LMFDB - Embedded newform 220.3.i.a.43.8

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			43.8
Character	$\chi$	$=$	220.43
Dual form			220.3.i.a.87.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.87429 - 0.697868i) q^{2} +(-0.715296 + 0.715296i) q^{3} +(3.02596 + 2.61602i) q^{4} +(-4.99120 + 0.296598i) q^{5} +(1.83986 - 0.841493i) q^{6} +(2.22084 - 2.22084i) q^{7} +(-3.84590 - 7.01492i) q^{8} +7.97670i q^{9} +(9.56196 + 2.92729i) q^{10} +(-10.8744 - 1.65777i) q^{11} +(-4.03569 + 0.293227i) q^{12} +(13.5930 - 13.5930i) q^{13} +(-5.71235 + 2.61265i) q^{14} +(3.35803 - 3.78234i) q^{15} +(2.31286 + 15.8320i) q^{16} +(9.03223 + 9.03223i) q^{17} +(5.56669 - 14.9507i) q^{18} -22.0371i q^{19} +(-15.8791 - 12.1596i) q^{20} +3.17711i q^{21} +(19.2249 + 10.6960i) q^{22} +(18.4603 - 18.4603i) q^{23} +(7.76870 + 2.26679i) q^{24} +(24.8241 - 2.96076i) q^{25} +(-34.9633 + 15.9911i) q^{26} +(-12.1434 - 12.1434i) q^{27} +(12.5299 - 0.910404i) q^{28} -17.1469 q^{29} +(-8.93351 + 4.74576i) q^{30} -48.4755i q^{31} +(6.71364 - 31.2878i) q^{32} +(8.96419 - 6.59260i) q^{33} +(-10.6257 - 23.2324i) q^{34} +(-10.4259 + 11.7433i) q^{35} +(-20.8672 + 24.1372i) q^{36} +(26.8510 - 26.8510i) q^{37} +(-15.3790 + 41.3039i) q^{38} +19.4460i q^{39} +(21.2762 + 33.8721i) q^{40} -42.9149i q^{41} +(2.21721 - 5.95484i) q^{42} +(-21.2909 - 21.2909i) q^{43} +(-28.5686 - 33.4639i) q^{44} +(-2.36588 - 39.8133i) q^{45} +(-47.4828 + 21.7171i) q^{46} +(-8.10647 - 8.10647i) q^{47} +(-12.9789 - 9.67016i) q^{48} +39.1358i q^{49} +(-48.5938 - 11.7746i) q^{50} -12.9214 q^{51} +(76.6912 - 5.57226i) q^{52} +(24.9928 + 24.9928i) q^{53} +(14.2858 + 31.2347i) q^{54} +(54.7678 + 5.04891i) q^{55} +(-24.1201 - 7.03787i) q^{56} +(15.7630 + 15.7630i) q^{57} +(32.1384 + 11.9663i) q^{58} +102.987 q^{59} +(20.0559 - 2.66053i) q^{60} +37.6033i q^{61} +(-33.8295 + 90.8573i) q^{62} +(17.7149 + 17.7149i) q^{63} +(-34.4181 + 53.9573i) q^{64} +(-63.8135 + 71.8768i) q^{65} +(-21.4023 + 6.10065i) q^{66} +(-56.7371 - 56.7371i) q^{67} +(3.70265 + 50.9597i) q^{68} +26.4091i q^{69} +(27.7366 - 14.7345i) q^{70} +52.4379i q^{71} +(55.9559 - 30.6776i) q^{72} +(-19.3554 + 19.3554i) q^{73} +(-69.0652 + 31.5882i) q^{74} +(-15.6387 + 19.8744i) q^{75} +(57.6494 - 66.6832i) q^{76} +(-27.8318 + 20.4686i) q^{77} +(13.5707 - 36.4475i) q^{78} +124.938i q^{79} +(-16.2397 - 78.3344i) q^{80} -54.4181 q^{81} +(-29.9490 + 80.4352i) q^{82} +(-39.9204 - 39.9204i) q^{83} +(-8.31139 + 9.61381i) q^{84} +(-47.7606 - 42.4027i) q^{85} +(25.0472 + 54.7637i) q^{86} +(12.2651 - 12.2651i) q^{87} +(30.1926 + 82.6584i) q^{88} +54.7788i q^{89} +(-23.3501 + 76.2729i) q^{90} -60.3755i q^{91} +(104.152 - 7.56756i) q^{92} +(34.6743 + 34.6743i) q^{93} +(9.53666 + 20.8512i) q^{94} +(6.53615 + 109.991i) q^{95} +(17.5778 + 27.1823i) q^{96} +(36.2543 - 36.2543i) q^{97} +(27.3116 - 73.3520i) q^{98} +(13.2235 - 86.7416i) 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 $

$2$	−1.87429	−	0.697868i	−0.937147	−	0.348934i
$2$	−1.87429	−	0.697868i	−0.937147	−	0.348934i
$3$	−0.715296	+	0.715296i	−0.238432	+	0.238432i	−0.816201	−	0.577769i	$-0.803924\pi$
$3$	−0.715296	+	0.715296i	−0.238432	+	0.238432i	0.577769	+	0.816201i	$0.303924\pi$
$4$	3.02596	+	2.61602i	0.756490	+	0.654005i
$5$	−4.99120	+	0.296598i	−0.998239	+	0.0593197i
$5$	−4.99120	+	0.296598i	−0.998239	+	0.0593197i
$6$	1.83986	−	0.841493i	0.306643	−	0.140249i
$7$	2.22084	−	2.22084i	0.317262	−	0.317262i	−0.530452	−	0.847715i	$-0.677978\pi$
$7$	2.22084	−	2.22084i	0.317262	−	0.317262i	0.847715	+	0.530452i	$0.177978\pi$
$8$	−3.84590	−	7.01492i	−0.480737	−	0.876865i
$9$			7.97670i			0.886300i
$10$	9.56196	+	2.92729i	0.956196	+	0.292729i
$11$	−10.8744	−	1.65777i	−0.988579	−	0.150706i
$11$	−10.8744	−	1.65777i	−0.988579	−	0.150706i
$12$	−4.03569	+	0.293227i	−0.336307	+	0.0244356i
$13$	13.5930	−	13.5930i	1.04561	−	1.04561i	0.0467036	−	0.998909i	$-0.485128\pi$
$13$	13.5930	−	13.5930i	1.04561	−	1.04561i	0.998909	−	0.0467036i	$-0.0148716\pi$
$14$	−5.71235	+	2.61265i	−0.408025	+	0.186618i
$15$	3.35803	−	3.78234i	0.223869	−	0.252156i
$16$	2.31286	+	15.8320i	0.144554	+	0.989497i
$17$	9.03223	+	9.03223i	0.531308	+	0.531308i	0.920961	−	0.389654i	$-0.127405\pi$
$17$	9.03223	+	9.03223i	0.531308	+	0.531308i	−0.389654	+	0.920961i	$0.627405\pi$
$18$	5.56669	−	14.9507i	0.309260	−	0.830594i
$19$		−	22.0371i		−	1.15985i	−0.814672	−	0.579923i	$-0.803083\pi$
$19$		−	22.0371i		−	1.15985i	0.814672	−	0.579923i	$-0.196917\pi$
$20$	−15.8791	−	12.1596i	−0.793953	−	0.607979i
$21$			3.17711i			0.151291i
$22$	19.2249	+	10.6960i	0.873857	+	0.486183i
$23$	18.4603	−	18.4603i	0.802620	−	0.802620i	−0.180884	−	0.983504i	$-0.557896\pi$
$23$	18.4603	−	18.4603i	0.802620	−	0.802620i	0.983504	+	0.180884i	$0.0578959\pi$
$24$	7.76870	+	2.26679i	0.323696	+	0.0944494i
$25$	24.8241	−	2.96076i	0.992962	−	0.118430i
$26$	−34.9633	+	15.9911i	−1.34474	+	0.615043i
$27$	−12.1434	−	12.1434i	−0.449755	−	0.449755i
$28$	12.5299	−	0.910404i	0.447497	−	0.0325144i
$29$	−17.1469			−0.591274			−0.295637	−	0.955300i	$-0.595532\pi$
$29$	−17.1469			−0.591274			−0.295637	+	0.955300i	$0.595532\pi$
$30$	−8.93351	+	4.74576i	−0.297784	+	0.158192i
$31$		−	48.4755i		−	1.56373i	−0.623451	−	0.781863i	$-0.714270\pi$
$31$		−	48.4755i		−	1.56373i	0.623451	−	0.781863i	$-0.285730\pi$
$32$	6.71364	−	31.2878i	0.209801	−	0.977744i
$33$	8.96419	−	6.59260i	0.271642	−	0.199776i
$34$	−10.6257	−	23.2324i	−0.312522	−	0.683305i
$35$	−10.4259	+	11.7433i	−0.297884	+	0.335523i
$36$	−20.8672	+	24.1372i	−0.579645	+	0.670477i
$37$	26.8510	−	26.8510i	0.725703	−	0.725703i	−0.244058	−	0.969761i	$-0.578479\pi$
$37$	26.8510	−	26.8510i	0.725703	−	0.725703i	0.969761	+	0.244058i	$0.0784786\pi$
$38$	−15.3790	+	41.3039i	−0.404710	+	1.08695i
$39$			19.4460i			0.498615i
$40$	21.2762	+	33.8721i	0.531906	+	0.846803i
$41$		−	42.9149i		−	1.04671i	−0.852116	−	0.523353i	$-0.824681\pi$
$41$		−	42.9149i		−	1.04671i	0.852116	−	0.523353i	$-0.175319\pi$
$42$	2.21721	−	5.95484i	0.0527906	−	0.141782i
$43$	−21.2909	−	21.2909i	−0.495138	−	0.495138i	0.414783	−	0.909920i	$-0.363858\pi$
$43$	−21.2909	−	21.2909i	−0.495138	−	0.495138i	−0.909920	+	0.414783i	$0.863858\pi$
$44$	−28.5686	−	33.4639i	−0.649287	−	0.760543i
$45$	−2.36588	−	39.8133i	−0.0525750	−	0.884740i
$46$	−47.4828	+	21.7171i	−1.03224	+	0.472112i
$47$	−8.10647	−	8.10647i	−0.172478	−	0.172478i	0.615589	−	0.788067i	$-0.288918\pi$
$47$	−8.10647	−	8.10647i	−0.172478	−	0.172478i	−0.788067	+	0.615589i	$0.788918\pi$
$48$	−12.9789	−	9.67016i	−0.270394	−	0.201462i
$49$			39.1358i			0.798689i
$50$	−48.5938	−	11.7746i	−0.971876	−	0.235492i
$51$	−12.9214			−0.253362
$52$	76.6912	−	5.57226i	1.47483	−	0.107159i
$53$	24.9928	+	24.9928i	0.471562	+	0.471562i	0.902420	−	0.430858i	$-0.141789\pi$
$53$	24.9928	+	24.9928i	0.471562	+	0.471562i	−0.430858	+	0.902420i	$0.641789\pi$
