LMFDB - Embedded newform 210.3.c.a.29.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(29,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("210.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.c (of order $2$, degree $1$, 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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.14
Character	$\chi$	$=$	210.29
Dual form			210.3.c.a.29.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(-2.88523 + 0.821846i) q^{3} +2.00000 q^{4} +(-4.52398 - 2.12923i) q^{5} +(-4.08034 + 1.16227i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(7.64914 - 4.74244i) q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(-2.88523 + 0.821846i) q^{3} +2.00000 q^{4} +(-4.52398 - 2.12923i) q^{5} +(-4.08034 + 1.16227i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(7.64914 - 4.74244i) q^{9} +(-6.39787 - 3.01119i) q^{10} -18.1525i q^{11} +(-5.77047 + 1.64369i) q^{12} -22.5480i q^{13} +3.74166i q^{14} +(14.8026 + 2.42532i) q^{15} +4.00000 q^{16} -0.457150 q^{17} +(10.8175 - 6.70682i) q^{18} -30.1627 q^{19} +(-9.04795 - 4.25847i) q^{20} +(-2.17440 - 7.63361i) q^{21} -25.6715i q^{22} -12.3975 q^{23} +(-8.16067 + 2.32453i) q^{24} +(15.9327 + 19.2652i) q^{25} -31.8877i q^{26} +(-18.1720 + 19.9694i) q^{27} +5.29150i q^{28} +4.70721i q^{29} +(20.9341 + 3.42992i) q^{30} +45.2664 q^{31} +5.65685 q^{32} +(14.9186 + 52.3743i) q^{33} -0.646507 q^{34} +(5.63342 - 11.9693i) q^{35} +(15.2983 - 9.48487i) q^{36} -32.9891i q^{37} -42.6564 q^{38} +(18.5310 + 65.0563i) q^{39} +(-12.7957 - 6.02238i) q^{40} -22.9427i q^{41} +(-3.07507 - 10.7956i) q^{42} +20.2697i q^{43} -36.3050i q^{44} +(-44.7023 + 5.16787i) q^{45} -17.5327 q^{46} -9.67333 q^{47} +(-11.5409 + 3.28739i) q^{48} -7.00000 q^{49} +(22.5323 + 27.2451i) q^{50} +(1.31898 - 0.375707i) q^{51} -45.0960i q^{52} +5.97465 q^{53} +(-25.6991 + 28.2411i) q^{54} +(-38.6510 + 82.1216i) q^{55} +7.48331i q^{56} +(87.0263 - 24.7891i) q^{57} +6.65700i q^{58} +112.848i q^{59} +(29.6053 + 4.85064i) q^{60} -56.3832 q^{61} +64.0163 q^{62} +(12.5473 + 20.2377i) q^{63} +8.00000 q^{64} +(-48.0100 + 102.007i) q^{65} +(21.0981 + 74.0684i) q^{66} -67.1684i q^{67} -0.914300 q^{68} +(35.7696 - 10.1888i) q^{69} +(7.96686 - 16.9272i) q^{70} +20.9402i q^{71} +(21.6350 - 13.4136i) q^{72} -97.7885i q^{73} -46.6536i q^{74} +(-61.8027 - 42.4903i) q^{75} -60.3253 q^{76} +48.0271 q^{77} +(26.2068 + 92.0034i) q^{78} -41.4047 q^{79} +(-18.0959 - 8.51693i) q^{80} +(36.0186 - 72.5511i) q^{81} -32.4459i q^{82} +121.926 q^{83} +(-4.34880 - 15.2672i) q^{84} +(2.06814 + 0.973379i) q^{85} +28.6657i q^{86} +(-3.86860 - 13.5814i) q^{87} -51.3431i q^{88} +26.8148i q^{89} +(-63.2186 + 7.30848i) q^{90} +59.6564 q^{91} -24.7950 q^{92} +(-130.604 + 37.2020i) q^{93} -13.6802 q^{94} +(136.455 + 64.2233i) q^{95} +(-16.3213 + 4.64907i) q^{96} -151.512i q^{97} -9.89949 q^{98} +(-86.0872 - 138.851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 48 q^{4} + 44 q^{9}+O(q^{10}) $ 24 * q + 48 * q^4 + 44 * q^9	$ 24 q + 48 q^{4} + 44 q^{9} + 16 q^{10} + 4 q^{15} + 96 q^{16} - 80 q^{19} - 28 q^{21} + 48 q^{25} - 56 q^{30} + 224 q^{31} + 128 q^{34} + 88 q^{36} - 92 q^{39} + 32 q^{40} - 72 q^{45} - 144 q^{46} - 168 q^{49} - 284 q^{51} - 144 q^{54} - 320 q^{55} + 8 q^{60} + 192 q^{64} + 224 q^{66} - 152 q^{69} - 56 q^{70} + 48 q^{75} - 160 q^{76} - 72 q^{79} - 212 q^{81} - 56 q^{84} - 64 q^{85} - 240 q^{90} + 168 q^{91} - 128 q^{94} - 876 q^{99}+O(q^{100}) $ 24 * q + 48 * q^4 + 44 * q^9 + 16 * q^10 + 4 * q^15 + 96 * q^16 - 80 * q^19 - 28 * q^21 + 48 * q^25 - 56 * q^30 + 224 * q^31 + 128 * q^34 + 88 * q^36 - 92 * q^39 + 32 * q^40 - 72 * q^45 - 144 * q^46 - 168 * q^49 - 284 * q^51 - 144 * q^54 - 320 * q^55 + 8 * q^60 + 192 * q^64 + 224 * q^66 - 152 * q^69 - 56 * q^70 + 48 * q^75 - 160 * q^76 - 72 * q^79 - 212 * q^81 - 56 * q^84 - 64 * q^85 - 240 * q^90 + 168 * q^91 - 128 * q^94 - 876 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$	−2.88523	+	0.821846i	−0.961744	+	0.273949i
$3$	−2.88523	+	0.821846i	−0.961744	+	0.273949i
$4$	2.00000			0.500000
$5$	−4.52398	−	2.12923i	−0.904795	−	0.425847i
