95$	−4.83934	−	114.280i	−0.0509405	−	1.20294i
$96$	−120.822	+	44.8308i	−1.25856	+	0.466988i
$97$	54.6816	−	54.6816i	0.563728	−	0.563728i	−0.366637	−	0.930364i	$-0.619491\pi$
$97$	54.6816	−	54.6816i	0.563728	−	0.563728i	0.930364	+	0.366637i	$0.119491\pi$
$98$	51.4786	+	85.4332i	0.525291	+	0.871767i
$99$	−70.6013	+	36.3367i	−0.713145	+	0.367037i
$100$	39.0850	−	92.0454i	0.390850	−	0.920454i
$101$		−	154.516i		−	1.52986i	−0.644112	−	0.764931i	$-0.722773\pi$
$101$		−	154.516i		−	1.52986i	0.644112	−	0.764931i	$-0.277227\pi$
$102$	−9.02731	+	5.43949i	−0.0885031	+	0.0533284i
$103$	106.792	−	106.792i	1.03681	−	1.03681i	0.0375172	−	0.999296i	$-0.488055\pi$
$103$	106.792	−	106.792i	1.03681	−	1.03681i	0.999296	−	0.0375172i	$-0.0119449\pi$
$104$	−13.3616	−	11.9406i	−0.128477	−	0.114814i
$105$	8.47112	+	200.043i	0.0806773	+	1.90517i
$106$	91.5720	+	22.7102i	0.863886	+	0.214247i
$107$	−38.8903	+	38.8903i	−0.363460	+	0.363460i	−0.865085	−	0.501625i	$-0.832736\pi$
$107$	−38.8903	+	38.8903i	−0.363460	+	0.363460i	0.501625	+	0.865085i	$0.332736\pi$
$108$	−27.4231	+	8.45894i	−0.253918	+	0.0783235i
$109$	−102.110			−0.936789			−0.468394	−	0.883520i	$-0.655167\pi$
$109$	−102.110			−0.936789			−0.468394	+	0.883520i	$0.655167\pi$
$110$	−95.9558	−	53.7818i	−0.872325	−	0.488926i
$111$			4.36125i			0.0392905i
$112$	156.322	+	29.5772i	1.39573	+	0.264082i
$113$	64.6218	+	64.6218i	0.571874	+	0.571874i	0.932652	−	0.360778i	$-0.117489\pi$
$113$	64.6218	+	64.6218i	0.571874	+	0.571874i	−0.360778	+	0.932652i	$0.617489\pi$
$114$	178.839	+	44.3527i	1.56876	+	0.389058i
$115$	−92.0763	+	100.219i	−0.800663	+	0.871473i
$116$	78.0157	−	147.613i	0.672550	−	1.27253i
$117$	11.4332	+	11.4332i	0.0977199	+	0.0977199i
$118$	126.934	−	76.4856i	1.07572	−	0.648183i
$119$	13.0113			0.109339
$120$	124.549	+	102.163i	1.03791	+	0.851356i
$121$	−70.3210	+	98.4680i	−0.581166	+	0.813785i
$122$	25.2514	+	41.9070i	0.206979	+	0.343500i
$123$	79.2764	+	79.2764i	0.644524	+	0.644524i
$124$	126.430	+	66.8197i	1.01959	+	0.538869i
$125$	−123.994	+	15.8279i	−0.991951	+	0.126623i
$126$	−139.332	−	34.5549i	−1.10581	−	0.274245i
$127$	7.48217	−	7.48217i	0.0589147	−	0.0589147i	−0.677036	−	0.735950i	$-0.736736\pi$
$127$	7.48217	−	7.48217i	0.0589147	−	0.0589147i	0.735950	+	0.677036i	$0.236736\pi$
$128$	101.549	−	77.9219i	0.793351	−	0.608765i
$129$	273.665			2.12144
$130$	−4.46715	+	21.9495i	−0.0343627	+	0.168842i
$131$	−25.7347			−0.196448			−0.0982242	−	0.995164i	$-0.531316\pi$
$131$	−25.7347			−0.196448			−0.0982242	+	0.995164i	$0.531316\pi$
$132$	126.653	−	123.927i	0.959495	−	0.938841i
$133$	−160.846	−	160.846i	−1.20937	−	1.20937i
$134$	−63.5617	−	15.7635i	−0.474341	−	0.117638i
$135$	26.4162	+	24.2699i	0.195676	+	0.179777i
$136$	6.97546	−	7.80557i	0.0512902	−	0.0573939i
$137$	−73.9786	+	73.9786i	−0.539990	+	0.539990i	−0.923526	−	0.383536i	$-0.874706\pi$
$137$	−73.9786	+	73.9786i	−0.539990	+	0.539990i	0.383536	+	0.923526i	$0.374706\pi$
$138$	−113.148	−	187.780i	−0.819916	−	1.36072i
$139$		−	107.789i		−	0.775458i	−0.921773	−	0.387729i	$-0.873260\pi$
$139$		−	107.789i		−	0.775458i	0.921773	−	0.387729i	$-0.126740\pi$
$140$	−66.6054	−	187.383i	−0.475753	−	1.33845i
$141$	−82.7639			−0.586978
$142$	130.750	+	216.991i	0.920773	+	1.52810i
$143$	23.4643	+	7.51834i	0.164086	+	0.0525758i
$144$	−95.4270	+	65.0614i	−0.662688	+	0.451815i
$145$	−208.515	+	8.82989i	−1.43804	+	0.0608958i
$146$	48.0815	−	193.874i	0.329325	−	1.32791i
$147$	142.019	+	142.019i	0.966117	+	0.966117i
$148$	−1.27682	−	4.13932i	−0.00862714	−	0.0279684i
$149$	29.1329			0.195523			0.0977613	−	0.995210i	$-0.468832\pi$
$149$	29.1329			0.195523			0.0977613	+	0.995210i	$0.468832\pi$
$150$	31.7736	−	198.838i	0.211824	−	1.32559i
$151$	286.899			1.89999			0.949996	−	0.312263i	$-0.101087\pi$
$151$	286.899			1.89999			0.949996	+	0.312263i	$0.101087\pi$
$152$	−182.723	+	10.2619i	−1.20213	+	0.0675122i
$153$	−6.67906	+	6.67906i	−0.0436540	+	0.0436540i
$154$	−212.884	+	50.3439i	−1.38236	+	0.326909i
$155$	−7.56272	−	178.591i	−0.0487917	−	1.15220i
$156$	−31.9016	−	16.8604i	−0.204497	−	0.108080i
$157$	76.1468	−	76.1468i	0.485011	−	0.485011i	−0.421716	−	0.906728i	$-0.638572\pi$
$157$	76.1468	−	76.1468i	0.485011	−	0.485011i	0.906728	+	0.421716i	$0.138572\pi$
$158$	−6.39410	−	10.6116i	−0.0404690	−	0.0671618i
$159$	189.976			1.19482
$160$	−148.120	−	60.5007i	−0.925753	−	0.378129i
$161$			270.651i			1.68106i
$162$	−160.786	+	96.8834i	−0.992509	+	0.598045i
$163$	54.2711	−	54.2711i	0.332952	−	0.332952i	−0.520755	−	0.853706i	$-0.674349\pi$
$163$	54.2711	−	54.2711i	0.332952	−	0.332952i	0.853706	+	0.520755i	$0.174349\pi$
$164$	−98.4517	−	52.0331i	−0.600315	−	0.317275i
$165$	−213.604	−	58.6017i	−1.29457	−	0.355162i
$166$	154.914	+	38.4193i	0.933219	+	0.231442i
$167$	133.358	−	133.358i	0.798550	−	0.798550i	−0.184316	−	0.982867i	$-0.559007\pi$
$167$	133.358	−	133.358i	0.798550	−	0.798550i	0.982867	+	0.184316i	$0.0590071\pi$
$168$	319.851	−	17.9631i	1.90388	−	0.106923i
$169$			163.983i			0.970312i
$170$	−12.8224	−	2.60962i	−0.0754261	−	0.0153507i
$171$	165.133			0.965691
$172$	−259.740	+	80.1194i	−1.51011	+	0.465811i
$173$	−125.321	+	125.321i	−0.724399	+	0.724399i	−0.969498	−	0.245099i	$-0.921180\pi$
$173$	−125.321	+	125.321i	−0.724399	+	0.724399i	0.245099	+	0.969498i	$0.421180\pi$
$174$	80.9261	−	326.310i	0.465093	−	1.87535i
$175$	−160.287	+	190.008i	−0.915926	+	1.08576i
$176$	−83.9271	+	154.700i	−0.476859	+	0.878980i
$177$	211.009	−	211.009i	1.19214	−	1.19214i
$178$	−110.580	−	183.518i	−0.621238	−	1.03100i
$179$	152.103			0.849738			0.424869	−	0.905255i	$-0.360320\pi$
$179$	152.103			0.849738			0.424869	+	0.905255i	$0.360320\pi$