$54$	14.2858	+	31.2347i	0.264551	+	0.578421i
$55$	54.7678	+	5.04891i	0.995778	+	0.0917984i
$56$	−24.1201	−	7.03787i	−0.430716	−	0.125676i
$57$	15.7630	+	15.7630i	0.276544	+	0.276544i
$58$	32.1384	+	11.9663i	0.554110	+	0.206316i
$59$	102.987			1.74555			0.872774	−	0.488124i	$-0.162319\pi$
$59$	102.987			1.74555			0.872774	+	0.488124i	$0.162319\pi$
$60$	20.0559	−	2.66053i	0.334266	−	0.0443422i
$61$			37.6033i			0.616447i	0.951314	+	0.308224i	$0.0997345\pi$
$61$			37.6033i			0.616447i	−0.951314	+	0.308224i	$0.900265\pi$
$62$	−33.8295	+	90.8573i	−0.545637	+	1.46544i
$63$	17.7149	+	17.7149i	0.281190	+	0.281190i
$64$	−34.4181	+	53.9573i	−0.537783	+	0.843083i
$65$	−63.8135	+	71.8768i	−0.981746	+	1.10580i
$66$	−21.4023	+	6.10065i	−0.324277	+	0.0924341i
$67$	−56.7371	−	56.7371i	−0.846823	−	0.846823i	0.142913	−	0.989735i	$-0.454353\pi$
$67$	−56.7371	−	56.7371i	−0.846823	−	0.846823i	−0.989735	+	0.142913i	$0.954353\pi$
$68$	3.70265	+	50.9597i	0.0544507	+	0.749407i
$69$			26.4091i			0.382741i
$70$	27.7366	−	14.7345i	0.396236	−	0.210493i
$71$			52.4379i			0.738562i	0.929318	+	0.369281i	$0.120396\pi$
$71$			52.4379i			0.738562i	−0.929318	+	0.369281i	$0.879604\pi$
$72$	55.9559	−	30.6776i	0.777165	−	0.426078i
$73$	−19.3554	+	19.3554i	−0.265142	+	0.265142i	−0.827139	−	0.561997i	$-0.810033\pi$
$73$	−19.3554	+	19.3554i	−0.265142	+	0.265142i	0.561997	+	0.827139i	$0.310033\pi$
$74$	−69.0652	+	31.5882i	−0.933313	+	0.426868i
$75$	−15.6387	+	19.8744i	−0.208517	+	0.264992i
$76$	57.6494	−	66.6832i	0.758545	−	0.877411i
$77$	−27.8318	+	20.4686i	−0.361452	+	0.265825i
$78$	13.5707	−	36.4475i	0.173984	−	0.467276i
$79$			124.938i			1.58149i	0.612147	+	0.790744i	$0.290306\pi$
$79$			124.938i			1.58149i	−0.612147	+	0.790744i	$0.709694\pi$
$80$	−16.2397	−	78.3344i	−0.202996	−	0.979180i
$81$	−54.4181			−0.671828
$82$	−29.9490	+	80.4352i	−0.365231	+	0.980918i
$83$	−39.9204	−	39.9204i	−0.480968	−	0.480968i	0.424472	−	0.905441i	$-0.360460\pi$
$83$	−39.9204	−	39.9204i	−0.480968	−	0.480968i	−0.905441	+	0.424472i	$0.860460\pi$
$84$	−8.31139	+	9.61381i	−0.0989452	+	0.114450i
$85$	−47.7606	−	42.4027i	−0.561889	−	0.498855i
$86$	25.0472	+	54.7637i	0.291246	+	0.636788i
$87$	12.2651	−	12.2651i	0.140979	−	0.140979i
$88$	30.1926	+	82.6584i	0.343098	+	0.939300i
$89$			54.7788i			0.615492i	0.951469	+	0.307746i	$0.0995746\pi$
$89$			54.7788i			0.615492i	−0.951469	+	0.307746i	$0.900425\pi$
$90$	−23.3501	+	76.2729i	−0.259445	+	0.847476i
$91$		−	60.3755i		−	0.663467i
$92$	104.152	−	7.56756i	1.13209	−	0.0822560i
$93$	34.6743	+	34.6743i	0.372842	+	0.372842i
$94$	9.53666	+	20.8512i	0.101454	+	0.221821i
$95$	6.53615	+	109.991i	0.0688016	+	1.15780i
$96$	17.5778	+	27.1823i	0.183102	+	0.283149i
$97$	36.2543	−	36.2543i	0.373756	−	0.373756i	−0.495087	−	0.868843i	$-0.664864\pi$
$97$	36.2543	−	36.2543i	0.373756	−	0.373756i	0.868843	+	0.495087i	$0.164864\pi$
$98$	27.3116	−	73.3520i	0.278690	−	0.748489i
$99$	13.2235	−	86.7416i	0.133571	−	0.876177i
$100$	82.8620	+	55.9811i	0.828620	+	0.559811i
$101$		−	130.016i		−	1.28729i	−0.765323	−	0.643646i	$-0.777421\pi$
$101$		−	130.016i		−	1.28729i	0.765323	−	0.643646i	$-0.222579\pi$
$102$	24.2186	+	9.01747i	0.237437	+	0.0884065i
$103$	−6.33217	+	6.33217i	−0.0614773	+	0.0614773i	−0.737177	−	0.675700i	$-0.763842\pi$
$103$	−6.33217	+	6.33217i	−0.0614773	+	0.0614773i	0.675700	+	0.737177i	$0.263842\pi$
$104$	−147.631	−	43.0763i	−1.41953	−	0.414195i
$105$	−0.942326	−	15.8576i	−0.00897453	−	0.151025i
$106$	−29.4022	−	64.2855i	−0.277379	−	0.606467i
$107$	105.599	−	105.599i	0.986904	−	0.986904i	−0.0130112	−	0.999915i	$-0.504142\pi$
$107$	105.599	−	105.599i	0.986904	−	0.986904i	0.999915	+	0.0130112i	$0.00414171\pi$
$108$	−4.97802	−	68.5127i	−0.0460928	−	0.634377i
$109$	28.9484			0.265582			0.132791	−	0.991144i	$-0.457606\pi$
$109$	28.9484			0.265582			0.132791	+	0.991144i	$0.457606\pi$
$110$	−99.1274	−	47.6838i	−0.901159	−	0.433490i
$111$			38.4129i			0.346062i
$112$	40.2966	+	30.0237i	0.359791	+	0.268069i
$113$	−150.357	−	150.357i	−1.33060	−	1.33060i	−0.904835	−	0.425761i	$-0.860006\pi$
$113$	−150.357	−	150.357i	−1.33060	−	1.33060i	−0.425761	−	0.904835i	$-0.639994\pi$
$114$	−18.5440	−	40.5451i	−0.162667	−	0.355659i
$115$	−86.6635	+	97.6141i	−0.753596	+	0.848818i
$116$	−51.8859	−	44.8567i	−0.447292	−	0.386696i
$117$	108.427	+	108.427i	0.926727	+	0.926727i
$118$	−193.029	−	71.8716i	−1.63584	−	0.609082i
$119$	40.1182			0.337128
$120$	−39.4474	−	9.00979i	−0.328729	−	0.0750816i
$121$	115.504	+	36.0543i	0.954575	+	0.297969i
$122$	26.2422	−	70.4796i	0.215100	−	0.577702i
$123$	30.6969	+	30.6969i	0.249568	+	0.249568i
$124$	126.813	−	146.685i	1.02268	−	1.18294i
$125$	−123.024	+	22.1405i	−0.984189	+	0.177124i
$126$	−20.8403	−	45.5657i	−0.165399	−	0.361633i
$127$	−12.1820	+	12.1820i	−0.0959211	+	0.0959211i	−0.753439	−	0.657518i	$-0.771606\pi$
$127$	−12.1820	+	12.1820i	−0.0959211	+	0.0959211i	0.657518	+	0.753439i	$0.271606\pi$
$128$	102.165	−	77.1126i	0.798162	−	0.602442i
$129$	30.4586			0.236114
$130$	169.766	−	90.1848i	1.30589	−	0.693729i
$131$	−206.414			−1.57568			−0.787840	−	0.615880i	$-0.788801\pi$
$131$	−206.414			−1.57568			−0.787840	+	0.615880i	$0.788801\pi$
$132$	44.3717	+	3.50157i	0.336149	+	0.0265270i
$133$	−48.9407	−	48.9407i	−0.367975	−	0.367975i
$134$	66.7470	+	145.937i	0.498112	+	1.08908i
$135$	64.2117	+	57.0082i	0.475642	+	0.422283i
$136$	28.6233	−	98.0974i	0.210465	−	0.721304i
$137$	54.2707	−	54.2707i	0.396136	−	0.396136i	−0.480732	−	0.876868i	$-0.659629\pi$
$137$	54.2707	−	54.2707i	0.396136	−	0.396136i	0.876868	+	0.480732i	$0.159629\pi$
$138$	18.4301	−	49.4985i	0.133551	−	0.358685i
$139$		−	82.8999i		−	0.596402i	−0.954503	−	0.298201i	$-0.903613\pi$
$139$		−	82.8999i		−	0.596402i	0.954503	−	0.298201i	$-0.0963866\pi$
$140$	−62.2692	+	8.26035i	−0.444780	+	0.0590025i
$141$	11.5971			0.0822486
$142$	36.5948	−	98.2841i	0.257710	−	0.692142i
$143$	−170.349	+	125.281i	−1.19125	+	0.876090i
$144$	−126.287	+	18.4490i	−0.876991	+	0.128118i
$145$	85.5837	−	5.08575i	0.590232	−	0.0350741i
$146$	49.7852	−	22.7702i	0.340995	−	0.155960i
$147$	−27.9937	−	27.9937i	−0.190433	−	0.190433i
$148$	151.493	−	11.0072i	1.02360	−	0.0743732i
$149$	−74.9458			−0.502992			−0.251496	−	0.967858i	$-0.580923\pi$
$149$	−74.9458			−0.502992			−0.251496	+	0.967858i	$0.580923\pi$
$150$	43.1813	−	26.3367i	0.287875	−	0.175578i
$151$	29.5062			0.195405			0.0977027	−	0.995216i	$-0.468851\pi$
$151$	29.5062			0.195405			0.0977027	+	0.995216i	$0.468851\pi$
$152$	−154.588	+	84.7523i	−1.01703	+	0.557581i
$153$	−72.0474	+	72.0474i	−0.470898	+	0.470898i
$154$	66.4493	−	18.9412i	0.431489	−	0.122995i
$155$	14.3777	+	241.951i	0.0927596	+	1.56097i
$156$	−50.8711	+	58.8428i	−0.326097	+	0.377197i
$157$	−20.6552	+	20.6552i	−0.131562	+	0.131562i	−0.769821	−	0.638260i	$-0.779655\pi$
$157$	−20.6552	+	20.6552i	−0.131562	+	0.131562i	0.638260	+	0.769821i	$0.279655\pi$