$5$	−4.52398	−	2.12923i	−0.904795	−	0.425847i
$6$	−4.08034	+	1.16227i	−0.680056	+	0.193711i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	2.82843			0.353553
$9$	7.64914	−	4.74244i	0.849904	−	0.526937i
$10$	−6.39787	−	3.01119i	−0.639787	−	0.301119i
$11$		−	18.1525i		−	1.65023i	−0.564965	−	0.825115i	$-0.691110\pi$
$11$		−	18.1525i		−	1.65023i	0.564965	−	0.825115i	$-0.308890\pi$
$12$	−5.77047	+	1.64369i	−0.480872	+	0.136974i
$13$		−	22.5480i		−	1.73446i	−0.497906	−	0.867231i	$-0.665897\pi$
$13$		−	22.5480i		−	1.73446i	0.497906	−	0.867231i	$-0.334103\pi$
$14$			3.74166i			0.267261i
$15$	14.8026	+	2.42532i	0.986842	+	0.161688i
$16$	4.00000			0.250000
$17$	−0.457150			−0.0268912			−0.0134456	−	0.999910i	$-0.504280\pi$
$17$	−0.457150			−0.0268912			−0.0134456	+	0.999910i	$0.504280\pi$
$18$	10.8175	−	6.70682i	0.600973	−	0.372601i
$19$	−30.1627			−1.58751			−0.793754	−	0.608239i	$-0.791876\pi$
$19$	−30.1627			−1.58751			−0.793754	+	0.608239i	$0.791876\pi$
$20$	−9.04795	−	4.25847i	−0.452398	−	0.212923i
$21$	−2.17440	−	7.63361i	−0.103543	−	0.363505i
$22$		−	25.6715i		−	1.16689i
$23$	−12.3975			−0.539021			−0.269510	−	0.962997i	$-0.586862\pi$
$23$	−12.3975			−0.539021			−0.269510	+	0.962997i	$0.586862\pi$
$24$	−8.16067	+	2.32453i	−0.340028	+	0.0968555i
$25$	15.9327	+	19.2652i	0.637309	+	0.770608i
$26$		−	31.8877i		−	1.22645i
$27$	−18.1720	+	19.9694i	−0.673037	+	0.739609i
$28$			5.29150i			0.188982i
$29$			4.70721i			0.162318i	0.996701	+	0.0811588i	$0.0258621\pi$
$29$			4.70721i			0.162318i	−0.996701	+	0.0811588i	$0.974138\pi$
$30$	20.9341	+	3.42992i	0.697803	+	0.114331i
$31$	45.2664			1.46021			0.730103	−	0.683337i	$-0.239472\pi$
$31$	45.2664			1.46021			0.730103	+	0.683337i	$0.239472\pi$
$32$	5.65685			0.176777
$33$	14.9186	+	52.3743i	0.452078	+	1.58710i
$34$	−0.646507			−0.0190149
$35$	5.63342	−	11.9693i	0.160955	−	0.341980i
$36$	15.2983	−	9.48487i	0.424952	−	0.263469i
$37$		−	32.9891i		−	0.891597i	−0.895133	−	0.445798i	$-0.852920\pi$
$37$		−	32.9891i		−	0.891597i	0.895133	−	0.445798i	$-0.147080\pi$
$38$	−42.6564			−1.12254
$39$	18.5310	+	65.0563i	0.475154	+	1.66811i
$40$	−12.7957	−	6.02238i	−0.319893	−	0.150560i
$41$		−	22.9427i		−	0.559578i	−0.960062	−	0.279789i	$-0.909736\pi$
$41$		−	22.9427i		−	0.559578i	0.960062	−	0.279789i	$-0.0902644\pi$
$42$	−3.07507	−	10.7956i	−0.0732159	−	0.257037i
$43$			20.2697i			0.471389i	0.971827	+	0.235694i	$0.0757365\pi$
$43$			20.2697i			0.471389i	−0.971827	+	0.235694i	$0.924264\pi$
$44$		−	36.3050i		−	0.825115i
$45$	−44.7023	+	5.16787i	−0.993384	+	0.114842i
$46$	−17.5327			−0.381145
$47$	−9.67333			−0.205816			−0.102908	−	0.994691i	$-0.532815\pi$
$47$	−9.67333			−0.205816			−0.102908	+	0.994691i	$0.532815\pi$
$48$	−11.5409	+	3.28739i	−0.240436	+	0.0684872i
$49$	−7.00000			−0.142857
$50$	22.5323	+	27.2451i	0.450646	+	0.544902i
$51$	1.31898	−	0.375707i	0.0258624	−	0.00736680i
$52$		−	45.0960i		−	0.867231i
$53$	5.97465			0.112729			0.0563646	−	0.998410i	$-0.482049\pi$
$53$	5.97465			0.112729			0.0563646	+	0.998410i	$0.482049\pi$
$54$	−25.6991	+	28.2411i	−0.475909	+	0.522983i
$55$	−38.6510	+	82.1216i	−0.702745	+	1.49312i
$56$			7.48331i			0.133631i
$57$	87.0263	−	24.7891i	1.52678	−	0.434896i
$58$			6.65700i			0.114776i
$59$			112.848i			1.91268i	0.292259	+	0.956339i	$0.405593\pi$
$59$			112.848i			1.91268i	−0.292259	+	0.956339i	$0.594407\pi$
$60$	29.6053	+	4.85064i	0.493421	+	0.0808440i
$61$	−56.3832			−0.924314			−0.462157	−	0.886798i	$-0.652924\pi$
$61$	−56.3832			−0.924314			−0.462157	+	0.886798i	$0.652924\pi$
$62$	64.0163			1.03252
$63$	12.5473	+	20.2377i	0.199164	+	0.321234i
$64$	8.00000			0.125000
$65$	−48.0100	+	102.007i	−0.738615	+	1.56933i
$66$	21.0981	+	74.0684i	0.319668	+	1.12225i
$67$		−	67.1684i		−	1.00251i	−0.865298	−	0.501257i	$-0.832871\pi$
$67$		−	67.1684i		−	1.00251i	0.865298	−	0.501257i	$-0.167129\pi$
$68$	−0.914300			−0.0134456
$69$	35.7696	−	10.1888i	0.518400	−	0.147664i
$70$	7.96686	−	16.9272i	0.113812	−	0.241817i
$71$			20.9402i			0.294932i	0.989067	+	0.147466i	$0.0471117\pi$
$71$			20.9402i			0.294932i	−0.989067	+	0.147466i	$0.952888\pi$