$180$	130.380	+	61.9987i	0.724331	+	0.344437i
$181$	76.9154			0.424947			0.212474	−	0.977167i	$-0.431848\pi$
$181$	76.9154			0.424947			0.212474	+	0.977167i	$0.431848\pi$
$182$	22.9903	+	38.1543i	0.126320	+	0.209639i
$183$	69.6637	+	69.6637i	0.380676	+	0.380676i
$184$	162.366	+	145.098i	0.882423	+	0.788578i
$185$	−3.66336	+	3.98734i	−0.0198019	+	0.0215532i
$186$	279.482	+	69.3124i	1.50259	+	0.372648i
$187$	−4.39206	+	13.7074i	−0.0234870	+	0.0733015i
$188$	78.5524	−	24.2303i	0.417832	−	0.128885i
$189$	71.3394			0.377457
$190$	126.251	+	190.771i	0.664479	+	1.00406i
$191$		−	4.70516i		−	0.0246343i	−0.999924	−	0.0123172i	$-0.996079\pi$
$191$		−	4.70516i		−	0.0246343i	0.999924	−	0.0123172i	$-0.00392078\pi$
$192$	160.699	−	201.511i	0.836973	−	1.04954i
$193$	118.695	−	118.695i	0.615000	−	0.615000i	−0.329245	−	0.944245i	$-0.606794\pi$
$193$	118.695	−	118.695i	0.615000	−	0.615000i	0.944245	+	0.329245i	$0.106794\pi$
$194$	−37.2291	+	150.115i	−0.191903	+	0.773790i
$195$	1.90828	+	45.0634i	0.00978604	+	0.231094i
$196$	−176.371	−	93.2143i	−0.899850	−	0.475583i
$197$	−210.870	−	210.870i	−1.07040	−	1.07040i	−0.997326	−	0.0730773i	$-0.976718\pi$
$197$	−210.870	−	210.870i	−1.07040	−	1.07040i	−0.0730773	−	0.997326i	$-0.523282\pi$
$198$	83.4363	−	135.122i	0.421395	−	0.682435i
$199$	−85.9689			−0.432004			−0.216002	−	0.976393i	$-0.569302\pi$
$199$	−85.9689			−0.432004			−0.216002	+	0.976393i	$0.569302\pi$
$200$	28.0560	+	198.022i	0.140280	+	0.990112i
$201$	−131.866			−0.656048
$202$	159.494	+	264.693i	0.789572	+	1.31036i
$203$	−293.480	+	293.480i	−1.44571	+	1.44571i
$204$	9.84951	−	18.6362i	0.0482819	−	0.0913541i
$205$	5.88915	+	139.070i	0.0287276	+	0.678392i
$206$	−72.7075	+	293.171i	−0.352949	+	1.42316i
$207$	−138.933	−	138.933i	−0.671173	−	0.671173i
$208$	35.2143	+	6.66282i	0.169300	+	0.0320328i
$209$	223.745	−	115.156i	1.07055	−	0.550986i
$210$	−220.998	−	333.939i	−1.05237	−	1.59019i
$211$	−309.119			−1.46502			−0.732509	−	0.680758i	$-0.761651\pi$
$211$	−309.119			−1.46502			−0.732509	+	0.680758i	$0.761651\pi$
$212$	−180.309	+	55.6182i	−0.850514	+	0.262350i
$213$	360.713	+	360.713i	1.69349	+	1.69349i
$214$	26.4779	−	106.764i	0.123728	−	0.498897i
$215$	250.203	+	229.874i	1.16374	+	1.06918i
$216$	38.2457	−	42.7971i	0.177063	−	0.198135i
$217$	−251.363	−	251.363i	−1.15835	−	1.15835i
$218$	174.919	−	105.399i	0.802382	−	0.483483i
$219$		−	402.213i		−	1.83659i
$220$	219.891	−	6.91603i	0.999506	−	0.0314365i
$221$	2.93104			0.0132626
$222$	−4.50174	−	7.47102i	−0.0202781	−	0.0336533i
$223$	61.5103	−	61.5103i	0.275831	−	0.275831i	−0.555611	−	0.831442i	$-0.687516\pi$
$223$	61.5103	−	61.5103i	0.275831	−	0.275831i	0.831442	+	0.555611i	$0.187516\pi$
$224$	−298.316	+	110.690i	−1.33177	+	0.494152i
$225$	−15.2565	−	179.816i	−0.0678069	−	0.799183i
$226$	−177.404	−	43.9967i	−0.784972	−	0.194676i
$227$	20.6804	−	20.6804i	0.0911031	−	0.0911031i	−0.660087	−	0.751190i	$-0.729480\pi$
$227$	20.6804	−	20.6804i	0.0911031	−	0.0911031i	0.751190	+	0.660087i	$0.229480\pi$
$228$	−352.141	+	108.622i	−1.54448	+	0.476410i
$229$			78.4887i			0.342746i	0.985206	+	0.171373i	$0.0548202\pi$
$229$			78.4887i			0.342746i	−0.985206	+	0.171373i	$0.945180\pi$
$230$	54.2834	−	266.723i	0.236015	−	1.15967i
$231$	−391.659	+	201.577i	−1.69549	+	0.872627i
$232$	18.7238	+	333.398i	0.0807062	+	1.43706i
$233$	−70.5031	+	70.5031i	−0.302588	+	0.302588i	−0.842026	−	0.539437i	$-0.818637\pi$
$233$	−70.5031	+	70.5031i	−0.302588	+	0.302588i	0.539437	+	0.842026i	$0.318637\pi$
$234$	−31.3872	−	7.78414i	−0.134133	−	0.0332656i
$235$	−75.6683	−	69.5201i	−0.321993	−	0.295830i
$236$	−138.495	+	262.047i	−0.586845	+	1.11037i
$237$	−17.6401	−	17.6401i	−0.0744306	−	0.0744306i
$238$	−22.2890	+	13.4304i	−0.0936511	+	0.0564304i
$239$		−	18.5291i		−	0.0775277i	−0.999248	−	0.0387638i	$-0.987658\pi$
$239$		−	18.5291i		−	0.0775277i	0.999248	−	0.0387638i	$-0.0123420\pi$
$240$	−318.812	−	46.4489i	−1.32838	−	0.193537i
$241$		−	306.272i		−	1.27084i	−0.772168	−	0.635419i	$-0.780828\pi$
$241$		−	306.272i		−	1.27084i	0.772168	−	0.635419i	$-0.219172\pi$
$242$	18.8233	−	241.267i	0.0777823	−	0.996970i
$243$	−221.624	+	221.624i	−0.912032	+	0.912032i
$244$	−86.5139	−	45.7238i	−0.354565	−	0.187393i
$245$	10.5501	+	249.137i	0.0430615	+	1.01688i
$246$	−217.635	−	53.9742i	−0.884693	−	0.219407i
$247$	−36.2335	−	36.2335i	−0.146694	−	0.146694i
$248$	−285.552	+	16.0368i	−1.15142	+	0.0646645i
$249$	321.387			1.29071
$250$	196.070	−	155.102i	0.784279	−	0.620408i
$251$		−	166.067i		−	0.661622i	−0.943697	−	0.330811i	$-0.892678\pi$
$251$		−	166.067i		−	0.661622i	0.943697	−	0.330811i	$-0.107322\pi$
$252$	274.351	−	84.6265i	1.08870	−	0.335819i
$253$	−285.131	−	91.3604i	−1.12700	−	0.361108i
$254$	−5.09412	+	20.5405i	−0.0200556	+	0.0808682i
$255$	−26.3251	+	1.11478i	−0.103236	+	0.00437167i
$256$	−93.5261	+	238.304i	−0.365336	+	0.930876i
$257$	−337.029	+	337.029i	−1.31140	+	1.31140i	−0.391010	+	0.920386i	$0.627874\pi$
$257$	−337.029	+	337.029i	−1.31140	+	1.31140i	−0.920386	+	0.391010i	$0.872126\pi$
$258$	−468.802	+	282.481i	−1.81706	+	1.09489i
$259$			10.7682i			0.0415759i
$260$	−15.0041	−	42.2116i	−0.0577081	−	0.162352i
$261$		−	301.303i		−	1.15442i
$262$	44.0849	−	26.5637i	0.168263	−	0.101388i
$263$	−292.846	−	292.846i	−1.11348	−	1.11348i	−0.992676	−	0.120808i	$-0.961452\pi$
$263$	−292.846	−	292.846i	−1.11348	−	1.11348i	−0.120808	−	0.992676i	$-0.538548\pi$
$264$	−89.0442	+	343.026i	−0.337289	+	1.29934i
$265$	173.689	+	159.576i	0.655429	+	0.602174i
$266$	441.564	+	109.509i	1.66001	+	0.411689i
$267$	−305.069	−	305.069i	−1.14258	−	1.14258i
$268$	125.156	−	38.6056i	0.466998	−	0.144051i