$158$	87.1900	−	234.170i	0.551835	−	1.48209i
$159$	−35.7545			−0.224871
$160$	−24.2292	+	158.155i	−0.151432	+	0.988468i
$161$		−	81.9945i		−	0.509282i
$162$	101.996	+	37.9767i	0.629602	+	0.234424i
$163$	−210.111	+	210.111i	−1.28902	+	1.28902i	−0.353645	+	0.935380i	$0.615058\pi$
$163$	−210.111	+	210.111i	−1.28902	+	1.28902i	−0.935380	+	0.353645i	$0.884942\pi$
$164$	112.266	−	129.859i	0.684551	−	0.791822i
$165$	−42.7867	+	35.5637i	−0.259313	+	0.215538i
$166$	46.9634	+	102.682i	0.282912	+	0.618565i
$167$	−38.3042	+	38.3042i	−0.229367	+	0.229367i	−0.812428	−	0.583061i	$-0.801855\pi$
$167$	−38.3042	+	38.3042i	−0.229367	+	0.229367i	0.583061	+	0.812428i	$0.301855\pi$
$168$	22.2872	−	12.2189i	0.132662	−	0.0727313i
$169$		−	200.537i		−	1.18661i
$170$	59.9259	+	112.806i	0.352505	+	0.663563i
$171$	175.783			1.02797
$172$	−8.72795	−	120.123i	−0.0507439	−	0.698390i
$173$	212.941	−	212.941i	1.23087	−	1.23087i	0.267242	−	0.963630i	$-0.413888\pi$
$173$	212.941	−	212.941i	1.23087	−	1.23087i	0.963630	−	0.267242i	$-0.0861122\pi$
$174$	−31.5479	+	14.4290i	−0.181310	+	0.0829254i
$175$	48.5548	−	61.7055i	0.277456	−	0.352603i
$176$	1.09478	−	175.997i	0.00622037	−	0.999981i
$177$	−73.6665	+	73.6665i	−0.416195	+	0.416195i
$178$	38.2284	−	102.672i	0.214766	−	0.576806i
$179$	228.179			1.27474			0.637370	−	0.770558i	$-0.280022\pi$
$179$	228.179			1.27474			0.637370	+	0.770558i	$0.280022\pi$
$180$	96.9934	−	126.663i	0.538852	−	0.703681i
$181$	−34.9814			−0.193267			−0.0966337	−	0.995320i	$-0.530808\pi$
$181$	−34.9814			−0.193267			−0.0966337	+	0.995320i	$0.530808\pi$
$182$	−42.1341	+	113.161i	−0.231506	+	0.621766i
$183$	−26.8975	−	26.8975i	−0.146981	−	0.146981i
$184$	−200.494	−	58.5009i	−1.08964	−	0.317940i
$185$	−126.055	+	141.983i	−0.681377	+	0.767474i
$186$	−40.7918	−	89.1880i	−0.219311	−	0.479506i
$187$	−83.2464	−	113.193i	−0.445168	−	0.605311i
$188$	−3.32314	−	45.7365i	−0.0176763	−	0.243279i
$189$	−53.9369			−0.285380
$190$	64.5088	−	210.717i	0.339520	−	1.10904i
$191$		−	236.391i		−	1.23765i	−0.785529	−	0.618825i	$-0.787609\pi$
$191$		−	236.391i		−	1.23765i	0.785529	−	0.618825i	$-0.212391\pi$
$192$	−13.9763	−	63.2146i	−0.0727934	−	0.329243i
$193$	136.099	−	136.099i	0.705178	−	0.705178i	−0.260339	−	0.965517i	$-0.583834\pi$
$193$	136.099	−	136.099i	0.705178	−	0.705178i	0.965517	+	0.260339i	$0.0838343\pi$
$194$	−93.2521	+	42.6506i	−0.480681	+	0.219848i
$195$	−5.76765	−	97.0587i	−0.0295777	−	0.497737i
$196$	−102.380	+	118.423i	−0.522347	+	0.604200i
$197$	−0.907559	−	0.907559i	−0.00460690	−	0.00460690i	0.704800	−	0.709406i	$-0.251037\pi$
$197$	−0.907559	−	0.907559i	−0.00460690	−	0.00460690i	−0.709406	+	0.704800i	$0.751037\pi$
$198$	−85.3189	+	153.351i	−0.430904	+	0.774500i
$199$	110.730			0.556432			0.278216	−	0.960519i	$-0.410257\pi$
$199$	110.730			0.556432			0.278216	+	0.960519i	$0.410257\pi$
$200$	−116.240	−	162.752i	−0.581202	−	0.813760i
$201$	81.1677			0.403820
$202$	−90.7344	+	243.689i	−0.449180	+	1.20638i
$203$	−38.0805	+	38.0805i	−0.187589	+	0.187589i
$204$	−39.0998	−	33.8028i	−0.191665	−	0.165700i
$205$	12.7285	+	214.197i	0.0620902	+	1.04486i
$206$	16.2874	−	7.44932i	0.0790649	−	0.0361618i
$207$	147.252	+	147.252i	0.711363	+	0.711363i
$208$	246.642	+	183.764i	1.18578	+	0.883483i
$209$	−36.5323	+	239.639i	−0.174796	+	1.14660i
$210$	−9.30031	+	30.3794i	−0.0442872	+	0.144664i
$211$	−161.308			−0.764492			−0.382246	−	0.924061i	$-0.624849\pi$
$211$	−161.308			−0.764492			−0.382246	+	0.924061i	$0.624849\pi$
$212$	10.2455	+	141.009i	0.0483278	+	0.665136i
$213$	−37.5087	−	37.5087i	−0.176097	−	0.176097i
$214$	−271.617	+	124.229i	−1.26924	+	0.580510i
$215$	112.582	+	99.9523i	0.523637	+	0.464894i
$216$	−38.4826	+	131.887i	−0.178160	+	0.610588i
$217$	−107.656	−	107.656i	−0.496111	−	0.496111i
$218$	−54.2579	−	20.2022i	−0.248889	−	0.0926706i
$219$		−	27.6897i		−	0.126437i
$220$	152.517	+	158.551i	0.693259	+	0.720689i
$221$	245.549			1.11108
$222$	26.8071	−	71.9970i	0.120753	−	0.324311i
$223$	81.9777	−	81.9777i	0.367613	−	0.367613i	−0.498993	−	0.866606i	$-0.666297\pi$
$223$	81.9777	−	81.9777i	0.367613	−	0.367613i	0.866606	+	0.498993i	$0.166297\pi$
$224$	−54.5752	−	84.3950i	−0.243639	−	0.376763i
$225$	23.6171	+	198.014i	0.104965	+	0.880063i
$226$	176.884	+	386.744i	0.782674	+	1.71126i
$227$	−116.079	+	116.079i	−0.511363	+	0.511363i	−0.914944	−	0.403581i	$-0.867765\pi$
$227$	−116.079	+	116.079i	−0.511363	+	0.511363i	0.403581	+	0.914944i	$0.367765\pi$
$228$	6.46186	+	88.9347i	0.0283415	+	0.390065i
$229$			27.8767i			0.121732i	0.998146	+	0.0608662i	$0.0193863\pi$
$229$			27.8767i			0.121732i	−0.998146	+	0.0608662i	$0.980614\pi$
$230$	230.555	−	122.478i	1.00241	−	0.532512i
$231$	5.26691	−	34.5491i	0.0228005	−	0.149563i
$232$	65.9454	+	120.284i	0.284247	+	0.518467i
$233$	−115.050	+	115.050i	−0.493777	+	0.493777i	−0.909494	−	0.415717i	$-0.863531\pi$
$233$	−115.050	+	115.050i	−0.493777	+	0.493777i	0.415717	+	0.909494i	$0.363531\pi$
$234$	−127.556	−	278.892i	−0.545113	−	1.19185i
$235$	42.8653	+	38.0566i	0.182406	+	0.161943i
$236$	311.636	+	269.417i	1.32049	+	1.14160i
$237$	−89.3674	−	89.3674i	−0.377078	−	0.377078i
$238$	−75.1933	−	27.9972i	−0.315938	−	0.117635i
$239$			314.014i			1.31387i	0.753949	+	0.656933i	$0.228146\pi$
$239$			314.014i			1.31387i	−0.753949	+	0.656933i	$0.771854\pi$
$240$	67.6485	+	44.4161i	0.281869	+	0.185067i
$241$			443.899i			1.84190i	0.389676	+	0.920952i	$0.372587\pi$
$241$			443.899i			1.84190i	−0.389676	+	0.920952i	$0.627413\pi$
$242$	−191.327	−	148.183i	−0.790606	−	0.612325i
$243$	148.215	−	148.215i	0.609940	−	0.609940i
$244$	−98.3710	+	113.786i	−0.403160	+	0.466336i
$245$	−11.6076	−	195.334i	−0.0473780	−	0.797283i
$246$	−36.1126	−	78.9574i	−0.146799	−	0.320965i
$247$	−299.549	−	299.549i	−1.21275	−	1.21275i
$248$	−340.051	+	186.432i	−1.37118	+	0.751741i
$249$	57.1098			0.229357
$250$	246.034	+	44.3564i	0.984134	+	0.177426i
$251$		−	240.731i		−	0.959089i	−0.877517	−	0.479545i	$-0.840802\pi$
$251$		−	240.731i		−	0.959089i	0.877517	−	0.479545i	$-0.159198\pi$
$252$	7.26202	+	99.9474i	0.0288175	+	0.396617i
$253$	−231.347	+	170.141i	−0.914413	+	0.672494i
$254$	31.3340	−	14.3312i	0.123362	−	0.0564221i
$255$	64.4934	−	3.83248i	0.252915	−	0.0150293i
$256$	−245.301	+	73.2342i	−0.958208	+	0.286071i
$257$	236.660	−	236.660i	0.920855	−	0.920855i	−0.0762349	−	0.997090i	$-0.524290\pi$
$257$	236.660	−	236.660i	0.920855	−	0.920855i	0.997090	+	0.0762349i	$0.0242899\pi$
$258$	−57.0885	−	21.2561i	−0.221273	−	0.0823881i
$259$		−	119.263i		−	0.460476i
$260$	−381.128	+	50.5587i	−1.46588	+	0.194457i
$261$		−	136.776i		−	0.524046i
$262$	386.881	+	144.050i	1.47664	+	0.549809i
$263$	84.5250	+	84.5250i	0.321388	+	0.321388i	0.849299	−	0.527911i	$-0.177025\pi$
$263$	84.5250	+	84.5250i	0.321388	+	0.321388i	−0.527911	+	0.849299i	$0.677025\pi$
$264$	−80.7219	−	37.5285i	−0.305765	−	0.142154i