$72$	21.6350	−	13.4136i	0.300486	−	0.186300i
$73$		−	97.7885i		−	1.33957i	−0.742556	−	0.669784i	$-0.766386\pi$
$73$		−	97.7885i		−	1.33957i	0.742556	−	0.669784i	$-0.233614\pi$
$74$		−	46.6536i		−	0.630454i
$75$	−61.8027	−	42.4903i	−0.824036	−	0.566538i
$76$	−60.3253			−0.793754
$77$	48.0271			0.623728
$78$	26.2068	+	92.0034i	0.335985	+	1.17953i
$79$	−41.4047			−0.524110			−0.262055	−	0.965053i	$-0.584400\pi$
$79$	−41.4047			−0.524110			−0.262055	+	0.965053i	$0.584400\pi$
$80$	−18.0959	−	8.51693i	−0.226199	−	0.106462i
$81$	36.0186	−	72.5511i	0.444674	−	0.895692i
$82$		−	32.4459i		−	0.395681i
$83$	121.926			1.46899			0.734496	−	0.678613i	$-0.237419\pi$
$83$	121.926			1.46899			0.734496	+	0.678613i	$0.237419\pi$
$84$	−4.34880	−	15.2672i	−0.0517715	−	0.181753i
$85$	2.06814	+	0.973379i	0.0243310	+	0.0114515i
$86$			28.6657i			0.333322i
$87$	−3.86860	−	13.5814i	−0.0444667	−	0.156108i
$88$		−	51.3431i		−	0.583444i
$89$			26.8148i			0.301289i	0.988588	+	0.150645i	$0.0481349\pi$
$89$			26.8148i			0.301289i	−0.988588	+	0.150645i	$0.951865\pi$
$90$	−63.2186	+	7.30848i	−0.702428	+	0.0812053i
$91$	59.6564			0.655565
$92$	−24.7950			−0.269510
$93$	−130.604	+	37.2020i	−1.40434	+	0.400022i
$94$	−13.6802			−0.145534
$95$	136.455	+	64.2233i	1.43637	+	0.676035i
$96$	−16.3213	+	4.64907i	−0.170014	+	0.0484278i
$97$		−	151.512i		−	1.56198i	−0.624542	−	0.780991i	$-0.714714\pi$
$97$		−	151.512i		−	1.56198i	0.624542	−	0.780991i	$-0.285286\pi$
$98$	−9.89949			−0.101015
$99$	−86.0872	−	138.851i	−0.869567	−	1.40254i
$100$	31.8655	+	38.5304i	0.318655	+	0.385304i
$101$		−	39.3218i		−	0.389324i	−0.980870	−	0.194662i	$-0.937639\pi$
$101$		−	39.3218i		−	0.389324i	0.980870	−	0.194662i	$-0.0623611\pi$
$102$	1.86532	−	0.531330i	0.0182875	−	0.00520912i
$103$			70.2101i			0.681651i	0.940127	+	0.340826i	$0.110707\pi$
$103$			70.2101i			0.681651i	−0.940127	+	0.340826i	$0.889293\pi$
$104$		−	63.7754i		−	0.613225i
$105$	−6.41679	+	39.1641i	−0.0611123	+	0.372991i
$106$	8.44943			0.0797116
$107$	−86.0409			−0.804121			−0.402060	−	0.915613i	$-0.631706\pi$
$107$	−86.0409			−0.804121			−0.402060	+	0.915613i	$0.631706\pi$
$108$	−36.3440	+	39.9389i	−0.336518	+	0.369805i
$109$	46.4448			0.426099			0.213049	−	0.977041i	$-0.431660\pi$
$109$	46.4448			0.426099			0.213049	+	0.977041i	$0.431660\pi$
$110$	−54.6607	+	116.137i	−0.496915	+	1.05580i
$111$	27.1120	+	95.1812i	0.244252	+	0.857488i
$112$			10.5830i			0.0944911i
$113$	60.7659			0.537752			0.268876	−	0.963175i	$-0.413348\pi$
$113$	60.7659			0.537752			0.268876	+	0.963175i	$0.413348\pi$
$114$	123.074	−	35.0570i	1.07959	−	0.307518i
$115$	56.0859	+	26.3971i	0.487703	+	0.229540i
$116$			9.41442i			0.0811588i
$117$	−106.933	−	172.473i	−0.913953	−	1.47413i
$118$			159.591i			1.35247i
$119$		−	1.20950i		−	0.0101639i
$120$	41.8682	+	6.85984i	0.348901	+	0.0571653i
$121$	−208.514			−1.72326
$122$	−79.7378			−0.653589
$123$	18.8554	+	66.1950i	0.153296	+	0.538171i
$124$	90.5328			0.730103
$125$	−31.0592	−	121.080i	−0.248474	−	0.968639i
$126$	17.7446	+	28.6205i	0.140830	+	0.227146i
$127$			145.061i			1.14221i	0.820876	+	0.571107i	$0.193486\pi$
$127$			145.061i			1.14221i	−0.820876	+	0.571107i	$0.806514\pi$
$128$	11.3137			0.0883883
$129$	−16.6586	−	58.4829i	−0.129136	−	0.453356i
$130$	−67.8964	+	144.259i	−0.522280	+	1.10969i
$131$			5.97035i			0.0455752i	0.999740	+	0.0227876i	$0.00725414\pi$
$131$			5.97035i			0.0455752i	−0.999740	+	0.0227876i	$0.992746\pi$
$132$	29.8372	+	104.749i	0.226039	+	0.793549i
$133$		−	79.8029i		−	0.600022i
$134$		−	94.9905i		−	0.708885i
$135$	124.729	−	51.6489i	0.923920	−	0.382585i
$136$	−1.29301			−0.00950746
$137$	129.294			0.943754			0.471877	−	0.881664i	$-0.343577\pi$
$137$	129.294			0.943754			0.471877	+	0.881664i	$0.343577\pi$
$138$	50.5859	−	14.4092i	0.366564	−	0.104414i
$139$	236.460			1.70115			0.850576	−	0.525851i	$-0.176253\pi$
$139$	236.460			1.70115			0.850576	+	0.525851i	$0.176253\pi$
$140$	11.2668	−	23.9386i	0.0804775	−	0.170990i
$141$	27.9098	−	7.94999i	0.197942	−	0.0563829i
$142$			29.6139i			0.208548i
$143$	−409.303			−2.86226
$144$	30.5965	−	18.9697i	0.212476	−	0.131734i