$269$		−	249.221i		−	0.926472i	−0.886235	−	0.463236i	$-0.846688\pi$
$269$		−	249.221i		−	0.926472i	0.886235	−	0.463236i	$-0.153312\pi$
$270$	−70.3040	−	14.3082i	−0.260385	−	0.0529935i
$271$	−341.070			−1.25856			−0.629280	−	0.777178i	$-0.716650\pi$
$271$	−341.070			−1.25856			−0.629280	+	0.777178i	$0.716650\pi$
$272$	−3.89228	+	20.5715i	−0.0143099	+	0.0756305i
$273$	63.4256	+	63.4256i	0.232328	+	0.232328i
$274$	50.3672	−	203.091i	0.183822	−	0.741207i
$275$	−146.067	−	233.001i	−0.531153	−	0.847276i
$276$	387.657	+	204.882i	1.40456	+	0.742327i
$277$	115.235	+	115.235i	0.416012	+	0.416012i	0.883827	−	0.467815i	$-0.154959\pi$
$277$	115.235	+	115.235i	0.416012	+	0.416012i	−0.467815	+	0.883827i	$0.654959\pi$
$278$	111.261	+	184.647i	0.400219	+	0.664198i
$279$	258.063			0.924957
$280$	307.518	+	252.246i	1.09828	+	0.900878i
$281$		−	106.476i		−	0.378919i	−0.981889	−	0.189459i	$-0.939326\pi$
$281$		−	106.476i		−	0.378919i	0.981889	−	0.189459i	$-0.0606735\pi$
$282$	141.779	−	85.4301i	0.502761	−	0.302944i
$283$	241.292	+	241.292i	0.852623	+	0.852623i	0.990456	−	0.137833i	$-0.0440137\pi$
$283$	241.292	+	241.292i	0.852623	+	0.852623i	−0.137833	+	0.990456i	$0.544014\pi$
$284$	−447.961	−	236.754i	−1.57733	−	0.833640i
$285$	339.212	+	311.650i	1.19022	+	1.09351i
$286$	−47.9561	+	11.3409i	−0.167679	+	0.0396535i
$287$	195.738	+	195.738i	0.682014	+	0.682014i
$288$	96.3139	−	209.954i	0.334423	−	0.729008i
$289$		−	287.288i		−	0.994075i
$290$	348.082	−	230.358i	1.20028	−	0.794339i
$291$			311.431i			1.07021i
$292$	117.754	+	381.746i	0.403266	+	1.30735i
$293$	170.285	−	170.285i	0.581178	−	0.581178i	−0.354049	−	0.935227i	$-0.615195\pi$
$293$	170.285	−	170.285i	0.581178	−	0.581178i	0.935227	+	0.354049i	$0.115195\pi$
$294$	−389.880	−	96.6916i	−1.32612	−	0.328883i
$295$	370.161	−	15.6750i	1.25478	−	0.0531357i
$296$	6.45991	+	5.77291i	0.0218240	+	0.0195031i
$297$	−24.0812	+	75.1560i	−0.0810814	+	0.253050i
$298$	−49.9060	+	30.0714i	−0.167470	+	0.100911i
$299$			60.9693i			0.203911i
$300$	150.814	+	373.417i	0.502713	+	1.24472i
$301$	675.696			2.24484
$302$	−491.471	+	296.141i	−1.62739	+	0.980599i
$303$	440.011	+	440.011i	1.45218	+	1.45218i
$304$	302.421	−	206.189i	0.994807	−	0.678252i
$305$	5.17506	+	122.207i	0.0169674	+	0.400680i
$306$	4.54734	−	18.3358i	0.0148606	−	0.0599208i
$307$	−157.116	+	157.116i	−0.511777	+	0.511777i	−0.915071	−	0.403293i	$-0.867865\pi$
$307$	−157.116	+	157.116i	−0.511777	+	0.511777i	0.403293	+	0.915071i	$0.367865\pi$
$308$	312.715	−	305.983i	1.01531	−	0.993452i
$309$			608.216i			1.96834i
$310$	197.300	+	298.129i	0.636450	+	0.961707i
$311$		−	298.440i		−	0.959614i	−0.877374	−	0.479807i	$-0.840707\pi$
$311$		−	298.440i		−	0.959614i	0.877374	−	0.479807i	$-0.159293\pi$
$312$	72.0525	−	4.04651i	0.230937	−	0.0129696i
$313$	71.9061	+	71.9061i	0.229732	+	0.229732i	0.812581	−	0.582849i	$-0.198062\pi$
$313$	71.9061	+	71.9061i	0.229732	+	0.229732i	−0.582849	+	0.812581i	$0.698062\pi$
$314$	−51.8434	+	209.043i	−0.165106	+	0.665742i
$315$	−264.278	−	242.805i	−0.838978	−	0.770809i
$316$	21.9068	+	11.5780i	0.0693253	+	0.0366394i
$317$	138.594	−	138.594i	0.437206	−	0.437206i	−0.453864	−	0.891071i	$-0.649955\pi$
$317$	138.594	−	138.594i	0.437206	−	0.437206i	0.891071	+	0.453864i	$0.149955\pi$
$318$	−325.438	+	196.096i	−1.02339	+	0.616654i
$319$	−210.114	−	408.247i	−0.658665	−	1.27977i
$320$	316.187	−	49.2514i	0.988085	−	0.153910i
$321$		−	221.494i		−	0.690011i
$322$	−279.370	−	463.639i	−0.867609	−	1.43987i
$323$	21.1669	−	21.1669i	0.0655321	−	0.0655321i
$324$	175.431	−	331.932i	0.541452	−	1.02448i
$325$	−36.1077	+	42.8028i	−0.111101	+	0.131701i
$326$	−36.9497	+	148.989i	−0.113343	+	0.457020i
$327$	290.776	−	290.776i	0.889223	−	0.889223i
$328$	222.362	−	12.4880i	0.677932	−	0.0380731i
$329$	−204.349			−0.621122
$330$	426.404	−	120.098i	1.29213	−	0.363933i
$331$			223.320i			0.674682i	0.941383	+	0.337341i	$0.109527\pi$
$331$			223.320i			0.674682i	−0.941383	+	0.337341i	$0.890473\pi$
$332$	−305.033	+	94.0906i	−0.918773	+	0.283405i
$333$	−5.52760	−	5.52760i	−0.0165994	−	0.0165994i
$334$	−90.7947	+	366.102i	−0.271841	+	1.09612i
$335$	−120.560	−	110.765i	−0.359882	−	0.330641i
$336$	−529.379	+	360.926i	−1.57553	+	1.07419i
$337$	−393.070	−	393.070i	−1.16638	−	1.16638i	−0.983052	−	0.183329i	$-0.941313\pi$
$337$	−393.070	−	393.070i	−1.16638	−	1.16638i	−0.183329	−	0.983052i	$-0.558687\pi$
$338$	−169.265	−	280.910i	−0.500784	−	0.831095i
$339$	−368.043			−1.08567
$340$	24.6591	−	8.76509i	0.0725269	−	0.0257797i
$341$	349.660	−	179.961i	1.02539	−	0.527744i
$342$	−282.881	+	170.453i	−0.827138	+	0.498400i
$343$	6.13113	+	6.13113i	0.0178750	+	0.0178750i
$344$	362.246	−	405.355i	1.05304	−	1.17836i
$345$	−23.1888	−	547.595i	−0.0672138	−	1.58723i
$346$	85.3229	−	344.039i	0.246598	−	0.994333i
$347$	316.110	−	316.110i	0.910981	−	0.910981i	−0.0853686	−	0.996349i	$-0.527207\pi$
$347$	316.110	−	316.110i	0.910981	−	0.910981i	0.996349	+	0.0853686i	$0.0272068\pi$
$348$	198.192	+	642.518i	0.569516	+	1.84632i
$349$	−115.743			−0.331643			−0.165821	−	0.986156i	$-0.553028\pi$
$349$	−115.743			−0.331643			−0.165821	+	0.986156i	$0.553028\pi$
$350$	78.4508	−	490.943i	0.224145	−	1.40270i
$351$	16.0705			0.0457850
$352$	−15.9128	−	351.640i	−0.0452067	−	0.998978i
$353$	−162.819	−	162.819i	−0.461244	−	0.461244i	0.437819	−	0.899063i	$-0.355751\pi$
$353$	−162.819	−	162.819i	−0.461244	−	0.461244i	−0.899063	+	0.437819i	$0.855751\pi$
$354$	−143.662	+	579.274i	−0.405825	+	1.63637i
$355$	26.7960	+	632.779i	0.0754817	+	1.78248i
$356$	378.859	+	200.232i	1.06421	+	0.562450i
$357$	−37.0519	+	37.0519i	−0.103787	+	0.103787i
$358$	−260.560	+	157.003i	−0.727821	+	0.438555i