$265$	−132.157	−	117.331i	−0.498705	−	0.442759i
$266$	57.5751	+	125.883i	0.216448	+	0.473246i
$267$	−39.1830	−	39.1830i	−0.146753	−	0.146753i
$268$	−23.2587	−	320.110i	−0.0867861	−	1.19444i
$269$			159.019i			0.591150i	0.955319	+	0.295575i	$0.0955113\pi$
$269$			159.019i			0.591150i	−0.955319	+	0.295575i	$0.904489\pi$
$270$	−80.5673	−	151.662i	−0.298397	−	0.561709i
$271$	266.913			0.984920			0.492460	−	0.870335i	$-0.336098\pi$
$271$	266.913			0.984920			0.492460	+	0.870335i	$0.336098\pi$
$272$	−122.108	+	163.888i	−0.448925	+	0.602530i
$273$	43.1864	+	43.1864i	0.158192	+	0.158192i
$274$	−139.593	+	63.8454i	−0.509463	+	0.233012i
$275$	−274.854	−	8.95609i	−0.999470	−	0.0325676i
$276$	−69.0869	+	79.9129i	−0.250315	+	0.289540i
$277$	−7.39230	−	7.39230i	−0.0266870	−	0.0266870i	0.693637	−	0.720324i	$-0.256007\pi$
$277$	−7.39230	−	7.39230i	−0.0266870	−	0.0266870i	−0.720324	+	0.693637i	$0.756007\pi$
$278$	−57.8532	+	155.379i	−0.208105	+	0.558917i
$279$	386.674			1.38593
$280$	122.475	+	27.9734i	0.437412	+	0.0999050i
$281$		−	441.260i		−	1.57032i	−0.619293	−	0.785160i	$-0.712581\pi$
$281$		−	441.260i		−	1.57032i	0.619293	−	0.785160i	$-0.287419\pi$
$282$	−21.7363	−	8.09322i	−0.0770791	−	0.0286994i
$283$	99.6962	+	99.6962i	0.352283	+	0.352283i	0.860959	−	0.508675i	$-0.169865\pi$
$283$	99.6962	+	99.6962i	0.352283	+	0.352283i	−0.508675	+	0.860959i	$0.669865\pi$
$284$	−137.179	+	158.675i	−0.483024	+	0.558715i
$285$	−83.3516	−	74.0011i	−0.292462	−	0.259653i
$286$	406.713	−	115.932i	1.42207	−	0.405357i
$287$	−95.3070	−	95.3070i	−0.332080	−	0.332080i
$288$	249.574	+	53.5527i	0.866575	+	0.185947i
$289$		−	125.838i		−	0.435425i
$290$	−163.958	−	50.1940i	−0.565373	−	0.173083i
$291$			51.8652i			0.178231i
$292$	−109.203	+	7.93450i	−0.373982	+	0.0271730i
$293$	−260.491	+	260.491i	−0.889047	+	0.889047i	−0.994432	−	0.105384i	$-0.966393\pi$
$293$	−260.491	+	260.491i	−0.889047	+	0.889047i	0.105384	+	0.994432i	$0.466393\pi$
$294$	32.9325	+	72.0043i	0.112015	+	0.244913i
$295$	−514.030	+	30.5459i	−1.74247	+	0.103545i
$296$	−291.624	−	85.0913i	−0.985216	−	0.287471i
$297$	111.921	+	152.182i	0.376837	+	0.512398i
$298$	140.470	+	52.3023i	0.471377	+	0.175511i
$299$		−	501.859i		−	1.67846i
$300$	−99.3140	+	19.2278i	−0.331047	+	0.0640926i
$301$	−94.5673			−0.314177
$302$	−55.3033	−	20.5915i	−0.183124	−	0.0681836i
$303$	93.0003	+	93.0003i	0.306932	+	0.306932i
$304$	348.890	−	50.9686i	1.14766	−	0.167660i
$305$	−11.1531	−	187.685i	−0.0365674	−	0.615362i
$306$	185.318	−	84.7584i	0.605613	−	0.276988i
$307$	−200.278	+	200.278i	−0.652371	+	0.652371i	−0.953563	−	0.301193i	$-0.902615\pi$
$307$	−200.278	+	200.278i	−0.652371	+	0.652371i	0.301193	+	0.953563i	$0.402615\pi$
$308$	−137.764	−	10.8716i	−0.447286	−	0.0352974i
$309$		−	9.05875i		−	0.0293163i
$310$	141.902	−	463.520i	0.457747	−	1.49523i
$311$		−	53.9933i		−	0.173612i	−0.996225	−	0.0868059i	$-0.972334\pi$
$311$		−	53.9933i		−	0.173612i	0.996225	−	0.0868059i	$-0.0276660\pi$
$312$	136.412	−	74.7873i	0.437218	−	0.239703i
$313$	229.397	+	229.397i	0.732897	+	0.732897i	0.971193	−	0.238296i	$-0.0765888\pi$
$313$	229.397	+	229.397i	0.732897	+	0.732897i	−0.238296	+	0.971193i	$0.576589\pi$
$314$	53.1285	−	24.2993i	0.169199	−	0.0773863i
$315$	−93.6730	−	83.1645i	−0.297375	−	0.264014i
$316$	−326.839	+	378.056i	−1.03430	+	1.19638i
$317$	143.530	−	143.530i	0.452776	−	0.452776i	−0.443499	−	0.896275i	$-0.646263\pi$
$317$	143.530	−	143.530i	0.452776	−	0.452776i	0.896275	+	0.443499i	$0.146263\pi$
$318$	67.0145	+	24.9519i	0.210737	+	0.0784652i
$319$	186.462	+	28.4256i	0.584520	+	0.0891084i
$320$	155.784	−	279.520i	0.486825	−	0.873500i
$321$			151.069i			0.470619i
$322$	−57.2213	+	153.682i	−0.177706	+	0.477273i
$323$	199.044	−	199.044i	0.616235	−	0.616235i
$324$	−164.667	−	142.359i	−0.508231	−	0.439379i
$325$	297.187	−	377.678i	0.914421	−	1.16209i
$326$	540.440	−	247.180i	1.65779	−	0.758221i
$327$	−20.7067	+	20.7067i	−0.0633232	+	0.0633232i
$328$	−301.045	+	165.047i	−0.917819	+	0.503191i
$329$	−36.0063			−0.109442
$330$	105.014	−	36.7974i	0.318223	−	0.111507i
$331$		−	331.244i		−	1.00074i	−0.865812	−	0.500369i	$-0.833198\pi$
$331$		−	331.244i		−	1.00074i	0.865812	−	0.500369i	$-0.166802\pi$
$332$	−16.3649	−	225.230i	−0.0492917	−	0.678404i
$333$	214.183	+	214.183i	0.643191	+	0.643191i
$334$	98.5248	−	45.0621i	0.294984	−	0.134916i
$335$	300.014	+	266.358i	0.895565	+	0.795098i
$336$	−50.2999	+	7.34821i	−0.149702	+	0.0218697i
$337$	−275.569	−	275.569i	−0.817712	−	0.817712i	0.168064	−	0.985776i	$-0.446249\pi$
$337$	−275.569	−	275.569i	−0.817712	−	0.817712i	−0.985776	+	0.168064i	$0.946249\pi$
$338$	−139.949	+	375.866i	−0.414049	+	1.11203i
$339$	215.100			0.634514
$340$	−33.5952	−	253.251i	−0.0988094	−	0.744857i
$341$	−80.3610	+	527.140i	−0.235663	+	1.54587i
$342$	−329.469	−	122.673i	−0.963360	−	0.358694i
$343$	195.735	+	195.735i	0.570656	+	0.570656i
$344$	−67.4713	+	231.237i	−0.196138	+	0.672200i
$345$	−7.83290	−	131.813i	−0.0227041	−	0.382067i
$346$	−547.718	+	250.509i	−1.58300	+	0.724014i
$347$	−51.3590	+	51.3590i	−0.148009	+	0.148009i	−0.777228	−	0.629219i	$-0.783375\pi$
$347$	−51.3590	+	51.3590i	−0.148009	+	0.148009i	0.629219	+	0.777228i	$0.283375\pi$
$348$	69.1997	−	5.02794i	0.198850	−	0.0144481i
$349$	398.578			1.14206			0.571029	−	0.820930i	$-0.306544\pi$
$349$	398.578			1.14206			0.571029	+	0.820930i	$0.306544\pi$
$350$	−134.068	+	81.7694i	−0.383052	+	0.233627i
$351$	−330.129			−0.940538
$352$	−124.874	+	329.105i	−0.354757	+	0.934959i
$353$	66.5648	+	66.5648i	0.188569	+	0.188569i	0.795077	−	0.606508i	$-0.207430\pi$
$353$	66.5648	+	66.5648i	0.188569	+	0.188569i	−0.606508	+	0.795077i	$0.707430\pi$
$354$	189.482	−	86.6632i	0.535260	−	0.244811i
$355$	−15.5530	−	261.728i	−0.0438113	−	0.737262i
$356$	−143.302	+	165.758i	−0.402535	+	0.465613i
$357$	−28.6964	+	28.6964i	−0.0803821	+	0.0803821i
$358$	−427.674	−	159.239i	−1.19462	−	0.444801i
$359$		−	164.580i		−	0.458439i	−0.973375	−	0.229220i	$-0.926383\pi$
$359$		−	164.580i		−	0.458439i	0.973375	−	0.229220i	$-0.0736174\pi$
$360$	−270.188	+	169.714i	−0.750522	+	0.471429i
$361$	−124.632			−0.345241
$362$	65.5654	+	24.4124i	0.181120	+	0.0674376i
$363$	−108.409	+	56.8298i	−0.298647	+	0.156556i
$364$	157.944	−	182.694i	0.433911	−	0.501906i
$365$	90.8658	−	102.347i	0.248947	−	0.280404i
$366$	31.6429	+	69.1848i	0.0864561	+	0.189029i
$367$	22.0064	+	22.0064i	0.0599630	+	0.0599630i	0.736452	−	0.676489i	$-0.236500\pi$
$367$	22.0064	+	22.0064i	0.0599630	+	0.0599630i	−0.676489	+	0.736452i	$0.736500\pi$
$368$	334.958	+	249.566i	0.910212	+	0.678169i
$369$	342.320			0.927696
$370$	335.349	−	178.148i	0.906348	−	0.481480i
$371$	111.010			0.299218
$372$	14.2143	+	195.632i	0.0382105	+	0.525892i
$373$	−17.8852	+	17.8852i	−0.0479496	+	0.0479496i	−0.730675	−	0.682725i	$-0.760795\pi$