$145$	10.0227	−	21.2953i	0.0691224	−	0.146864i
$146$		−	138.294i		−	0.947218i
$147$	20.1966	−	5.75292i	0.137392	−	0.0391355i
$148$		−	65.9782i		−	0.445798i
$149$			97.1922i			0.652297i	0.945319	+	0.326148i	$0.105751\pi$
$149$			97.1922i			0.652297i	−0.945319	+	0.326148i	$0.894249\pi$
$150$	−87.4022	−	60.0904i	−0.582681	−	0.400603i
$151$	124.132			0.822066			0.411033	−	0.911621i	$-0.365168\pi$
$151$	124.132			0.822066			0.411033	+	0.911621i	$0.365168\pi$
$152$	−85.3129			−0.561269
$153$	−3.49680	+	2.16800i	−0.0228549	+	0.0141700i
$154$	67.9205			0.441042
$155$	−204.784	−	96.3827i	−1.32119	−	0.621824i
$156$	37.0620	+	130.113i	0.237577	+	0.834055i
$157$		−	50.4117i		−	0.321093i	−0.987028	−	0.160547i	$-0.948674\pi$
$157$		−	50.4117i		−	0.321093i	0.987028	−	0.160547i	$-0.0513257\pi$
$158$	−58.5551			−0.370602
$159$	−17.2383	+	4.91025i	−0.108417	+	0.0308820i
$160$	−25.5915	−	12.0448i	−0.159947	−	0.0752798i
$161$		−	32.8006i		−	0.203731i
$162$	50.9380	−	102.603i	0.314432	−	0.633350i
$163$		−	131.802i		−	0.808599i	−0.914627	−	0.404300i	$-0.867515\pi$
$163$		−	131.802i		−	0.808599i	0.914627	−	0.404300i	$-0.132485\pi$
$164$		−	45.8854i		−	0.279789i
$165$	44.0257	−	268.705i	0.266822	−	1.62852i
$166$	172.430			1.03873
$167$	189.086			1.13225			0.566125	−	0.824320i	$-0.308442\pi$
$167$	189.086			1.13225			0.566125	+	0.824320i	$0.308442\pi$
$168$	−6.15014	−	21.5911i	−0.0366079	−	0.128518i
$169$	−339.413			−2.00836
$170$	2.92478	+	1.37657i	0.0172046	+	0.00809744i
$171$	−230.718	+	143.044i	−1.34923	+	0.836517i
$172$			40.5394i			0.235694i
$173$	292.614			1.69141			0.845706	−	0.533650i	$-0.179180\pi$
$173$	292.614			1.69141			0.845706	+	0.533650i	$0.179180\pi$
$174$	−5.47103	−	19.2070i	−0.0314427	−	0.110385i
$175$	−50.9709	+	42.1540i	−0.291263	+	0.240880i
$176$		−	72.6101i		−	0.412557i
$177$	−92.7437	−	325.593i	−0.523976	−	1.83951i
$178$			37.9218i			0.213044i
$179$		−	199.436i		−	1.11417i	−0.830456	−	0.557084i	$-0.811920\pi$
$179$		−	199.436i		−	1.11417i	0.830456	−	0.557084i	$-0.188080\pi$
$180$	−89.4045	+	10.3357i	−0.496692	+	0.0574208i
$181$	42.2460			0.233403			0.116702	−	0.993167i	$-0.462768\pi$
$181$	42.2460			0.233403			0.116702	+	0.993167i	$0.462768\pi$
$182$	84.3669			0.463555
$183$	162.679	−	46.3383i	0.888954	−	0.253215i
$184$	−35.0654			−0.190573
$185$	−70.2415	+	149.242i	−0.379684	+	0.806713i
$186$	−184.702	+	52.6116i	−0.993022	+	0.282858i
$187$			8.29842i			0.0443766i
$188$	−19.3467			−0.102908
$189$	−52.8342	−	48.0786i	−0.279546	−	0.254384i
$190$	192.977	+	90.8255i	1.01567	+	0.478029i
$191$		−	212.909i		−	1.11471i	−0.830276	−	0.557353i	$-0.811817\pi$
$191$		−	212.909i		−	1.11471i	0.830276	−	0.557353i	$-0.188183\pi$
$192$	−23.0819	+	6.57477i	−0.120218	+	0.0342436i
$193$			81.8019i			0.423844i	0.977287	+	0.211922i	$0.0679723\pi$
$193$			81.8019i			0.423844i	−0.977287	+	0.211922i	$0.932028\pi$
$194$		−	214.271i		−	1.10449i
$195$	54.6861	−	333.770i	0.280442	−	1.71164i
$196$	−14.0000			−0.0714286
$197$	140.887			0.715162			0.357581	−	0.933882i	$-0.383602\pi$
$197$	140.887			0.715162			0.357581	+	0.933882i	$0.383602\pi$
$198$	−121.746	−	196.365i	−0.614877	−	0.991743i
$199$	−119.398			−0.599989			−0.299995	−	0.953941i	$-0.596985\pi$
$199$	−119.398			−0.599989			−0.299995	+	0.953941i	$0.596985\pi$
$200$	45.0646	+	54.4902i	0.225323	+	0.272451i
$201$	55.2021	+	193.797i	0.274638	+	0.964162i
$202$		−	55.6094i		−	0.275294i
$203$	−12.4541			−0.0613503
$204$	2.63797	−	0.751414i	0.0129312	−	0.00368340i
$205$	−48.8503	+	103.792i	−0.238294	+	0.506303i
$206$			99.2921i			0.482000i
$207$	−94.8300	+	58.7942i	−0.458116	+	0.284030i
$208$		−	90.1920i		−	0.433616i
$209$			547.528i			2.61975i
$210$	−9.07472	+	55.3864i	−0.0432129	+	0.263745i
$211$	16.6761			0.0790339			0.0395169	−	0.999219i	$-0.487418\pi$
$211$	16.6761			0.0790339			0.0395169	+	0.999219i	$0.487418\pi$
$212$	11.9493			0.0563646
$213$	−17.2096	−	60.4173i	−0.0807962	−	0.283649i
$214$	−121.680			−0.568599
$215$	43.1590	−	91.6998i	0.200739	−	0.426510i
$216$	−51.3981	+	56.4821i	−0.237954	+	0.261491i
$217$			119.764i			0.551906i
$218$	65.6828			0.301297
$219$	80.3671	+	282.143i	0.366973	+	1.28832i