$359$			680.992i			1.89691i	0.316907	+	0.948457i	$0.397356\pi$
$359$			680.992i			1.89691i	−0.316907	+	0.948457i	$0.602644\pi$
$360$	−287.342	+	28.3728i	−0.798173	+	0.0788132i
$361$	−162.330			−0.449667
$362$	−131.760	+	79.3931i	−0.363977	+	0.219318i
$363$	−80.1534	−	480.656i	−0.220808	−	1.32412i
$364$	−78.7668	−	41.6294i	−0.216392	−	0.114366i
$365$	337.851	−	367.730i	0.925620	−	1.00748i
$366$	−191.245	−	47.4295i	−0.522528	−	0.129589i
$367$	−40.4515	−	40.4515i	−0.110222	−	0.110222i	0.649845	−	0.760067i	$-0.274834\pi$
$367$	−40.4515	−	40.4515i	−0.110222	−	0.110222i	−0.760067	+	0.649845i	$0.774834\pi$
$368$	−427.913	−	80.9644i	−1.16281	−	0.220012i
$369$	−200.956			−0.544595
$370$	2.15973	−	10.6119i	0.00583710	−	0.0286808i
$371$	469.062			1.26432
$372$	−550.311	+	169.749i	−1.47933	+	0.456315i
$373$	−58.9579	+	58.9579i	−0.158064	+	0.158064i	−0.781708	−	0.623644i	$-0.785651\pi$
$373$	−58.9579	+	58.9579i	−0.158064	+	0.158064i	0.623644	+	0.781708i	$0.285651\pi$
$374$	−6.62513	−	28.0149i	−0.0177142	−	0.0749063i
$375$	308.021	−	398.167i	0.821391	−	1.06178i
$376$	−109.553	+	122.591i	−0.291365	+	0.326039i
$377$	−66.1118	+	66.1118i	−0.175363	+	0.175363i
$378$	−122.208	+	73.6375i	−0.323301	+	0.194808i
$379$	−162.871			−0.429740			−0.214870	−	0.976643i	$-0.568933\pi$
$379$	−162.871			−0.429740			−0.214870	+	0.976643i	$0.568933\pi$
$380$	−413.191	−	196.482i	−1.08734	−	0.517059i
$381$			42.6136i			0.111847i
$382$	4.85673	+	8.06017i	0.0127140	+	0.0210999i
$383$	10.3018	−	10.3018i	0.0268975	−	0.0268975i	−0.693530	−	0.720428i	$-0.743946\pi$
$383$	10.3018	−	10.3018i	0.0268975	−	0.0268975i	0.720428	+	0.693530i	$0.243946\pi$
$384$	−67.2820	+	511.074i	−0.175213	+	1.33092i
$385$	−527.402	−	144.691i	−1.36987	−	0.375821i
$386$	−80.8117	+	325.849i	−0.209357	+	0.844168i
$387$	−346.854	+	346.854i	−0.896263	+	0.896263i
$388$	−91.1757	−	295.583i	−0.234989	−	0.761812i
$389$			181.531i			0.466661i	0.972397	+	0.233331i	$0.0749625\pi$
$389$			181.531i			0.466661i	−0.972397	+	0.233331i	$0.925038\pi$
$390$	−49.7840	−	75.2260i	−0.127651	−	0.192887i
$391$	−35.6170			−0.0910920
$392$	398.348	−	22.3715i	1.01619	−	0.0570702i
$393$	73.2841	−	73.2841i	0.186474	−	0.186474i
$394$	578.892	+	143.567i	1.46927	+	0.364384i
$395$	−1.31041	−	30.9450i	−0.00331750	−	0.0783418i
$396$	−3.45544	+	317.595i	−0.00872585	+	0.802007i
$397$	317.675	−	317.675i	0.800189	−	0.800189i	−0.182936	−	0.983125i	$-0.558560\pi$
$397$	317.675	−	317.675i	0.800189	−	0.800189i	0.983125	+	0.182936i	$0.0585601\pi$
$398$	147.269	−	88.7383i	0.370022	−	0.222960i
$399$	916.072			2.29592
$400$	−252.463	−	310.262i	−0.631157	−	0.775655i
$401$	−84.5433			−0.210831			−0.105416	−	0.994428i	$-0.533617\pi$
$401$	−84.5433			−0.210831			−0.105416	+	0.994428i	$0.533617\pi$
$402$	225.892	−	136.114i	0.561921	−	0.338591i
$403$	−56.6241	−	56.6241i	−0.140507	−	0.140507i
$404$	−546.440	−	288.801i	−1.35258	−	0.714855i
$405$	−468.879	+	19.8554i	−1.15773	+	0.0490257i
$406$	199.811	−	805.679i	0.492146	−	1.98443i
$407$	−11.3443	−	3.63488i	−0.0278729	−	0.00893091i
$408$	2.36389	+	42.0916i	0.00579385	+	0.103166i
$409$	579.741			1.41746			0.708730	−	0.705480i	$-0.249269\pi$
$409$	579.741			1.41746			0.708730	+	0.705480i	$0.249269\pi$
$410$	−153.639	−	232.156i	−0.374729	−	0.566233i
$411$		−	421.334i		−	1.02514i
$412$	−178.064	−	577.266i	−0.432194	−	1.40113i
$413$	520.993	−	520.993i	1.26148	−	1.26148i
$414$	381.407	+	94.5903i	0.921273	+	0.228479i
$415$	293.833	+	269.959i	0.708032	+	0.650503i
$416$	−67.2013	+	24.9350i	−0.161542	+	0.0599399i
$417$	306.947	+	306.947i	0.736084	+	0.736084i
$418$	−264.421	+	428.221i	−0.632586	+	1.02445i
$419$	114.028			0.272144			0.136072	−	0.990699i	$-0.456552\pi$
$419$	114.028			0.272144			0.136072	+	0.990699i	$0.456552\pi$
$420$	723.277	+	343.936i	1.72209	+	0.818896i
$421$	39.7800			0.0944893			0.0472447	−	0.998883i	$-0.484956\pi$
$421$	39.7800			0.0944893			0.0472447	+	0.998883i	$0.484956\pi$
$422$	529.535	−	319.076i	1.25482	−	0.756105i
$423$	104.898	−	104.898i	0.247986	−	0.247986i
$424$	251.468	−	281.394i	0.593085	−	0.663665i
$425$	−25.0045	−	21.0934i	−0.0588342	−	0.0496314i
$426$	−990.251	−	245.586i	−2.32453	−	0.576493i
$427$	172.004	+	172.004i	0.402819	+	0.402819i
$428$	64.8454	+	210.223i	0.151508	+	0.491174i
$429$	−88.2285	+	45.4090i	−0.205661	+	0.105848i
$430$	−665.889	−	135.521i	−1.54858	−	0.315166i
$431$	365.459			0.847933			0.423966	−	0.905678i	$-0.360637\pi$
$431$	365.459			0.847933			0.423966	+	0.905678i	$0.360637\pi$
$432$	−21.3409	+	112.791i	−0.0494003	+	0.261091i
$433$	−199.441	−	199.441i	−0.460602	−	0.460602i	0.438251	−	0.898853i	$-0.355598\pi$
$433$	−199.441	−	199.441i	−0.460602	−	0.460602i	−0.898853	+	0.438251i	$0.855598\pi$
$434$	690.057	+	171.137i	1.58999	+	0.394324i
$435$	568.639	−	618.928i	1.30722	−	1.42282i
$436$	−190.851	+	361.108i	−0.437731	+	0.828230i
$437$	440.297	+	440.297i	1.00755	+	1.00755i
$438$	415.170	+	689.011i	0.947877	+	1.57308i
$439$			522.498i			1.19020i	0.803652	+	0.595100i	$0.202888\pi$
$439$			522.498i			1.19020i	−0.803652	+	0.595100i	$0.797112\pi$
$440$	−369.546	+	238.822i	−0.839876	+	0.542778i
$441$	−360.001			−0.816328
$442$	−5.02101	+	3.02546i	−0.0113597	+	0.00684492i
$443$	−389.894	+	389.894i	−0.880122	+	0.880122i	−0.993547	−	0.113424i	$-0.963818\pi$
$443$	−389.894	+	389.894i	−0.880122	+	0.880122i	0.113424	+	0.993547i	$0.463818\pi$
$444$	15.4234	+	8.15147i	0.0347374	+	0.0183592i
$445$	−22.6625	−	535.167i	−0.0509269	−	1.20262i
$446$	−41.8783	+	168.862i	−0.0938976	+	0.378614i
$447$	−82.9609	+	82.9609i	−0.185595	+	0.185595i
$448$	396.775	−	497.544i	0.885658	−	1.11059i
$449$		−	740.798i		−	1.64988i	−0.565218	−	0.824942i	$-0.691208\pi$