$373$	−17.8852	+	17.8852i	−0.0479496	+	0.0479496i	0.682725	+	0.730675i	$0.260795\pi$
$374$	77.0345	+	270.252i	0.205974	+	0.722599i
$375$	72.1613	−	103.835i	0.192430	−	0.276894i
$376$	−25.6895	+	88.0429i	−0.0683232	+	0.234157i
$377$	−233.078	+	233.078i	−0.618243	+	0.618243i
$378$	101.094	+	37.6408i	0.267443	+	0.0995789i
$379$	−519.305			−1.37020			−0.685099	−	0.728450i	$-0.740241\pi$
$379$	−519.305			−1.37020			−0.685099	+	0.728450i	$0.740241\pi$
$380$	−267.961	+	349.928i	−0.705162	+	0.920863i
$381$		−	17.4275i		−	0.0457414i
$382$	−164.970	+	443.067i	−0.431858	+	1.15986i
$383$	191.782	−	191.782i	0.500737	−	0.500737i	−0.410930	−	0.911667i	$-0.634796\pi$
$383$	191.782	−	191.782i	0.500737	−	0.500737i	0.911667	+	0.410930i	$0.134796\pi$
$384$	−17.9197	+	128.236i	−0.0466660	+	0.333949i
$385$	132.843	−	110.417i	0.345047	−	0.286798i
$386$	−350.070	+	160.111i	−0.906917	+	0.414795i
$387$	169.831	−	169.831i	0.438841	−	0.438841i
$388$	204.546	−	14.8620i	0.527181	−	0.0383042i
$389$			514.704i			1.32315i	0.749880	+	0.661574i	$0.230111\pi$
$389$			514.704i			1.32315i	−0.749880	+	0.661574i	$0.769889\pi$
$390$	−56.9240	+	185.942i	−0.145959	+	0.476774i
$391$	333.475			0.852877
$392$	274.534	−	150.512i	0.700342	−	0.383960i
$393$	147.647	−	147.647i	0.375693	−	0.375693i
$394$	1.06768	+	2.33439i	0.00270984	+	0.00592485i
$395$	−37.0563	−	623.588i	−0.0938133	−	1.57870i
$396$	266.932	−	227.883i	0.674070	−	0.575463i
$397$	181.692	−	181.692i	0.457663	−	0.457663i	−0.440225	−	0.897888i	$-0.645101\pi$
$397$	181.692	−	181.692i	0.457663	−	0.457663i	0.897888	+	0.440225i	$0.145101\pi$
$398$	−207.541	−	77.2749i	−0.521459	−	0.194158i
$399$	70.0142			0.175474
$400$	104.289	+	386.165i	0.260723	+	0.965414i
$401$	264.079			0.658551			0.329275	−	0.944234i	$-0.393196\pi$
$401$	264.079			0.658551			0.329275	+	0.944234i	$0.393196\pi$
$402$	−152.132	−	56.6444i	−0.378438	−	0.140906i
$403$	−658.925	−	658.925i	−1.63505	−	1.63505i
$404$	340.126	−	393.425i	0.841896	−	0.973823i
$405$	271.611	−	16.1403i	0.670645	−	0.0398526i
$406$	97.9493	−	44.7989i	0.241254	−	0.110342i
$407$	−336.500	+	247.475i	−0.826782	+	0.608047i
$408$	49.6946	+	90.6428i	0.121800	+	0.222164i
$409$	−154.396			−0.377496			−0.188748	−	0.982026i	$-0.560443\pi$
$409$	−154.396			−0.377496			−0.188748	+	0.982026i	$0.560443\pi$
$410$	125.624	−	410.351i	0.306401	−	1.00086i
$411$			77.6392i			0.188903i
$412$	−35.7260	+	2.59579i	−0.0867135	+	0.00630047i
$413$	228.718	−	228.718i	0.553797	−	0.553797i
$414$	−173.231	−	378.756i	−0.418433	−	0.914870i
$415$	211.091	+	187.410i	0.508652	+	0.451591i
$416$	−334.036	−	516.552i	−0.802971	−	1.24171i
$417$	59.2980	+	59.2980i	0.142201	+	0.142201i
$418$	235.709	−	423.659i	0.563897	−	1.01354i
$419$	−105.235			−0.251159			−0.125579	−	0.992084i	$-0.540079\pi$
$419$	−105.235			−0.251159			−0.125579	+	0.992084i	$0.540079\pi$
$420$	38.6323	−	50.4495i	0.0919818	−	0.120118i
$421$	−154.459			−0.366885			−0.183443	−	0.983030i	$-0.558724\pi$
$421$	−154.459			−0.366885			−0.183443	+	0.983030i	$0.558724\pi$
$422$	302.338	+	112.572i	0.716441	+	0.266757i
$423$	64.6629	−	64.6629i	0.152867	−	0.152867i
$424$	79.2026	−	271.442i	0.186799	−	0.640194i
$425$	250.959	+	197.474i	0.590491	+	0.464645i
$426$	44.1262	+	96.4784i	0.103583	+	0.226475i
$427$	83.5107	+	83.5107i	0.195576	+	0.195576i
$428$	595.786	−	43.2889i	1.39202	−	0.101142i
$429$	32.2369	−	211.463i	0.0751443	−	0.492920i
$430$	−141.258	−	265.907i	−0.328508	−	0.618390i
$431$	−134.177			−0.311315			−0.155657	−	0.987811i	$-0.549750\pi$
$431$	−134.177			−0.311315			−0.155657	+	0.987811i	$0.549750\pi$
$432$	164.167	−	220.339i	0.380017	−	0.510044i
$433$	−470.363	−	470.363i	−1.08629	−	1.08629i	−0.995907	−	0.0903823i	$-0.971191\pi$
$433$	−470.363	−	470.363i	−1.08629	−	1.08629i	−0.0903823	−	0.995907i	$-0.528809\pi$
$434$	126.649	+	276.909i	0.291819	+	0.638039i
$435$	−57.5799	+	64.8555i	−0.132368	+	0.149093i
$436$	87.5967	+	75.7297i	0.200910	+	0.173692i
$437$	−406.810	−	406.810i	−0.930915	−	0.930915i
$438$	−19.3238	+	51.8986i	−0.0441182	+	0.118490i
$439$			663.345i			1.51104i	0.655128	+	0.755518i	$0.272615\pi$
$439$			663.345i			1.51104i	−0.655128	+	0.755518i	$0.727385\pi$
$440$	−175.214	−	403.609i	−0.398213	−	0.917293i
$441$	−312.174			−0.707879
$442$	−460.232	−	171.361i	−1.04125	−	0.387695i
$443$	−362.609	+	362.609i	−0.818530	+	0.818530i	−0.985895	−	0.167365i	$-0.946474\pi$
$443$	−362.609	+	362.609i	−0.818530	+	0.818530i	0.167365	+	0.985895i	$0.446474\pi$
$444$	−100.489	+	116.236i	−0.226326	+	0.261792i
$445$	−16.2473	−	273.411i	−0.0365107	−	0.614408i
$446$	−210.860	+	96.4407i	−0.472780	+	0.216235i
$447$	53.6084	−	53.6084i	0.119929	−	0.119929i
$448$	43.3934	+	196.267i	0.0968603	+	0.438097i
$449$			246.087i			0.548078i	0.961719	+	0.274039i	$0.0883597\pi$
$449$			246.087i			0.548078i	−0.961719	+	0.274039i	$0.911640\pi$
$450$	93.9224	−	387.618i	0.208716	−	0.861374i
$451$	−71.1429	+	466.673i	−0.157745	+	1.03475i
$452$	−61.6372	−	848.314i	−0.136365	−	1.87680i
$453$	−21.1057	+	21.1057i	−0.0465909	+	0.0465909i
$454$	298.575	−	136.559i	0.657654	−	0.300790i
$455$	17.9073	+	301.346i	0.0393566	+	0.662298i
$456$	49.9533	−	171.199i	0.109547	−	0.375437i
$457$	−181.041	−	181.041i	−0.396150	−	0.396150i	0.480723	−	0.876873i	$-0.340374\pi$
$457$	−181.041	−	181.041i	−0.396150	−	0.396150i	−0.876873	+	0.480723i	$0.840374\pi$
$458$	19.4543	−	52.2491i	0.0424766	−	0.114081i
$459$		−	219.363i		−	0.477916i
$460$	−517.601	+	68.6626i	−1.12522	+	0.149267i
$461$			663.725i			1.43975i	0.694103	+	0.719876i	$0.255801\pi$
$461$			663.725i			1.43975i	−0.694103	+	0.719876i	$0.744199\pi$
$462$	−33.9824	+	61.0795i	−0.0735551	+	0.132207i
$463$	−276.754	+	276.754i	−0.597742	+	0.597742i	−0.939711	−	0.341970i	$-0.888906\pi$
$463$	−276.754	+	276.754i	−0.597742	+	0.597742i	0.341970	+	0.939711i	$0.388906\pi$
$464$	−39.6584	−	271.469i	−0.0854708	−	0.585063i
$465$	−183.351	−	162.782i	−0.394303	−	0.350069i
$466$	295.927	−	135.348i	0.635037	−	0.290446i
$467$	446.447	+	446.447i	0.955989	+	0.955989i	0.999072	−	0.0430827i	$-0.0137179\pi$
$467$	446.447	+	446.447i	0.955989	+	0.955989i	−0.0430827	+	0.999072i	$0.513718\pi$
$468$	44.4483	+	611.743i	0.0949750	+	1.30714i
$469$	−252.008			−0.537330
$470$	−53.7837	−	101.244i	−0.114433	−	0.215412i
$471$		−	29.5491i		−	0.0627370i
$472$	−396.079	−	722.448i	−0.839150	−	1.53061i
$473$	196.230	+	266.821i	0.414862	+	0.564103i
$474$	105.134	+	229.867i	0.221802	+	0.484952i
$475$	−65.2464	−	547.049i	−0.137361	−	1.15168i
$476$	121.396	+	104.950i	0.255034	+	0.220483i
$477$	−199.360	+	199.360i	−0.417946	+	0.417946i
$478$	219.140	−	588.554i	0.458453	−	1.23129i
$479$		−	36.0860i		−	0.0753362i	−0.999290	−	0.0376681i	$-0.988007\pi$
$479$		−	36.0860i		−	0.0753362i	0.999290	−	0.0376681i	$-0.0119930\pi$
$480$	−95.7965	−	130.459i	−0.199576	−	0.271789i
$481$		−	729.970i		−	1.51761i
$482$	309.783	−	831.997i	0.642703	−	1.72614i