$220$	−77.3019	+	164.243i	−0.351372	+	0.746560i
$221$			10.3078i			0.0466417i
$222$	38.3421	+	134.607i	0.172712	+	0.606336i
$223$			72.2345i			0.323922i	0.986797	+	0.161961i	$0.0517818\pi$
$223$			72.2345i			0.323922i	−0.986797	+	0.161961i	$0.948218\pi$
$224$			14.9666i			0.0668153i
$225$	213.236	+	71.8022i	0.947714	+	0.319121i
$226$	85.9360			0.380248
$227$	−104.070			−0.458458			−0.229229	−	0.973373i	$-0.573620\pi$
$227$	−104.070			−0.458458			−0.229229	+	0.973373i	$0.573620\pi$
$228$	174.053	−	49.5781i	0.763388	−	0.217448i
$229$	329.701			1.43974			0.719871	−	0.694107i	$-0.244201\pi$
$229$	329.701			1.43974			0.719871	+	0.694107i	$0.244201\pi$
$230$	79.3174	+	37.3312i	0.344858	+	0.162309i
$231$	−138.569	+	39.4709i	−0.599867	+	0.170870i
$232$			13.3140i			0.0573879i
$233$	72.7668			0.312304			0.156152	−	0.987733i	$-0.450091\pi$
$233$	72.7668			0.312304			0.156152	+	0.987733i	$0.450091\pi$
$234$	−151.225	−	243.913i	−0.646262	−	1.04237i
$235$	43.7619	+	20.5968i	0.186221	+	0.0876459i
$236$			225.696i			0.956339i
$237$	119.462	−	34.0283i	0.504060	−	0.143579i
$238$		−	1.71050i		−	0.00718697i
$239$			291.494i			1.21964i	0.792540	+	0.609819i	$0.208758\pi$
$239$			291.494i			1.21964i	−0.792540	+	0.609819i	$0.791242\pi$
$240$	59.2105	+	9.70128i	0.246710	+	0.0404220i
$241$	281.683			1.16881			0.584404	−	0.811463i	$-0.301328\pi$
$241$	281.683			1.16881			0.584404	+	0.811463i	$0.301328\pi$
$242$	−294.883			−1.21853
$243$	−44.2962	+	238.929i	−0.182289	+	0.983245i
$244$	−112.766			−0.462157
$245$	31.6678	+	14.9046i	0.129256	+	0.0608352i
$246$	26.6655	+	93.6138i	0.108396	+	0.380544i
$247$			680.108i			2.75347i
$248$	128.033			0.516261
$249$	−351.786	+	100.205i	−1.41279	+	0.402428i
$250$	−43.9243	−	171.233i	−0.175697	−	0.684931i
$251$		−	209.382i		−	0.834193i	−0.908862	−	0.417096i	$-0.863048\pi$
$251$		−	209.382i		−	0.834193i	0.908862	−	0.417096i	$-0.136952\pi$
$252$	25.0946	+	40.4754i	0.0995818	+	0.160617i
$253$			225.045i			0.889508i
$254$			205.147i			0.807667i
$255$	−6.76702	−	1.10873i	−0.0265373	−	0.00434798i
$256$	16.0000			0.0625000
$257$	−357.735			−1.39197			−0.695983	−	0.718058i	$-0.745031\pi$
$257$	−357.735			−1.39197			−0.695983	+	0.718058i	$0.745031\pi$
$258$	−23.5588	−	82.7073i	−0.0913132	−	0.320571i
$259$	87.2809			0.336992
$260$	−96.0200	+	204.013i	−0.369308	+	0.784667i
$261$	22.3236	+	36.0061i	0.0855312	+	0.137954i
$262$			8.44335i			0.0322265i
$263$	−149.990			−0.570304			−0.285152	−	0.958482i	$-0.592044\pi$
$263$	−149.990			−0.570304			−0.285152	+	0.958482i	$0.592044\pi$
$264$	42.1961	+	148.137i	0.159834	+	0.561124i
$265$	−27.0292	−	12.7214i	−0.101997	−	0.0480054i
$266$		−	112.858i		−	0.424279i
$267$	−22.0376	−	77.3668i	−0.0825379	−	0.289763i
$268$		−	134.337i		−	0.501257i
$269$			165.001i			0.613386i	0.951808	+	0.306693i	$0.0992225\pi$
$269$			165.001i			0.613386i	−0.951808	+	0.306693i	$0.900777\pi$
$270$	176.394	−	73.0426i	0.653310	−	0.270528i
$271$	−0.273030			−0.00100749			−0.000503745	−	1.00000i	$-0.500160\pi$
$271$	−0.273030			−0.00100749			−0.000503745		1.00000i	$0.500160\pi$
$272$	−1.82860			−0.00672279
$273$	−172.123	+	49.0284i	−0.630486	+	0.179591i
$274$	182.850			0.667335
$275$	349.712	−	289.219i	1.27168	−	1.05171i
$276$	71.5392	−	20.3776i	0.259200	−	0.0738320i
$277$		−	86.4554i		−	0.312113i	−0.987748	−	0.156057i	$-0.950122\pi$
$277$		−	86.4554i		−	0.312113i	0.987748	−	0.156057i	$-0.0498782\pi$
$278$	334.405			1.20290
$279$	346.249	−	214.673i	1.24104	−	0.769437i
$280$	15.9337	−	33.8543i	0.0569062	−	0.120908i
$281$		−	301.513i		−	1.07300i	−0.843900	−	0.536500i	$-0.819746\pi$
$281$		−	301.513i		−	1.07300i	0.843900	−	0.536500i	$-0.180254\pi$
$282$	39.4704	−	11.2430i	0.139966	−	0.0398687i
$283$		−	74.3380i		−	0.262679i	−0.991337	−	0.131339i	$-0.958072\pi$
$283$		−	74.3380i		−	0.262679i	0.991337	−	0.131339i	$-0.0419277\pi$
$284$			41.8803i			0.147466i
$285$	−446.487	−	73.1541i	−1.56662	−	0.256681i
$286$	−578.842			−2.02392
$287$	60.7006			0.211500
$288$	43.2701	−	26.8273i	0.150243	−	0.0931502i
$289$	−288.791			−0.999277
$290$	14.1743	−	30.1161i	0.0488769	−	0.103849i
$291$	124.520	+	437.148i	0.427903	+	1.50223i