$449$		−	740.798i		−	1.64988i	0.565218	−	0.824942i	$-0.308792\pi$
$450$	211.744	+	292.286i	0.470542	+	0.649524i
$451$	−272.283	+	140.137i	−0.603731	+	0.310725i
$452$	349.315	−	107.750i	0.772821	−	0.238385i
$453$	−816.994	+	816.994i	−1.80352	+	1.80352i
$454$	−14.0799	+	56.7731i	−0.0310131	+	0.125051i
$455$	4.71165	+	111.264i	0.0103553	+	0.244536i
$456$	491.114	−	549.559i	1.07700	−	1.20517i
$457$	−600.921	−	600.921i	−1.31493	−	1.31493i	−0.917737	−	0.397188i	$-0.869986\pi$
$457$	−600.921	−	600.921i	−1.31493	−	1.31493i	−0.397188	−	0.917737i	$-0.630014\pi$
$458$	−81.0171	−	134.455i	−0.176893	−	0.293570i
$459$			9.38807i			0.0204533i
$460$	182.325	+	512.941i	0.396359	+	1.11509i
$461$			845.625i			1.83433i	0.398510	+	0.917164i	$0.369527\pi$
$461$			845.625i			1.83433i	−0.398510	+	0.917164i	$0.630473\pi$
$462$	462.861	−	749.587i	1.00186	−	1.62248i
$463$	210.135	−	210.135i	0.453856	−	0.453856i	−0.442776	−	0.896632i	$-0.646006\pi$
$463$	210.135	−	210.135i	0.453856	−	0.453856i	0.896632	+	0.442776i	$0.146006\pi$
$464$	−376.213	−	551.800i	−0.810803	−	1.18922i
$465$	530.106	+	487.033i	1.14001	+	1.04738i
$466$	48.0010	−	193.549i	0.103006	−	0.415342i
$467$	107.813	+	107.813i	0.230863	+	0.230863i	0.813053	−	0.582190i	$-0.197804\pi$
$467$	107.813	+	107.813i	0.230863	+	0.230863i	−0.582190	+	0.813053i	$0.697804\pi$
$468$	61.8027	−	19.0637i	0.132057	−	0.0407344i
$469$	−325.584			−0.694209
$470$	201.383	+	40.9854i	0.428475	+	0.0872030i
$471$			433.682i			0.920770i
$472$	−33.2390	−	591.856i	−0.0704217	−	1.25393i
$473$	−228.086	+	711.845i	−0.482212	+	1.50496i
$474$	48.4266	+	12.0100i	0.102166	+	0.0253375i
$475$	48.3501	+	569.863i	0.101790	+	1.19971i
$476$	24.3190	−	46.0140i	0.0510904	−	0.0966680i
$477$	−240.783	+	240.783i	−0.504785	+	0.504785i
$478$	19.1260	+	31.7413i	0.0400126	+	0.0664043i
$479$			480.160i			1.00242i	0.865325	+	0.501210i	$0.167112\pi$
$479$			480.160i			1.00242i	−0.865325	+	0.501210i	$0.832888\pi$
$480$	594.085	−	249.513i	1.23768	−	0.519818i
$481$			2.42573i			0.00504310i
$482$	316.138	+	524.658i	0.655888	+	1.08850i
$483$	−770.727	−	770.727i	−1.59571	−	1.59571i
$484$	216.794	+	432.731i	0.447921	+	0.894073i
$485$	−261.596	+	284.731i	−0.539372	+	0.587073i
$486$	150.889	−	608.415i	0.310472	−	1.25188i
$487$	−638.632	−	638.632i	−1.31136	−	1.31136i	−0.920414	−	0.390946i	$-0.872148\pi$
$487$	−638.632	−	638.632i	−1.31136	−	1.31136i	−0.390946	−	0.920414i	$-0.627852\pi$
$488$	195.399	−	10.9737i	0.400408	−	0.0224872i
$489$			309.093i			0.632092i
$490$	−275.235	−	415.893i	−0.561704	−	0.848762i
$491$	−580.338			−1.18195			−0.590976	−	0.806690i	$-0.701257\pi$
$491$	−580.338			−1.18195			−0.590976	+	0.806690i	$0.701257\pi$
$492$	428.531	−	132.185i	0.870999	−	0.268669i
$493$	−38.6212	−	38.6212i	−0.0783391	−	0.0783391i
$494$	99.4704	+	24.6690i	0.201357	+	0.0499373i
$495$	345.004	−	196.456i	0.696977	−	0.396881i
$496$	472.611	−	322.223i	0.952845	−	0.649642i
$497$	890.621	+	890.621i	1.79199	+	1.79199i
$498$	−550.551	+	331.740i	−1.10552	+	0.666144i
$499$	−430.230			−0.862184			−0.431092	−	0.902308i	$-0.641872\pi$
$499$	−430.230			−0.862184			−0.431092	+	0.902308i	$0.641872\pi$
$500$	−175.779	+	468.083i	−0.351557	+	0.936166i
$501$			759.520i			1.51601i
$502$	171.417	+	284.481i	0.341468	+	0.566695i
$503$	−154.450	−	154.450i	−0.307059	−	0.307059i	0.536709	−	0.843767i	$-0.319667\pi$
$503$	−154.450	−	154.450i	−0.307059	−	0.307059i	−0.843767	+	0.536709i	$0.819667\pi$
$504$	−382.624	+	428.158i	−0.759175	+	0.849520i
$505$	32.6868	+	771.888i	0.0647263	+	1.52849i
$506$	582.746	−	137.811i	1.15167	−	0.272354i
$507$	−466.969	−	466.969i	−0.921044	−	0.921044i
$508$	−12.4757	−	40.4451i	−0.0245585	−	0.0796164i
$509$			376.470i			0.739626i	0.929106	+	0.369813i	$0.120578\pi$
$509$			376.470i			0.739626i	−0.929106	+	0.369813i	$0.879422\pi$
$510$	43.9455	−	29.0828i	0.0861676	−	0.0570251i
$511$		−	993.089i		−	1.94342i
$512$	−85.7660	−	504.765i	−0.167512	−	0.985870i
$513$	116.055	−	116.055i	0.226229	−	0.226229i
$514$	229.461	−	925.233i	0.446422	−	1.80006i
$515$	−510.890	+	556.072i	−0.992019	+	1.07975i
$516$	511.500	−	967.808i	0.991279	−	1.87560i
$517$	68.9796	−	215.281i	0.133423	−	0.416405i
$518$	−11.1151	−	18.4464i	−0.0214576	−	0.0356108i
$519$		−	713.747i		−	1.37523i
$520$	69.2742	+	56.8231i	0.133220	+	0.109275i
$521$	−418.288			−0.802856			−0.401428	−	0.915891i	$-0.631486\pi$
$521$	−418.288			−0.802856			−0.401428	+	0.915891i	$0.631486\pi$
$522$	311.009	+	516.146i	0.595802	+	0.988786i
$523$	133.914	+	133.914i	0.256050	+	0.256050i	0.823446	−	0.567395i	$-0.192049\pi$
$523$	133.914	+	133.914i	0.256050	+	0.256050i	−0.567395	+	0.823446i	$0.692049\pi$
$524$	−48.1000	+	91.0100i	−0.0917939	+	0.173683i
$525$	−84.6353	−	997.526i	−0.161210	−	1.90005i
$526$	803.940	+	199.380i	1.52840	+	0.379049i
$527$	33.0787	−	33.0787i	0.0627679	−	0.0627679i
$528$	−201.540	−	679.534i	−0.381704	−	1.28700i
$529$		−	211.878i		−	0.400526i
$530$	−462.254	−	94.0778i	−0.872177	−	0.177505i
$531$			534.880i			1.00731i
$532$	−869.457	+	268.193i	−1.63432	+	0.504122i
$533$	44.0937	+	44.0937i	0.0827273	+	0.0827273i
$534$	837.495	+	207.702i	1.56834	+	0.388955i
$535$	186.050	−	202.504i	0.347758	−	0.378513i
$536$	−174.548	+	195.320i	−0.325650	+	0.364404i
$537$	−433.140	+	433.140i	−0.806592	+	0.806592i
$538$	257.249	+	426.927i	0.478158	+	0.793545i
$539$	−487.779	+	251.047i	−0.904971	+	0.465765i
$540$	135.203	−	48.0580i	0.250376	−	0.0889963i
$541$			235.939i			0.436116i	0.975936	+	0.218058i	$0.0699721\pi$
$541$			235.939i			0.436116i	−0.975936	+	0.218058i	$0.930028\pi$
$542$	584.269	−	352.057i	1.07799	−	0.649552i
$543$	−219.030	+	219.030i	−0.403370	+	0.403370i
$544$	−14.5665	−	39.2576i	−0.0267767	−	0.0721648i