$483$	58.6503	+	58.6503i	0.121429	+	0.121429i
$484$	255.190	+	411.259i	0.527253	+	0.849708i
$485$	−170.200	+	191.706i	−0.350927	+	0.395269i
$486$	−381.234	+	174.364i	−0.784433	+	0.358775i
$487$	−121.404	−	121.404i	−0.249289	−	0.249289i	0.571390	−	0.820679i	$-0.306405\pi$
$487$	−121.404	−	121.404i	−0.249289	−	0.249289i	−0.820679	+	0.571390i	$0.806405\pi$
$488$	263.784	−	144.619i	0.540541	−	0.296349i
$489$		−	300.583i		−	0.614690i
$490$	−114.562	+	374.215i	−0.233799	+	0.763703i
$491$	746.205			1.51977			0.759883	−	0.650060i	$-0.225256\pi$
$491$	746.205			1.51977			0.759883	+	0.650060i	$0.225256\pi$
$492$	12.5838	+	173.191i	0.0255768	+	0.352015i
$493$	−154.875	−	154.875i	−0.314148	−	0.314148i
$494$	352.397	+	770.488i	0.713354	+	1.55969i
$495$	−40.2737	+	436.866i	−0.0813610	+	0.882558i
$496$	767.461	−	112.117i	1.54730	−	0.226042i
$497$	116.456	+	116.456i	0.234318	+	0.234318i
$498$	−107.041	−	39.8551i	−0.214941	−	0.0800304i
$499$	−795.445			−1.59408			−0.797039	−	0.603928i	$-0.793601\pi$
$499$	−795.445			−1.59408			−0.797039	+	0.603928i	$0.793601\pi$
$500$	−430.184	−	254.836i	−0.860369	−	0.509672i
$501$		−	54.7978i		−	0.109377i
$502$	−167.999	+	451.202i	−0.334659	+	0.898808i
$503$	591.542	+	591.542i	1.17603	+	1.17603i	0.980747	+	0.195281i	$0.0625618\pi$
$503$	591.542	+	591.542i	1.17603	+	1.17603i	0.195281	+	0.980747i	$0.437438\pi$
$504$	56.1390	−	192.399i	0.111387	−	0.381744i
$505$	38.5627	+	648.938i	0.0763617	+	1.28503i
$506$	552.347	−	157.445i	1.09160	−	0.311156i
$507$	143.444	+	143.444i	0.282926	+	0.282926i
$508$	−68.7305	+	4.99385i	−0.135296	+	0.00983042i
$509$		−	435.062i		−	0.854739i	−0.904077	−	0.427370i	$-0.859440\pi$
$509$		−	435.062i		−	0.854739i	0.904077	−	0.427370i	$-0.140560\pi$
$510$	−123.554	−	37.8247i	−0.242263	−	0.0741662i
$511$			85.9703i			0.168239i
$512$	510.875	+	33.9257i	0.997802	+	0.0662611i
$513$	−267.604	+	267.604i	−0.521646	+	0.521646i
$514$	−608.727	+	278.413i	−1.18429	+	0.541659i
$515$	29.7270	−	33.4832i	0.0577223	−	0.0650159i
$516$	92.1666	+	79.6805i	0.178617	+	0.154420i
$517$	74.7141	+	101.591i	0.144515	+	0.196502i
$518$	−83.2302	+	223.535i	−0.160676	+	0.431534i
$519$			304.631i			0.586958i
$520$	749.630	+	171.215i	1.44160	+	0.329260i
$521$	−107.146			−0.205655			−0.102828	−	0.994699i	$-0.532789\pi$
$521$	−107.146			−0.205655			−0.102828	+	0.994699i	$0.532789\pi$
$522$	−95.4516	+	256.358i	−0.182858	+	0.491108i
$523$	120.994	+	120.994i	0.231347	+	0.231347i	0.813255	−	0.581908i	$-0.197694\pi$
$523$	120.994	+	120.994i	0.231347	+	0.231347i	−0.581908	+	0.813255i	$0.697694\pi$
$524$	−624.601	−	539.984i	−1.19199	−	1.03050i
$525$	9.40666	+	78.8688i	0.0179175	+	0.150226i
$526$	−99.4375	−	217.412i	−0.189045	−	0.413331i
$527$	437.842	−	437.842i	0.830819	−	0.830819i
$528$	125.107	+	126.673i	0.236944	+	0.239911i
$529$		−	152.563i		−	0.288399i
$530$	165.819	+	312.141i	0.312866	+	0.588945i
$531$			821.499i			1.54708i
$532$	−20.0626	−	276.122i	−0.0377117	−	0.519027i
$533$	−583.341	−	583.341i	−1.09445	−	1.09445i
$534$	46.0959	+	100.785i	0.0863220	+	0.188736i
$535$	−495.744	+	558.384i	−0.926623	+	1.04371i
$536$	−179.801	+	616.212i	−0.335449	+	1.14965i
$537$	−163.215	+	163.215i	−0.303939	+	0.303939i
$538$	110.975	−	298.049i	0.206273	−	0.553995i
$539$	64.8779	−	425.577i	0.120367	−	0.789567i
$540$	45.1670	+	340.484i	0.0836426	+	0.630525i
$541$		−	96.6598i		−	0.178669i	−0.996002	−	0.0893344i	$-0.971526\pi$
$541$		−	96.6598i		−	0.178669i	0.996002	−	0.0893344i	$-0.0284740\pi$
$542$	−500.274	−	186.270i	−0.923015	−	0.343672i
$543$	25.0221	−	25.0221i	0.0460812	−	0.0460812i
$544$	343.238	−	221.960i	0.630952	−	0.408014i
$545$	−144.487	+	8.58605i	−0.265114	+	0.0157542i
$546$	−50.8055	−	111.082i	−0.0930505	−	0.203447i
$547$	−338.435	+	338.435i	−0.618710	+	0.618710i	−0.945201	−	0.326490i	$-0.894134\pi$
$547$	−338.435	+	338.435i	−0.618710	+	0.618710i	0.326490	+	0.945201i	$0.394134\pi$
$548$	306.194	−	22.2476i	0.558748	−	0.0405978i
$549$	−299.950			−0.546358
$550$	508.907	+	208.598i	0.925286	+	0.379270i
$551$			377.868i			0.685786i
$552$	185.258	−	101.567i	0.335612	−	0.183998i
$553$	277.466	+	277.466i	0.501746	+	0.501746i
$554$	8.69649	+	19.0142i	0.0156976	+	0.0343216i
$555$	−11.3932	−	191.726i	−0.0205283	−	0.345452i
$556$	216.868	−	250.852i	0.390050	−	0.451172i
$557$	218.540	+	218.540i	0.392352	+	0.392352i	0.875525	−	0.483173i	$-0.160516\pi$
$557$	218.540	+	218.540i	0.392352	+	0.392352i	−0.483173	+	0.875525i	$0.660516\pi$
$558$	−724.742	−	269.848i	−1.29882	−	0.483598i
$559$	−578.813			−1.03544
$560$	−210.033	−	137.902i	−0.375060	−	0.246254i
$561$	140.512	+	21.4207i	0.250468	+	0.0381831i
$562$	−307.941	+	827.051i	−0.547938	+	1.47162i
$563$	192.400	+	192.400i	0.341740	+	0.341740i	0.857021	−	0.515281i	$-0.172312\pi$
$563$	192.400	+	192.400i	0.341740	+	0.341740i	−0.515281	+	0.857021i	$0.672312\pi$
$564$	35.0922	+	30.3381i	0.0622202	+	0.0537910i
$565$	795.059	+	705.868i	1.40718	+	1.24932i
$566$	−117.285	−	256.435i	−0.207218	−	0.453065i
$567$	−120.854	+	120.854i	−0.213146	+	0.213146i
$568$	367.848	−	201.671i	0.647619	−	0.355055i
$569$	770.119			1.35346			0.676730	−	0.736231i	$-0.263396\pi$
$569$	770.119			1.35346			0.676730	+	0.736231i	$0.263396\pi$
$570$	104.583	+	196.868i	0.183478	+	0.345383i
$571$	−353.045			−0.618293			−0.309147	−	0.951014i	$-0.600043\pi$
$571$	−353.045			−0.618293			−0.309147	+	0.951014i	$0.600043\pi$
$572$	−843.206	−	66.5412i	−1.47414	−	0.116331i
$573$	169.090	+	169.090i	0.295095	+	0.295095i
$574$	112.122	+	245.145i	0.195334	+	0.427082i
$575$	403.602	−	512.915i	0.701917	−	0.892027i
$576$	−430.402	−	274.543i	−0.747225	−	0.476637i
$577$	−382.173	+	382.173i	−0.662344	+	0.662344i	−0.955932	−	0.293588i	$-0.905151\pi$
$577$	−382.173	+	382.173i	−0.662344	+	0.662344i	0.293588	+	0.955932i	$0.405151\pi$
$578$	−87.8181	+	235.857i	−0.151935	+	0.408057i
$579$			194.703i			0.336274i
$580$	272.277	+	208.500i	0.469443	+	0.359482i
$581$	−177.313			−0.305186
$582$	36.1951	−	97.2107i	0.0621909	−	0.167029i
$583$	−230.349	−	313.213i	−0.395109	−	0.537244i
$584$	210.215	+	61.3376i	0.359958	+	0.105030i
$585$	−573.340	−	509.021i	−0.980068	−	0.870121i
$586$	670.025	−	306.448i	1.14339	−	0.522949i
$587$	286.984	+	286.984i	0.488899	+	0.488899i	0.907959	−	0.419059i	$-0.137640\pi$
$587$	286.984	+	286.984i	0.488899	+	0.488899i	−0.419059	+	0.907959i	$0.637640\pi$
$588$	−11.4757	−	157.940i	−0.0195164	−	0.268605i
$589$	−1068.26			−1.81368
$590$	984.760	+	301.473i	1.66909	+	0.510972i
$591$	1.29835			0.00219687
$592$	487.207	+	363.001i	0.822984	+	0.613178i
$593$	−548.319	+	548.319i	−0.924652	+	0.924652i	−0.997354	−	0.0727017i	$-0.976838\pi$
$593$	−548.319	+	548.319i	−0.924652	+	0.924652i	0.0727017	+	0.997354i	$0.476838\pi$
$594$	−103.569	−	363.340i	−0.174358	−	0.611684i
$595$	−200.238	+	11.8990i	−0.336534	+	0.0199983i
$596$	−226.783	−	196.060i	−0.380508	−	0.328959i
$597$	−79.2047	+	79.2047i	−0.132671	+	0.132671i