$292$		−	195.577i		−	0.669784i
$293$	−354.478			−1.20982			−0.604911	−	0.796293i	$-0.706791\pi$
$293$	−354.478			−1.20982			−0.604911	+	0.796293i	$0.706791\pi$
$294$	28.5623	−	8.13586i	0.0971508	−	0.0276730i
$295$	240.280	−	510.522i	0.814508	−	1.73058i
$296$		−	93.3072i		−	0.315227i
$297$	362.496	+	329.867i	1.22052	+	1.11066i
$298$			137.451i			0.461243i
$299$			279.538i			0.934911i
$300$	−123.605	−	84.9807i	−0.412018	−	0.283269i
$301$	−53.6286			−0.178168
$302$	175.549			0.581288
$303$	32.3164	+	113.452i	0.106655	+	0.374430i
$304$	−120.651			−0.396877
$305$	255.076	+	120.053i	0.836315	+	0.393616i
$306$	−4.94522	+	3.06602i	−0.0161609	+	0.0100197i
$307$			388.852i			1.26662i	0.773898	+	0.633310i	$0.218304\pi$
$307$			388.852i			1.26662i	−0.773898	+	0.633310i	$0.781696\pi$
$308$	96.0541			0.311864
$309$	−57.7019	−	202.572i	−0.186738	−	0.655574i
$310$	−289.608	−	136.306i	−0.934221	−	0.439696i
$311$		−	153.969i		−	0.495078i	−0.968878	−	0.247539i	$-0.920378\pi$
$311$		−	153.969i		−	0.495078i	0.968878	−	0.247539i	$-0.0796219\pi$
$312$	52.4136	+	184.007i	0.167992	+	0.589766i
$313$		−	114.895i		−	0.367076i	−0.983013	−	0.183538i	$-0.941245\pi$
$313$		−	114.895i		−	0.367076i	0.983013	−	0.183538i	$-0.0587550\pi$
$314$		−	71.2929i		−	0.227047i
$315$	−13.6729	−	118.271i	−0.0434061	−	0.375464i
$316$	−82.8094			−0.262055
$317$	−8.21324			−0.0259093			−0.0129546	−	0.999916i	$-0.504124\pi$
$317$	−8.21324			−0.0259093			−0.0129546	+	0.999916i	$0.504124\pi$
$318$	−24.3786	+	6.94414i	−0.0766622	+	0.0218369i
$319$	85.4477			0.267861
$320$	−36.1918	−	17.0339i	−0.113099	−	0.0532308i
$321$	248.248	−	70.7124i	0.773359	−	0.220288i
$322$		−	46.3871i		−	0.144059i
$323$	13.7889			0.0426899
$324$	72.0372	−	145.102i	0.222337	−	0.447846i
$325$	434.392	−	359.251i	1.33659	−	1.10539i
$326$		−	186.396i		−	0.571766i
$327$	−134.004	+	38.1705i	−0.409798	+	0.116729i
$328$		−	64.8917i		−	0.197841i
$329$		−	25.5932i		−	0.0777910i
$330$	62.2617	−	380.006i	0.188672	−	1.15153i
$331$	−623.239			−1.88290			−0.941449	−	0.337157i	$-0.890535\pi$
$331$	−623.239			−1.88290			−0.941449	+	0.337157i	$0.890535\pi$
$332$	243.853			0.734496
$333$	−156.449	−	252.338i	−0.469816	−	0.757772i
$334$	267.407			0.800621
$335$	−143.017	+	303.868i	−0.426917	+	0.907070i
$336$	−8.69760	−	30.5344i	−0.0258857	−	0.0908763i
$337$			279.891i			0.830538i	0.909699	+	0.415269i	$0.136312\pi$
$337$			279.891i			0.830538i	−0.909699	+	0.415269i	$0.863688\pi$
$338$	−480.002			−1.42012
$339$	−175.324	+	49.9403i	−0.517180	+	0.147316i
$340$	4.13627	+	1.94676i	0.0121655	+	0.00572576i
$341$		−	821.699i		−	2.40967i
$342$	−326.285	+	202.295i	−0.954049	+	0.591507i
$343$		−	18.5203i		−	0.0539949i
$344$			57.3314i			0.166661i
$345$	−183.515	−	30.0679i	−0.531928	−	0.0871532i
$346$	413.819			1.19601
$347$	−466.444			−1.34422			−0.672110	−	0.740452i	$-0.734612\pi$
$347$	−466.444			−1.34422			−0.672110	+	0.740452i	$0.734612\pi$
$348$	−7.73720	−	27.1628i	−0.0222333	−	0.0780540i
$349$	−56.3961			−0.161593			−0.0807967	−	0.996731i	$-0.525746\pi$
$349$	−56.3961			−0.161593			−0.0807967	+	0.996731i	$0.525746\pi$
$350$	−72.0838	+	59.6148i	−0.205954	+	0.170328i
$351$	450.271	+	409.742i	1.28282	+	1.16736i
$352$		−	102.686i		−	0.291722i
$353$	237.617			0.673137			0.336568	−	0.941659i	$-0.390734\pi$
$353$	237.617			0.673137			0.336568	+	0.941659i	$0.390734\pi$
$354$	−131.159	−	460.458i	−0.370507	−	1.30073i
$355$	44.5865	−	94.7328i	0.125596	−	0.266853i
$356$			53.6295i			0.150645i
$357$	0.994027	+	3.48970i	0.00278439	+	0.00977508i
$358$		−	282.045i		−	0.787836i
$359$		−	312.908i		−	0.871610i	−0.900041	−	0.435805i	$-0.856464\pi$
$359$		−	312.908i		−	0.871610i	0.900041	−	0.435805i	$-0.143536\pi$
$360$	−126.437	+	14.6170i	−0.351214	+	0.0406027i
$361$	548.785			1.52018
$362$	59.7449			0.165041
$363$	601.612	−	171.367i	1.65733	−	0.472084i
$364$	119.313			0.327783
$365$	−208.215	+	442.393i	−0.570451	+	1.21204i
$366$	230.062	−	65.5322i	0.628585	−	0.179050i
$367$			58.1239i			0.158376i	0.996860	+	0.0791878i	$0.0252327\pi$
$367$			58.1239i			0.158376i	−0.996860	+	0.0791878i	$0.974767\pi$
$368$	−49.5899			−0.134755