$545$	510.093	−	21.6007i	0.935950	−	0.0396342i
$546$	−174.120	−	43.1823i	−0.318901	−	0.0790885i
$547$	439.184	−	439.184i	0.802897	−	0.802897i	−0.180651	−	0.983547i	$-0.557820\pi$
$547$	439.184	−	439.184i	0.802897	−	0.802897i	0.983547	+	0.180651i	$0.0578203\pi$
$548$	123.352	+	399.894i	0.225094	+	0.729734i
$549$	−176.589			−0.321655
$550$	490.727	+	248.370i	0.892230	+	0.451581i
$551$			954.870i			1.73298i
$552$	−875.558	+	49.1719i	−1.58616	+	0.0890795i
$553$	−43.5543	−	43.5543i	−0.0787601	−	0.0787601i
$554$	−316.351	−	78.4562i	−0.571031	−	0.141618i
$555$	−0.922591	−	21.7867i	−0.00166233	−	0.0392553i
$556$	−381.191	−	201.465i	−0.685595	−	0.362346i
$557$	129.675	+	129.675i	0.232809	+	0.232809i	0.813864	−	0.581055i	$-0.197360\pi$
$557$	129.675	+	129.675i	0.232809	+	0.232809i	−0.581055	+	0.813864i	$0.697360\pi$
$558$	−442.074	+	266.376i	−0.792248	+	0.477377i
$559$	152.213			0.272295
$560$	−787.165	−	114.685i	−1.40565	−	0.204795i
$561$	−26.5270	−	51.5413i	−0.0472852	−	0.0918740i
$562$	109.906	+	182.399i	0.195563	+	0.324553i
$563$	122.317	+	122.317i	0.217259	+	0.217259i	0.807342	−	0.590084i	$-0.200905\pi$
$563$	122.317	+	122.317i	0.217259	+	0.217259i	−0.590084	+	0.807342i	$0.700905\pi$
$564$	−154.692	+	292.692i	−0.274276	+	0.518957i
$565$	−336.490	−	309.149i	−0.595557	−	0.547167i
$566$	−662.410	−	164.280i	−1.17034	−	0.290248i
$567$	−659.935	+	659.935i	−1.16391	+	1.16391i
$568$	1011.76	−	56.8211i	1.78127	−	0.100037i
$569$	−664.396			−1.16766			−0.583828	−	0.811877i	$-0.698446\pi$
$569$	−664.396			−1.16766			−0.583828	+	0.811877i	$0.698446\pi$
$570$	−902.776	−	183.733i	−1.58382	−	0.322338i
$571$	−112.058			−0.196249			−0.0981244	−	0.995174i	$-0.531284\pi$
$571$	−112.058			−0.196249			−0.0981244	+	0.995174i	$0.531284\pi$
$572$	70.4448	−	68.9284i	0.123155	−	0.120504i
$573$	13.3988	+	13.3988i	0.0233835	+	0.0233835i
$574$	−537.353	−	133.265i	−0.936154	−	0.232170i
$575$	438.769	−	520.126i	0.763076	−	0.904567i
$576$	51.7275	+	459.078i	0.0898046	+	0.797011i
$577$	−596.807	+	596.807i	−1.03433	+	1.03433i	−0.0349381	+	0.999389i	$0.511123\pi$
$577$	−596.807	+	596.807i	−1.03433	+	1.03433i	−0.999389	+	0.0349381i	$0.988877\pi$
$578$	296.542	+	492.138i	0.513049	+	0.851450i
$579$			676.009i			1.16755i
$580$	−358.503	+	753.910i	−0.618108	+	1.29984i
$581$	793.523			1.36579
$582$	−321.463	−	533.496i	−0.552342	−	0.916659i
$583$	−158.336	+	494.156i	−0.271588	+	0.847609i
$584$	−595.762	−	532.403i	−1.02014	−	0.911649i
$585$	−59.5336	−	54.6963i	−0.101767	−	0.0934980i
$586$	−115.936	+	467.477i	−0.197843	+	0.797743i
$587$	175.036	+	175.036i	0.298188	+	0.298188i	0.840304	−	0.542116i	$-0.182377\pi$
$587$	175.036	+	175.036i	0.298188	+	0.298188i	−0.542116	+	0.840304i	$0.682377\pi$
$588$	767.690	−	236.802i	1.30559	−	0.402724i
$589$	−817.837			−1.38852
$590$	−617.924	+	408.938i	−1.04733	+	0.693114i
$591$	1200.98			2.03211
$592$	−17.0250	−	3.22126i	−0.0287585	−	0.00544132i
$593$	−20.0943	+	20.0943i	−0.0338858	+	0.0338858i	−0.723847	−	0.689961i	$-0.757628\pi$
$593$	−20.0943	+	20.0943i	−0.0338858	+	0.0338858i	0.689961	+	0.723847i	$0.257628\pi$
$594$	−36.3248	−	153.603i	−0.0611529	−	0.258590i
$595$	−64.9982	+	2.75245i	−0.109241	+	0.00462596i
$596$	54.4514	−	103.027i	0.0913614	−	0.172865i
$597$	244.811	−	244.811i	0.410069	−	0.410069i
$598$	−62.9333	−	104.443i	−0.105240	−	0.174654i
$599$	816.363			1.36288			0.681438	−	0.731875i	$-0.261355\pi$
$599$	816.363			1.36288			0.681438	+	0.731875i	$0.261355\pi$
$600$	−643.797	−	484.009i	−1.07300	−	0.806681i
$601$		−	322.762i		−	0.537041i	−0.963274	−	0.268521i	$-0.913465\pi$
$601$		−	322.762i		−	0.537041i	0.963274	−	0.268521i	$-0.0865348\pi$
$602$	−1157.50	+	697.463i	−1.92276	+	1.15858i
$603$	167.131	−	167.131i	0.277167	−	0.277167i
$604$	536.234	−	1014.61i	0.887804	−	1.67981i
$605$	330.460	−	506.775i	0.546215	−	0.837645i
$606$	−1207.95	−	299.575i	−1.99331	−	0.494348i
$607$	177.668	−	177.668i	0.292698	−	0.292698i	−0.545447	−	0.838145i	$-0.683640\pi$
$607$	177.668	−	177.668i	0.292698	−	0.292698i	0.838145	+	0.545447i	$0.183640\pi$
$608$	−305.232	+	665.374i	−0.502026	+	1.09437i
$609$		−	1671.47i		−	2.74461i
$610$	−135.009	−	204.005i	−0.221327	−	0.334435i
$611$	−46.0334			−0.0753411
$612$	11.1366	+	36.1039i	0.0181971	+	0.0589933i
$613$	−235.040	+	235.040i	−0.383425	+	0.383425i	−0.872335	−	0.488909i	$-0.837395\pi$
$613$	−235.040	+	235.040i	−0.383425	+	0.383425i	0.488909	+	0.872335i	$0.337395\pi$
$614$	106.970	−	431.324i	0.174218	−	0.702482i
$615$	−412.798	−	379.257i	−0.671216	−	0.616678i
$616$	−219.855	+	846.952i	−0.356908	+	1.37492i
$617$	191.061	−	191.061i	0.309661	−	0.309661i	−0.535117	−	0.844778i	$-0.679733\pi$
$617$	191.061	−	191.061i	0.309661	−	0.309661i	0.844778	+	0.535117i	$0.179733\pi$
$618$	−627.809	−	1041.90i	−1.01587	−	1.68593i
$619$	−638.728			−1.03187			−0.515936	−	0.856627i	$-0.672556\pi$
$619$	−638.728			−1.03187			−0.515936	+	0.856627i	$0.672556\pi$
$620$	−645.717	−	307.054i	−1.04148	−	0.495249i
$621$	−195.284			−0.314467
$622$	308.054	+	511.242i	0.495263	+	0.821933i
$623$	−753.234	−	753.234i	−1.20904	−	1.20904i
$624$	−119.253	+	81.3054i	−0.191110	+	0.130297i
$625$	616.066	−	105.298i	0.985705	−	0.168478i
$626$	−197.401	−	48.9562i	−0.315337	−	0.0782048i
$627$	−309.227	+	965.081i	−0.493185	+	1.53920i
$628$	−126.967	−	411.614i	−0.202176	−	0.655436i
$629$	−1.41706			−0.00225288
$630$	703.348	+	143.145i	1.11643	+	0.227215i
$631$			615.225i			0.975000i	0.873123	+	0.487500i	$0.162091\pi$
$631$			615.225i			0.975000i	−0.873123	+	0.487500i	$0.837909\pi$
$632$	−49.4784	+	2.77874i	−0.0782887	+	0.00439674i
$633$	880.269	−	880.269i	1.39063	−	1.39063i