$598$	−350.232	+	940.632i	−0.585672	+	1.57296i
$599$	280.389			0.468095			0.234047	−	0.972225i	$-0.424803\pi$
$599$	280.389			0.468095			0.234047	+	0.972225i	$0.424803\pi$
$600$	199.562	+	33.2696i	0.332604	+	0.0554493i
$601$			277.723i			0.462101i	0.972942	+	0.231050i	$0.0742162\pi$
$601$			277.723i			0.462101i	−0.972942	+	0.231050i	$0.925784\pi$
$602$	177.247	+	65.9955i	0.294430	+	0.109627i
$603$	452.575	−	452.575i	0.750539	−	0.750539i
$604$	89.2846	+	77.1889i	0.147822	+	0.127796i
$605$	−587.195	−	145.696i	−0.970570	−	0.240820i
$606$	−109.408	−	239.212i	−0.180541	−	0.394739i
$607$	546.262	−	546.262i	0.899937	−	0.899937i	−0.0954931	−	0.995430i	$-0.530443\pi$
$607$	546.262	−	546.262i	0.899937	−	0.899937i	0.995430	+	0.0954931i	$0.0304428\pi$
$608$	−689.491	−	147.949i	−1.13403	−	0.243337i
$609$		−	54.4777i		−	0.0894544i
$610$	−110.076	+	359.561i	−0.180452	+	0.589444i
$611$	−220.382			−0.360690
$612$	−406.490	+	29.5349i	−0.664199	+	0.0482597i
$613$	247.426	−	247.426i	0.403632	−	0.403632i	−0.475879	−	0.879511i	$-0.657870\pi$
$613$	247.426	−	247.426i	0.403632	−	0.403632i	0.879511	+	0.475879i	$0.157870\pi$
$614$	515.147	−	235.612i	0.839002	−	0.383733i
$615$	−162.319	−	144.110i	−0.263933	−	0.234325i
$616$	250.624	+	116.518i	0.406856	+	0.189152i
$617$	−146.415	+	146.415i	−0.237302	+	0.237302i	−0.815732	−	0.578430i	$-0.803666\pi$
$617$	−146.415	+	146.415i	−0.237302	+	0.237302i	0.578430	+	0.815732i	$0.303666\pi$
$618$	−6.32182	+	16.9788i	−0.0102295	+	0.0274737i
$619$	−126.439			−0.204264			−0.102132	−	0.994771i	$-0.532566\pi$
$619$	−126.439			−0.204264			−0.102132	+	0.994771i	$0.532566\pi$
$620$	−589.442	+	769.745i	−0.950712	+	1.24152i
$621$	−448.340			−0.721964
$622$	−37.6802	+	101.199i	−0.0605791	+	0.162700i
$623$	121.655	+	121.655i	0.195272	+	0.195272i
$624$	−307.868	+	44.9758i	−0.493378	+	0.0720767i
$625$	607.468	−	146.996i	0.971948	−	0.235194i
$626$	−269.868	−	590.046i	−0.431099	−	0.942565i
$627$	−145.282	−	197.544i	−0.231709	−	0.315063i
$628$	−116.536	+	8.46733i	−0.185567	+	0.0134830i
$629$	485.049			0.771143
$630$	117.533	+	221.246i	0.186560	+	0.351184i
$631$			477.322i			0.756453i	0.925713	+	0.378226i	$0.123466\pi$
$631$			477.322i			0.756453i	−0.925713	+	0.378226i	$0.876534\pi$
$632$	876.427	−	480.497i	1.38675	−	0.760281i
$633$	115.383	−	115.383i	0.182279	−	0.182279i
$634$	−369.182	+	168.852i	−0.582306	+	0.266329i
$635$	57.1895	−	64.4158i	0.0900622	−	0.101442i
$636$	−108.192	−	93.5346i	−0.170113	−	0.147067i
$637$	531.971	+	531.971i	0.835119	+	0.835119i
$638$	−329.647	−	183.404i	−0.516689	−	0.287467i
$639$	−418.282			−0.654588
$640$	−487.053	+	415.186i	−0.761020	+	0.648728i
$641$	612.843			0.956073			0.478037	−	0.878340i	$-0.341349\pi$
$641$	612.843			0.956073			0.478037	+	0.878340i	$0.341349\pi$
$642$	105.426	−	283.147i	0.164215	−	0.441040i
$643$	444.097	−	444.097i	0.690663	−	0.690663i	−0.271714	−	0.962378i	$-0.587591\pi$
$643$	444.097	−	444.097i	0.690663	−	0.690663i	0.962378	+	0.271714i	$0.0875906\pi$
$644$	214.499	−	248.112i	0.333073	−	0.385267i
$645$	−152.025	+	9.03398i	−0.235698	+	0.0140062i
$646$	−511.973	+	234.160i	−0.792528	+	0.362477i
$647$	757.476	+	757.476i	1.17075	+	1.17075i	0.982031	+	0.188719i	$0.0604336\pi$
$647$	757.476	+	757.476i	1.17075	+	1.17075i	0.188719	+	0.982031i	$0.439566\pi$
$648$	209.287	+	381.738i	0.322973	+	0.589103i
$649$	−1119.92	−	170.729i	−1.72561	−	0.263065i
$650$	−820.585	+	500.482i	−1.26244	+	0.769973i
$651$	154.012			0.236578
$652$	−1185.44	+	86.1324i	−1.81816	+	0.132105i
$653$	268.042	+	268.042i	0.410478	+	0.410478i	0.881905	−	0.471427i	$-0.156261\pi$
$653$	268.042	+	268.042i	0.410478	+	0.410478i	−0.471427	+	0.881905i	$0.656261\pi$
$654$	53.2610	−	24.3599i	0.0814388	−	0.0372475i
$655$	1030.25	−	61.2221i	1.57291	−	0.0934688i
$656$	679.427	−	99.2562i	1.03571	−	0.151305i
$657$	−154.392	−	154.392i	−0.234996	−	0.234996i
$658$	67.4863	+	25.1276i	0.102563	+	0.0381879i
$659$			340.314i			0.516409i	0.966090	+	0.258205i	$0.0831309\pi$
$659$			340.314i			0.516409i	−0.966090	+	0.258205i	$0.916869\pi$
$660$	−222.506	−	4.31647i	−0.337131	−	0.00654010i
$661$	255.455			0.386468			0.193234	−	0.981153i	$-0.438102\pi$
$661$	255.455			0.386468			0.193234	+	0.981153i	$0.438102\pi$
$662$	−231.165	+	620.849i	−0.349192	+	0.937839i
$663$	−175.641	+	175.641i	−0.264918	+	0.264918i
$664$	−126.508	+	433.568i	−0.190525	+	0.652964i
$665$	258.788	+	229.757i	0.389155	+	0.345499i
$666$	−251.970	−	550.912i	−0.378333	−	0.827196i
$667$	−316.537	+	316.537i	−0.474568	+	0.474568i
$668$	−216.112	+	15.7023i	−0.323521	+	0.0235065i
$669$			117.277i			0.175301i
$670$	−376.432	−	708.604i	−0.561839	−	1.05762i
$671$	62.3374	−	408.912i	0.0929023	−	0.609407i
$672$	99.4049	+	21.3300i	0.147924	+	0.0317410i
$673$	891.991	−	891.991i	1.32540	−	1.32540i	0.416057	−	0.909339i	$-0.363412\pi$
$673$	891.991	−	891.991i	1.32540	−	1.32540i	0.909339	−	0.416057i	$-0.136588\pi$
$674$	324.187	+	708.809i	0.480989	+	1.05164i
$675$	−337.401	−	265.494i	−0.499854	−	0.393325i
$676$	524.610	−	606.817i	0.776050	−	0.897659i
$677$	597.002	+	597.002i	0.881835	+	0.881835i	0.993721	−	0.111886i	$-0.0356891\pi$
$677$	597.002	+	597.002i	0.881835	+	0.881835i	−0.111886	+	0.993721i	$0.535689\pi$
$678$	−403.161	−	150.112i	−0.594633	−	0.221404i
$679$		−	161.030i		−	0.237157i
$680$	−113.769	+	498.113i	−0.167307	+	0.732519i
$681$		−	166.062i		−	0.243851i
$682$	518.495	−	931.934i	0.760256	−	1.36647i
$683$	−131.657	+	131.657i	−0.192763	+	0.192763i	−0.796889	−	0.604126i	$-0.793522\pi$
$683$	−131.657	+	131.657i	−0.192763	+	0.192763i	0.604126	+	0.796889i	$0.293522\pi$
$684$	531.912	+	459.852i	0.777650	+	0.672299i
$685$	−254.779	+	286.972i	−0.371940	+	0.418937i
$686$	−230.268	−	503.463i	−0.335667	−	0.733910i
$687$	−19.9401	−	19.9401i	−0.0290249	−	0.0290249i
$688$	287.834	−	386.320i	0.418363	−	0.561511i
$689$	679.452			0.986143
$690$	−77.3070	+	252.523i	−0.112039	+	0.365975i
$691$		−	113.690i		−	0.164530i	−0.996610	−	0.0822651i	$-0.973785\pi$
$691$		−	113.690i		−	0.164530i	0.996610	−	0.0822651i	$-0.0262154\pi$
$692$	1201.41	−	87.2924i	1.73614	−	0.126145i
$693$	−163.272	−	222.006i	−0.235601	−	0.320355i
$694$	132.104	−	60.4201i	0.190351	−	0.0870607i
$695$	24.5880	+	413.770i	0.0353784	+	0.595352i
$696$	−133.209	−	38.8684i	−0.191393	−	0.0558454i
$697$	387.618	−	387.618i	0.556123	−	0.556123i
$698$	−747.053	−	278.155i	−1.07028	−	0.398503i
$699$		−	164.590i		−	0.235465i
$700$	308.348	−	59.6980i	0.440497	−	0.0852828i
$701$		−	881.751i		−	1.25785i	−0.777467	−	0.628923i	$-0.783496\pi$
$701$		−	881.751i		−	1.25785i	0.777467	−	0.628923i	$-0.216504\pi$
$702$	618.759	+	230.386i	0.881422	+	0.328186i
$703$	−591.717	−	591.717i	−0.841703	−	0.841703i
$704$	463.724	−	529.695i	0.658698	−	0.752407i
$705$	−57.8832	+	3.43967i	−0.0821038	+	0.00487896i
$706$	−78.3085	−	171.215i	−0.110919	−	0.242515i