$369$	−108.804	−	175.492i	−0.294862	−	0.475587i
$370$	−99.3364	+	211.060i	−0.268477	+	0.570432i
$371$			15.8074i			0.0426077i
$372$	−261.208	+	74.4040i	−0.702172	+	0.200011i
$373$			435.852i			1.16850i	0.811572	+	0.584252i	$0.198612\pi$
$373$			435.852i			1.16850i	−0.811572	+	0.584252i	$0.801388\pi$
$374$			11.7357i			0.0313790i
$375$	189.122	+	323.818i	0.504325	+	0.863514i
$376$	−27.3603			−0.0727668
$377$	106.138			0.281534
$378$	−74.7188	−	67.9934i	−0.197669	−	0.179877i
$379$	−639.393			−1.68705			−0.843526	−	0.537089i	$-0.819524\pi$
$379$	−639.393			−1.68705			−0.843526	+	0.537089i	$0.819524\pi$
$380$	272.910	+	128.447i	0.718185	+	0.338017i
$381$	−119.218	−	418.535i	−0.312908	−	1.09852i
$382$		−	301.098i		−	0.788216i
$383$	240.793			0.628702			0.314351	−	0.949307i	$-0.398213\pi$
$383$	240.793			0.628702			0.314351	+	0.949307i	$0.398213\pi$
$384$	−32.6427	+	9.29813i	−0.0850070	+	0.0242139i
$385$	−217.273	−	102.261i	−0.564346	−	0.265613i
$386$			115.685i			0.299703i
$387$	96.1279	+	155.046i	0.248392	+	0.400635i
$388$		−	303.025i		−	0.780991i
$389$			160.718i			0.413157i	0.978430	+	0.206579i	$0.0662329\pi$
$389$			160.718i			0.413157i	−0.978430	+	0.206579i	$0.933767\pi$
$390$	77.3379	−	472.022i	0.198302	−	1.21031i
$391$	5.66750			0.0144949
$392$	−19.7990			−0.0505076
$393$	−4.90671	−	17.2258i	−0.0124853	−	0.0438317i
$394$	199.244			0.505696
$395$	187.314	+	88.1603i	0.474212	+	0.223191i
$396$	−172.174	−	277.702i	−0.434784	−	0.701268i
$397$			212.339i			0.534859i	0.963577	+	0.267430i	$0.0861743\pi$
$397$			212.339i			0.534859i	−0.963577	+	0.267430i	$0.913826\pi$
$398$	−168.854			−0.424256
$399$	65.5857	+	230.250i	0.164375	+	0.577067i
$400$	63.7309	+	77.0608i	0.159327	+	0.192652i
$401$		−	194.436i		−	0.484879i	−0.970167	−	0.242439i	$-0.922052\pi$
$401$		−	194.436i		−	0.484879i	0.970167	−	0.242439i	$-0.0779476\pi$
$402$	78.0676	+	274.070i	0.194198	+	0.681766i
$403$		−	1020.67i		−	2.53267i
$404$		−	78.6435i		−	0.194662i
$405$	−317.425	+	251.527i	−0.783767	+	0.621055i
$406$	−17.6128			−0.0433812
$407$	−598.835			−1.47134
$408$	3.73065	−	1.06266i	0.00914375	−	0.00260456i
$409$	294.951			0.721152			0.360576	−	0.932730i	$-0.382580\pi$
$409$	294.951			0.721152			0.360576	+	0.932730i	$0.382580\pi$
$410$	−69.0848	+	146.784i	−0.168499	+	0.358010i
$411$	−373.044	+	106.260i	−0.907650	+	0.258540i
$412$			140.420i			0.340826i
$413$	−298.568			−0.722925
$414$	−134.110	+	83.1476i	−0.323937	+	0.200840i
$415$	−551.592	−	259.610i	−1.32914	−	0.625565i
$416$		−	127.551i		−	0.306613i
$417$	−682.243	+	194.334i	−1.63607	+	0.466029i
$418$			774.322i			1.85244i
$419$		−	618.346i		−	1.47577i	−0.674929	−	0.737883i	$-0.735826\pi$
$419$		−	618.346i		−	1.47577i	0.674929	−	0.737883i	$-0.264174\pi$
$420$	−12.8336	+	78.3281i	−0.0305562	+	0.186496i
$421$	172.506			0.409752			0.204876	−	0.978788i	$-0.434321\pi$
$421$	172.506			0.409752			0.204876	+	0.978788i	$0.434321\pi$
$422$	23.5836			0.0558854
$423$	−73.9926	+	45.8752i	−0.174923	+	0.108452i
$424$	16.8989			0.0398558
$425$	−7.28365	−	8.80708i	−0.0171380	−	0.0207226i
$426$	−24.3380	−	85.4429i	−0.0571316	−	0.200570i
$427$		−	149.176i		−	0.349358i
$428$	−172.082			−0.402060
$429$	1180.94	−	336.384i	2.75276	−	0.784113i
$430$	61.0360	−	129.683i	0.141944	−	0.301588i
$431$			180.443i			0.418662i	0.977845	+	0.209331i	$0.0671287\pi$
$431$			180.443i			0.418662i	−0.977845	+	0.209331i	$0.932871\pi$
$432$	−72.6880	+	79.8778i	−0.168259	+	0.184902i
$433$		−	440.096i		−	1.01639i	−0.861243	−	0.508194i	$-0.830313\pi$
$433$		−	440.096i		−	1.01639i	0.861243	−	0.508194i	$-0.169687\pi$
$434$			169.371i			0.390257i
$435$	−11.4165	+	69.6791i	−0.0262448	+	0.160182i
$436$	92.8896			0.213049
$437$	373.941			0.855700
$438$	113.656	+	399.010i	0.259489	+	0.910982i
$439$	389.346			0.886894			0.443447	−	0.896301i	$-0.353756\pi$
$439$	389.346			0.886894			0.443447	+	0.896301i	$0.353756\pi$
$440$	−109.321	+	232.275i	−0.248458	+	0.527898i
$441$	−53.5440	+	33.1971i	−0.121415	+	0.0752768i
$442$			14.5775i			0.0329807i
$443$	521.471			1.17714			0.588568	−	0.808448i	$-0.299692\pi$
$443$	521.471			1.17714			0.588568	+	0.808448i	$0.299692\pi$