$634$	−94.3599	+	380.478i	−0.148833	+	0.600123i
$635$	−35.7946	+	38.9602i	−0.0563694	+	0.0613546i
$636$	355.079	−	671.844i	0.558300	−	1.05636i
$637$	78.9913	+	78.9913i	0.124005	+	0.124005i
$638$	781.334	+	482.464i	1.22466	+	0.756213i
$639$	−914.361			−1.43093
$640$	−490.806	+	410.743i	−0.766884	+	0.641785i
$641$	−1006.58			−1.57033			−0.785163	−	0.619289i	$-0.787421\pi$
$641$	−1006.58			−1.57033			−0.785163	+	0.619289i	$0.787421\pi$
$642$	228.629	+	379.429i	0.356119	+	0.591011i
$643$	311.119	−	311.119i	0.483856	−	0.483856i	−0.422505	−	0.906361i	$-0.638849\pi$
$643$	311.119	−	311.119i	0.483856	−	0.483856i	0.906361	+	0.422505i	$0.138849\pi$
$644$	957.149	+	505.866i	1.48626	+	0.785507i
$645$	−1367.10	+	57.8920i	−2.11954	+	0.0897551i
$646$	−14.4111	+	58.1086i	−0.0223083	+	0.0899513i
$647$	154.257	+	154.257i	0.238419	+	0.238419i	0.816195	−	0.577776i	$-0.196079\pi$
$647$	154.257	+	154.257i	0.238419	+	0.238419i	−0.577776	+	0.816195i	$0.696079\pi$
$648$	42.1035	+	749.697i	0.0649745	+	1.15694i
$649$	373.000	+	724.730i	0.574730	+	1.11669i
$650$	17.6725	−	110.594i	0.0271885	−	0.170145i
$651$	1431.60			2.19908
$652$	−90.4914	−	293.364i	−0.138790	−	0.449946i
$653$	179.979	+	179.979i	0.275619	+	0.275619i	0.831357	−	0.555738i	$-0.187564\pi$
$653$	179.979	+	179.979i	0.275619	+	0.275619i	−0.555738	+	0.831357i	$0.687564\pi$
$654$	−197.970	+	798.256i	−0.302707	+	1.22057i
$655$	128.558	−	5.44401i	0.196272	−	0.00831146i
$656$	−368.026	+	250.917i	−0.561015	+	0.382496i
$657$	509.780	+	509.780i	0.775921	+	0.775921i
$658$	350.060	−	210.932i	0.532006	−	0.320565i
$659$		−	981.949i		−	1.49006i	−0.667032	−	0.745029i	$-0.732435\pi$
$659$		−	981.949i		−	1.49006i	0.667032	−	0.745029i	$-0.267565\pi$
$660$	−606.484	+	645.873i	−0.918915	+	0.978596i
$661$	−719.192			−1.08804			−0.544018	−	0.839074i	$-0.683098\pi$
$661$	−719.192			−1.08804			−0.544018	+	0.839074i	$0.683098\pi$
$662$	−230.514	−	382.557i	−0.348208	−	0.577881i
$663$	−8.34663	+	8.34663i	−0.0125892	+	0.0125892i
$664$	425.414	−	476.041i	0.640684	−	0.716929i
$665$	837.534	+	769.482i	1.25945	+	1.15712i
$666$	15.1747	+	3.76338i	0.0227849	+	0.00565073i
$667$	803.369	−	803.369i	1.20445	−	1.20445i
$668$	−222.360	−	720.871i	−0.332875	−	1.07915i
$669$			350.322i			0.523651i
$670$	320.859	+	65.3010i	0.478893	+	0.0974642i
$671$	−239.267	+	123.145i	−0.356583	+	0.183524i
$672$	534.299	−	1164.72i	0.795087	−	1.73321i
$673$	−121.985	+	121.985i	−0.181256	+	0.181256i	−0.791903	−	0.610647i	$-0.790909\pi$
$673$	−121.985	+	121.985i	−0.181256	+	0.181256i	0.610647	+	0.791903i	$0.290909\pi$
$674$	1079.08	+	267.616i	1.60101	+	0.397056i
$675$	−137.097	−	115.652i	−0.203107	−	0.171337i
$676$	579.919	+	306.495i	0.857868	+	0.453395i
$677$	−376.043	−	376.043i	−0.555456	−	0.555456i	0.372555	−	0.928010i	$-0.378482\pi$
$677$	−376.043	−	376.043i	−0.555456	−	0.555456i	−0.928010	+	0.372555i	$0.878482\pi$
$678$	630.476	−	379.899i	0.929906	−	0.560324i
$679$			768.941i			1.13246i
$680$	−33.1949	+	40.4685i	−0.0488160	+	0.0595126i
$681$			117.782i			0.172955i
$682$	−413.226	+	669.205i	−0.605903	+	0.981239i
$683$	836.119	−	836.119i	1.22419	−	1.22419i	0.258056	−	0.966130i	$-0.416918\pi$
$683$	836.119	−	836.119i	1.22419	−	1.22419i	0.966130	−	0.258056i	$-0.0830818\pi$
$684$	308.645	−	583.987i	0.451236	−	0.853783i
$685$	353.912	−	385.212i	0.516660	−	0.562353i
$686$	−16.8316	−	4.17429i	−0.0245358	−	0.00608497i
$687$	−223.510	−	223.510i	−0.325343	−	0.325343i
$688$	−202.132	+	1068.31i	−0.293797	+	1.55277i
$689$	105.665			0.153360
$690$	604.959	+	914.121i	0.876752	+	1.32481i
$691$		−	581.249i		−	0.841170i	−0.907253	−	0.420585i	$-0.861825\pi$
$691$		−	581.249i		−	0.841170i	0.907253	−	0.420585i	$-0.138175\pi$
$692$	208.959	+	677.427i	0.301965	+	0.978941i
$693$	240.917	−	751.889i	0.347644	−	1.08498i
$694$	−215.219	+	867.806i	−0.310114	+	1.25044i
$695$	22.8019	+	538.461i	0.0328085	+	0.774763i
$696$	−1002.73	−	896.089i	−1.44070	−	1.28748i
$697$	−25.7586	+	25.7586i	−0.0369564	+	0.0369564i
$698$	198.274	−	119.472i	0.284060	−	0.171163i
$699$		−	401.540i		−	0.574449i
$700$	372.369	+	921.988i	0.531955	+	1.31713i
$701$		−	235.942i		−	0.336579i	−0.985738	−	0.168290i	$-0.946176\pi$
$701$		−	235.942i		−	0.336579i	0.985738	−	0.168290i	$-0.0538244\pi$
$702$	−27.5296	+	16.5882i	−0.0392160	+	0.0236299i
$703$	17.5177	+	17.5177i	0.0249185	+	0.0249185i
$704$	390.227	+	585.951i	0.554300	+	0.832317i
$705$	413.449	−	17.5081i	0.586453	−	0.0248342i
$706$	446.981	+	110.853i	0.633117	+	0.157015i
$707$	1086.41	+	1086.41i	1.53665	+	1.53665i
$708$	−351.834	−	1140.61i	−0.496941	−	1.61104i
$709$		−	194.649i		−	0.274540i	−0.990534	−	0.137270i	$-0.956167\pi$
$709$		−	194.649i		−	0.274540i	0.990534	−	0.137270i	$-0.0438328\pi$
$710$	−699.066	−	1056.32i	−0.984601	−	1.48778i
$711$	44.7153			0.0628907
$712$	−855.686	+	48.0559i	−1.20181	+	0.0674942i
$713$	688.078	+	688.078i	0.965046	+	0.965046i
$714$	25.2262	−	101.717i	0.0353309	−	0.142461i
$715$	−118.807	−	32.5943i	−0.166164	−	0.0455865i
$716$	284.291	−	537.907i	0.397055	−	0.751267i
$717$	52.7649	+	52.7649i	0.0735912	+	0.0735912i
$718$	−702.929	−	1166.57i	−0.979010	−	1.62475i
$719$	−763.366			−1.06171			−0.530853	−	0.847464i	$-0.678128\pi$
$719$	−763.366			−1.06171			−0.530853	+	0.847464i	$0.678128\pi$
$720$	462.945	−	345.203i	0.642979	−	0.479448i
$721$			1501.72i			2.08283i
$722$	278.079	−	167.559i	0.385150	−	0.232076i
$723$	872.162	+	872.162i	1.20631	+	1.20631i
$724$	143.760	−	272.009i	0.198564	−	0.375702i
$725$	1039.77	−	88.2199i	1.43417	−	0.121683i
$726$	633.447	+	740.652i	0.872516	+	1.02018i
$727$	349.567	+	349.567i	0.480834	+	0.480834i	0.905398	−	0.424564i	$-0.139573\pi$
$727$	349.567	+	349.567i	0.480834	+	0.480834i	−0.424564	+	0.905398i	$0.639573\pi$