$707$	−288.745	−	288.745i	−0.408409	−	0.408409i
$708$	−415.625	+	30.1986i	−0.587041	+	0.0426535i
$709$		−	571.537i		−	0.806117i	−0.915174	−	0.403059i	$-0.867947\pi$
$709$		−	571.537i		−	0.806117i	0.915174	−	0.403059i	$-0.132053\pi$
$710$	−153.501	+	501.409i	−0.216198	+	0.706210i
$711$	−996.590			−1.40167
$712$	384.268	−	210.674i	0.539703	−	0.295890i
$713$	−894.870	−	894.870i	−1.25508	−	1.25508i
$714$	73.8118	−	33.7592i	0.103378	−	0.0472818i
$715$	813.086	−	675.826i	1.13718	−	0.945212i
$716$	690.459	+	596.920i	0.964328	+	0.833687i
$717$	−224.613	−	224.613i	−0.313268	−	0.313268i
$718$	−114.855	+	308.471i	−0.159965	+	0.429625i
$719$	−967.150			−1.34513			−0.672566	−	0.740037i	$-0.734808\pi$
$719$	−967.150			−1.34513			−0.672566	+	0.740037i	$0.734808\pi$
$720$	624.850	−	129.539i	0.867847	−	0.179915i
$721$			28.1254i			0.0390089i
$722$	233.597	+	86.9767i	0.323542	+	0.120466i
$723$	−317.519	−	317.519i	−0.439169	−	0.439169i
$724$	−105.852	−	91.5121i	−0.146205	−	0.126398i
$725$	−425.656	+	50.7679i	−0.587112	+	0.0700247i
$726$	242.850	−	30.8607i	0.334504	−	0.0425079i
$727$	209.678	+	209.678i	0.288415	+	0.288415i	0.836453	−	0.548038i	$-0.184625\pi$
$727$	209.678	+	209.678i	0.288415	+	0.288415i	−0.548038	+	0.836453i	$0.684625\pi$
$728$	−423.529	+	232.198i	−0.581770	+	0.318953i
$729$		−	277.727i		−	0.380970i
$730$	−241.734	+	128.417i	−0.331143	+	0.175913i
$731$		−	384.609i		−	0.526141i
$732$	−11.0263	−	151.755i	−0.0150632	−	0.207316i
$733$	−2.42183	+	2.42183i	−0.00330400	+	0.00330400i	−0.708757	−	0.705453i	$-0.750744\pi$
$733$	−2.42183	+	2.42183i	−0.00330400	+	0.00330400i	0.705453	+	0.708757i	$0.250744\pi$
$734$	−25.8889	−	56.6041i	−0.0352710	−	0.0771173i
$735$	148.025	+	131.419i	0.201394	+	0.178801i
$736$	−453.646	−	701.517i	−0.616367	−	0.953148i
$737$	522.923	+	711.037i	0.709530	+	0.964772i
$738$	−641.608	−	238.894i	−0.869387	−	0.323705i
$739$			895.710i			1.21206i	0.795443	+	0.606028i	$0.207238\pi$
$739$			895.710i			1.21206i	−0.795443	+	0.606028i	$0.792762\pi$
$740$	−752.866	+	99.8718i	−1.01739	+	0.134962i
$741$	428.532			0.578316
$742$	−208.065	−	77.4702i	−0.280411	−	0.104407i
$743$	−1025.20	−	1025.20i	−1.37981	−	1.37981i	−0.844926	−	0.534883i	$-0.820356\pi$
$743$	−1025.20	−	1025.20i	−1.37981	−	1.37981i	−0.534883	−	0.844926i	$-0.679644\pi$
$744$	109.884	−	376.592i	0.147693	−	0.506171i
$745$	374.069	−	22.2288i	0.502106	−	0.0298373i
$746$	46.0036	−	21.0406i	0.0616671	−	0.0282046i
$747$	318.433	−	318.433i	0.426282	−	0.426282i
$748$	44.2152	−	560.292i	0.0591113	−	0.749054i
$749$		−	469.035i		−	0.626215i
$750$	−207.715	+	144.259i	−0.276953	+	0.192345i
$751$			57.9172i			0.0771201i	0.999256	+	0.0385601i	$0.0122771\pi$
$751$			57.9172i			0.0771201i	−0.999256	+	0.0385601i	$0.987723\pi$
$752$	109.592	−	147.090i	0.145734	−	0.195599i
$753$	172.194	+	172.194i	0.228678	+	0.228678i
$754$	599.513	−	274.199i	0.795111	−	0.363659i
$755$	−147.271	+	8.75149i	−0.195061	+	0.0115914i
$756$	−163.211	−	141.100i	−0.215887	−	0.186640i
$757$	438.030	−	438.030i	0.578639	−	0.578639i	−0.355889	−	0.934528i	$-0.615822\pi$
$757$	438.030	−	438.030i	0.578639	−	0.578639i	0.934528	+	0.355889i	$0.115822\pi$
$758$	973.330	+	362.406i	1.28408	+	0.478109i
$759$	43.7801	−	287.183i	0.0576813	−	0.378370i
$760$	746.442	−	468.866i	0.982161	−	0.616929i
$761$			488.849i			0.642377i	0.947015	+	0.321189i	$0.104082\pi$
$761$			488.849i			0.642377i	−0.947015	+	0.321189i	$0.895918\pi$
$762$	−12.1621	+	32.6642i	−0.0159607	+	0.0428664i
$763$	64.2897	−	64.2897i	0.0842591	−	0.0842591i
$764$	618.404	−	715.310i	0.809430	−	0.936269i
$765$	338.234	−	380.972i	0.442135	−	0.498002i
$766$	−493.296	+	225.618i	−0.643989	+	0.294540i
$767$	1399.90	−	1399.90i	1.82517	−	1.82517i
$768$	123.079	−	227.847i	0.160259	−	0.296676i
$769$	524.235			0.681710			0.340855	−	0.940116i	$-0.389283\pi$
$769$	524.235			0.681710			0.340855	+	0.940116i	$0.389283\pi$
$770$	−326.044	+	114.248i	−0.423433	+	0.148374i
$771$			338.564i			0.439123i
$772$	767.870	−	55.7923i	0.994651	−	0.0722698i

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+(-1.87429 - 0.697868i) q^{2} +(-0.715296 + 0.715296i) q^{3} +(3.02596 + 2.61602i) q^{4} +(-4.99120 + 0.296598i) q^{5} +(1.83986 - 0.841493i) q^{6} +(2.22084 - 2.22084i) q^{7} +(-3.84590 - 7.01492i) q^{8} +7.97670i q^{9} +(9.56196 + 2.92729i) q^{10} +(-10.8744 - 1.65777i) q^{11} +(-4.03569 + 0.293227i) q^{12} +(13.5930 - 13.5930i) q^{13} +(-5.71235 + 2.61265i) q^{14} +(3.35803 - 3.78234i) q^{15} +(2.31286 + 15.8320i) q^{16} +(9.03223 + 9.03223i) q^{17} +(5.56669 - 14.9507i) q^{18} -22.0371i q^{19} +(-15.8791 - 12.1596i) q^{20} +3.17711i q^{21} +(19.2249 + 10.6960i) q^{22} +(18.4603 - 18.4603i) q^{23} +(7.76870 + 2.26679i) q^{24} +(24.8241 - 2.96076i) q^{25} +(-34.9633 + 15.9911i) q^{26} +(-12.1434 - 12.1434i) q^{27} +(12.5299 - 0.910404i) q^{28} -17.1469 q^{29} +(-8.93351 + 4.74576i) q^{30} -48.4755i q^{31} +(6.71364 - 31.2878i) q^{32} +(8.96419 - 6.59260i) q^{33} +(-10.6257 - 23.2324i) q^{34} +(-10.4259 + 11.7433i) q^{35} +(-20.8672 + 24.1372i) q^{36} +(26.8510 - 26.8510i) q^{37} +(-15.3790 + 41.3039i) q^{38} +19.4460i q^{39} +(21.2762 + 33.8721i) q^{40} -42.9149i q^{41} +(2.21721 - 5.95484i) q^{42} +(-21.2909 - 21.2909i) q^{43} +(-28.5686 - 33.4639i) q^{44} +(-2.36588 - 39.8133i) q^{45} +(-47.4828 + 21.7171i) q^{46} +(-8.10647 - 8.10647i) q^{47} +(-12.9789 - 9.67016i) q^{48} +39.1358i q^{49} +(-48.5938 - 11.7746i) q^{50} -12.9214 q^{51} +(76.6912 - 5.57226i) q^{52} +(24.9928 + 24.9928i) q^{53} +(14.2858 + 31.2347i) q^{54} +(54.7678 + 5.04891i) q^{55} +(-24.1201 - 7.03787i) q^{56} +(15.7630 + 15.7630i) q^{57} +(32.1384 + 11.9663i) q^{58} +102.987 q^{59} +(20.0559 - 2.66053i) q^{60} +37.6033i q^{61} +(-33.8295 + 90.8573i) q^{62} +(17.7149 + 17.7149i) q^{63} +(-34.4181 + 53.9573i) q^{64} +(-63.8135 + 71.8768i) q^{65} +(-21.4023 + 6.10065i) q^{66} +(-56.7371 - 56.7371i) q^{67} +(3.70265 + 50.9597i) q^{68} +26.4091i q^{69} +(27.7366 - 14.7345i) q^{70} +52.4379i q^{71} +(55.9559 - 30.6776i) q^{72} +(-19.3554 + 19.3554i) q^{73} +(-69.0652 + 31.5882i) q^{74} +(-15.6387 + 19.8744i) q^{75} +(57.6494 - 66.6832i) q^{76} +(-27.8318 + 20.4686i) q^{77} +(13.5707 - 36.4475i) q^{78} +124.938i q^{79} +(-16.2397 - 78.3344i) q^{80} -54.4181 q^{81} +(-29.9490 + 80.4352i) q^{82} +(-39.9204 - 39.9204i) q^{83} +(-8.31139 + 9.61381i) q^{84} +(-47.7606 - 42.4027i) q^{85} +(25.0472 + 54.7637i) q^{86} +(12.2651 - 12.2651i) q^{87} +(30.1926 + 82.6584i) q^{88} +54.7788i q^{89} +(-23.3501 + 76.2729i) q^{90} -60.3755i q^{91} +(104.152 - 7.56756i) q^{92} +(34.6743 + 34.6743i) q^{93} +(9.53666 + 20.8512i) q^{94} +(6.53615 + 109.991i) q^{95} +(17.5778 + 27.1823i) q^{96} +(36.2543 - 36.2543i) q^{97} +(27.3116 - 73.3520i) q^{98} +(13.2235 - 86.7416i) 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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