$728$	177.902	−	9.99108i	0.244371	−	0.0137240i
$729$		−	417.486i		−	0.572683i
$730$	−199.180	+	978.675i	−0.272849	+	1.34065i
$731$			88.9198i			0.121641i
$732$	376.570	−	116.157i	0.514439	−	0.158684i
$733$	840.241	−	840.241i	1.14630	−	1.14630i	0.159031	−	0.987274i	$-0.449163\pi$
$733$	840.241	−	840.241i	1.14630	−	1.14630i	0.987274	−	0.159031i	$-0.0508371\pi$
$734$	111.050	+	27.5408i	0.151294	+	0.0375215i
$735$	−739.503	−	679.417i	−1.00613	−	0.924377i
$736$	816.609	−	303.002i	1.10952	−	0.411687i
$737$	109.903	−	343.002i	0.149123	−	0.465404i
$738$	344.247	−	207.429i	0.466459	−	0.281069i
$739$		−	684.775i		−	0.926624i	−0.886195	−	0.463312i	$-0.846661\pi$
$739$		−	684.775i		−	0.926624i	0.886195	−	0.463312i	$-0.153339\pi$
$740$	7.25401	+	20.4080i	0.00980272	+	0.0275783i
$741$	206.362			0.278492
$742$	−803.526	+	484.172i	−1.08292	+	0.652523i
$743$	243.103	+	243.103i	0.327191	+	0.327191i	0.851518	−	0.524326i	$-0.175683\pi$
$743$	243.103	+	243.103i	0.327191	+	0.327191i	−0.524326	+	0.851518i	$0.675683\pi$
$744$	767.492	−	858.827i	1.03157	−	1.15434i
$745$	−145.534	+	6.16286i	−0.195348	+	0.00827229i
$746$	40.1406	−	161.855i	0.0538077	−	0.216964i
$747$	−407.337	+	407.337i	−0.545298	+	0.545298i
$748$	40.2666	+	41.1524i	0.0538323	+	0.0550166i
$749$		−	546.881i		−	0.730148i
$750$	−116.663	+	1000.02i	−0.155550	+	1.33336i
$751$		−	309.826i		−	0.412552i	−0.978494	−	0.206276i	$-0.933866\pi$
$751$		−	309.826i		−	0.412552i	0.978494	−	0.206276i	$-0.0661344\pi$
$752$	61.1303	−	323.086i	0.0812903	−	0.429636i
$753$	472.905	+	472.905i	0.628028	+	0.628028i
$754$	45.0112	−	181.494i	0.0596966	−	0.240709i
$755$	−1433.21	+	60.6914i	−1.89829	+	0.0803860i
$756$	133.338	−	252.289i	0.176373	−	0.333716i
$757$	−863.112	+	863.112i	−1.14017	+	1.14017i	−0.151756	+	0.988418i	$0.548493\pi$
$757$	−863.112	+	863.112i	−1.14017	+	1.14017i	−0.988418	+	0.151756i	$0.951507\pi$
$758$	279.007	−	168.118i	0.368083	−	0.221792i
$759$	1072.12	−	551.795i	1.41255	−	0.727002i
$760$	910.627	−	89.9172i	1.19819	−	0.118312i
$761$		−	1464.71i		−	1.92472i	−0.271775	−	0.962361i	$-0.587611\pi$
$761$		−	1464.71i		−	1.92472i	0.271775	−	0.962361i	$-0.412389\pi$
$762$	−43.9863	−	72.9991i	−0.0577248	−	0.0957993i
$763$	717.943	−	717.943i	0.940947	−	0.940947i
$764$	−16.6396	−	8.79427i	−0.0217796	−	0.0115108i
$765$	31.9525	−	34.7783i	0.0417679	−	0.0454618i
$766$	−7.01380	+	28.2810i	−0.00915639	+	0.0369204i
$767$	117.363	−	117.363i	0.153016	−	0.153016i
$768$	−412.281	−	944.944i	−0.536824	−	1.23040i
$769$	−764.250			−0.993824			−0.496912	−	0.867801i	$-0.665533\pi$
$769$	−764.250			−0.993824			−0.496912	+	0.867801i	$0.665533\pi$
$770$	1052.82	−	296.528i	1.36729	−	0.385102i
$771$		−	1919.50i		−	2.48962i
$772$	−197.911	−	641.610i	−0.256362	−	0.831101i

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+(-1.71305 + 1.03221i) q^{2} +(-2.84767 + 2.84767i) q^{3} +(1.86907 - 3.53646i) q^{4} +(-4.99552 + 0.211543i) q^{5} +(1.93880 - 7.81761i) q^{6} +(-7.03107 + 7.03107i) q^{7} +(0.448578 + 7.98741i) q^{8} -7.21849i q^{9} +(8.33922 - 5.51883i) q^{10} +(-5.03383 - 9.78062i) q^{11} +(4.74819 + 15.3932i) q^{12} +(-1.58388 + 1.58388i) q^{13} +(4.78700 - 19.3021i) q^{14} +(13.6232 - 14.8280i) q^{15} +(-9.01315 - 13.2198i) q^{16} +(-0.925270 - 0.925270i) q^{17} +(7.45103 + 12.3656i) q^{18} +22.8764i q^{19} +(-8.58887 + 18.0619i) q^{20} -40.0444i q^{21} +(18.7189 + 11.5587i) q^{22} +(19.2468 - 19.2468i) q^{23} +(-24.0230 - 21.4681i) q^{24} +(24.9105 - 2.11354i) q^{25} +(1.07836 - 4.34817i) q^{26} +(-5.07315 - 5.07315i) q^{27} +(11.7236 + 38.0067i) q^{28} +41.7404 q^{29} +(-8.03154 + 39.4632i) q^{30} +35.7503i q^{31} +(29.0856 + 13.3427i) q^{32} +(42.1867 + 13.5173i) q^{33} +(2.54011 + 0.629956i) q^{34} +(33.6365 - 36.6113i) q^{35} +(-25.5279 - 13.4919i) q^{36} +(0.765756 - 0.765756i) q^{37} +(-23.6133 - 39.1884i) q^{38} -9.02075i q^{39} +(-3.93057 - 39.8064i) q^{40} -27.8390i q^{41} +(41.3344 + 68.5980i) q^{42} +(-48.0507 - 48.0507i) q^{43} +(-43.9974 - 0.478692i) q^{44} +(1.52702 + 36.0601i) q^{45} +(-13.1039 + 52.8375i) q^{46} +(14.5319 + 14.5319i) q^{47} +(63.3122 + 11.9792i) q^{48} -49.8720i q^{49} +(-40.4913 + 29.3335i) q^{50} +5.26974 q^{51} +(2.64095 + 8.56172i) q^{52} +(-33.3564 - 33.3564i) q^{53} +(13.9271 + 3.45398i) q^{54} +(27.2157 + 47.7944i) q^{55} +(-59.3141 - 53.0061i) q^{56} +(-65.1445 - 65.1445i) q^{57} +(-71.5033 + 43.0850i) q^{58} -74.0986 q^{59} +(-26.9760 - 75.8926i) q^{60} -24.4634i q^{61} +(-36.9019 - 61.2419i) q^{62} +(50.7538 + 50.7538i) q^{63} +(-63.5976 + 7.16596i) q^{64} +(7.57725 - 8.24737i) q^{65} +(-86.2207 + 20.3899i) q^{66} +(23.1532 + 23.1532i) q^{67} +(-5.00158 + 1.54279i) q^{68} +109.617i q^{69} +(-19.8303 + 97.4369i) q^{70} -126.669i q^{71} +(57.6571 - 3.23806i) q^{72} +(-70.6214 + 70.6214i) q^{73} +(-0.521353 + 2.10220i) q^{74} +(-64.9183 + 76.9556i) q^{75} +(80.9016 + 42.7576i) q^{76} +(104.162 + 33.3750i) q^{77} +(9.31134 + 15.4530i) q^{78} +6.19455i q^{79} +(47.8220 + 64.1331i) q^{80} +93.8598 q^{81} +(28.7358 + 47.6896i) q^{82} +(-56.4297 - 56.4297i) q^{83} +(-141.616 - 74.8458i) q^{84} +(4.81794 + 4.42648i) q^{85} +(131.912 + 32.7146i) q^{86} +(-118.863 + 118.863i) q^{87} +(75.8638 - 44.5947i) q^{88} +107.129i q^{89} +(-39.8376 - 60.1966i) q^{90} -22.2728i q^{91} +(-32.0920 - 104.039i) q^{92} +(-101.805 - 101.805i) q^{93} +(-39.8937 - 9.89379i) q^{94} +(-4.83934 - 114.280i) q^{95} +(-120.822 + 44.8308i) q^{96} +(54.6816 - 54.6816i) q^{97} +(51.4786 + 85.4332i) q^{98} +(-70.6013 + 36.3367i) 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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