$444$	54.2239	+	190.362i	0.122126	+	0.428744i
$445$	57.0949	−	121.309i	0.128303	−	0.272605i
$446$			102.155i			0.229047i
$447$	−79.8771	−	280.422i	−0.178696	−	0.627343i
$448$			21.1660i			0.0472456i
$449$		−	596.122i		−	1.32767i	−0.747880	−	0.663833i	$-0.768928\pi$
$449$		−	596.122i		−	1.32767i	0.747880	−	0.663833i	$-0.231072\pi$
$450$	301.561	+	101.544i	0.670135	+	0.225653i
$451$	−416.468			−0.923431
$452$	121.532			0.268876
$453$	−358.149	+	102.017i	−0.790617	+	0.225204i
$454$	−147.177			−0.324179
$455$	−269.884	−	127.022i	−0.593152	−	0.279170i
$456$	246.147	−	70.1141i	0.539797	−	0.153759i
$457$		−	320.229i		−	0.700721i	−0.936615	−	0.350360i	$-0.886059\pi$
$457$		−	320.229i		−	0.700721i	0.936615	−	0.350360i	$-0.113941\pi$
$458$	466.268			1.01805
$459$	8.30732	−	9.12903i	0.0180987	−	0.0198890i
$460$	112.172	+	52.7942i	0.243852	+	0.114770i
$461$			141.935i			0.307885i	0.988080	+	0.153943i	$0.0491971\pi$
$461$			141.935i			0.307885i	−0.988080	+	0.153943i	$0.950803\pi$
$462$	−195.967	+	55.8202i	−0.424170	+	0.120823i
$463$			233.394i			0.504090i	0.967716	+	0.252045i	$0.0811031\pi$
$463$			233.394i			0.504090i	−0.967716	+	0.252045i	$0.918897\pi$
$464$			18.8288i			0.0405794i
$465$	670.062	+	109.785i	1.44099	+	0.236098i
$466$	102.908			0.220832
$467$	388.847			0.832649			0.416325	−	0.909216i	$-0.363318\pi$
$467$	388.847			0.832649			0.416325	+	0.909216i	$0.363318\pi$
$468$	−213.865	−	344.946i	−0.456977	−	0.737063i
$469$	177.711			0.378915
$470$	61.8887	+	29.1282i	0.131678	+	0.0619750i
$471$	41.4306	+	145.449i	0.0879631	+	0.308810i
$472$			319.182i			0.676234i
$473$	367.947			0.777900
$474$	168.945	−	48.1233i	0.356424	−	0.101526i
$475$	−480.573	−	581.090i	−1.01173	−	1.22335i
$476$		−	2.41901i		−	0.00508195i
$477$	45.7009	−	28.3344i	0.0958091	−	0.0594013i
$478$			412.234i			0.862415i
$479$		−	891.549i		−	1.86127i	−0.365946	−	0.930636i	$-0.619255\pi$
$479$		−	891.549i		−	1.86127i	0.365946	−	0.930636i	$-0.380745\pi$
$480$	83.7363	+	13.7197i	0.174451	+	0.0285827i
$481$	−743.838			−1.54644
$482$	398.360			0.826472
$483$	26.9571	+	94.6375i	0.0558118	+	0.195937i
$484$	−417.028			−0.861628
$485$	−322.605	+	685.438i	−0.665165	+	1.41327i
$486$	−62.6443	+	337.896i	−0.128898	+	0.695259i
$487$			228.917i			0.470056i	0.971989	+	0.235028i	$0.0755182\pi$
$487$			228.917i			0.470056i	−0.971989	+	0.235028i	$0.924482\pi$
$488$	−159.476			−0.326794
$489$	108.321	+	380.278i	0.221515	+	0.777666i
$490$	44.7851	+	21.0783i	0.0913981	+	0.0430170i
$491$			328.951i			0.669960i	0.942225	+	0.334980i	$0.108730\pi$
$491$			328.951i			0.669960i	−0.942225	+	0.334980i	$0.891270\pi$
$492$	37.7107	+	132.390i	0.0766478	+	0.269085i
$493$		−	2.15190i		−	0.00436491i
$494$			961.818i			1.94700i
$495$	93.8099	+	811.459i	0.189515	+	1.63931i
$496$	181.066			0.365052
$497$	−55.4025			−0.111474
$498$	−497.500	+	141.711i	−0.998996	+	0.284560i
$499$	169.653			0.339985			0.169993	−	0.985445i	$-0.445626\pi$
$499$	169.653			0.339985			0.169993	+	0.985445i	$0.445626\pi$
$500$	−62.1184	−	242.160i	−0.124237	−	0.484319i
$501$	−545.556	+	155.399i	−1.08893	+	0.310178i
$502$		−	296.111i		−	0.589864i
$503$	−353.801			−0.703381			−0.351691	−	0.936116i	$-0.614393\pi$
$503$	−353.801			−0.703381			−0.351691	+	0.936116i	$0.614393\pi$
$504$	35.4891	+	57.2409i	0.0704150	+	0.113573i
$505$	−83.7252	+	177.891i	−0.165792	+	0.352259i
$506$			318.262i			0.628977i
$507$	979.285	−	278.945i	1.93153	−	0.550188i
$508$			290.122i			0.571107i
$509$			909.175i			1.78620i	0.449859	+	0.893099i	$0.351474\pi$
$509$			909.175i			1.78620i	−0.449859	+	0.893099i	$0.648526\pi$
$510$	−9.57001	−	1.56799i	−0.0187647	−	0.00307449i
$511$	258.724			0.506309
$512$	22.6274			0.0441942
$513$	548.115	−	602.331i	1.06845	−	1.17414i
$514$	−505.914			−0.984269
$515$	149.494	−	317.629i	0.290279	−	0.616755i
$516$	−33.3172	−	116.966i	−0.0645682	−	0.226678i
$517$			175.595i			0.339643i
$518$	123.434			0.238289
$519$	−844.260	+	240.484i	−1.62670	+	0.463360i
$520$	−135.793	+	288.518i	−0.261140	+	0.554843i
$521$		−	77.7672i		−	0.149265i	−0.997211	−	0.0746326i	$-0.976222\pi$
$521$		−	77.7672i		−	0.149265i	0.997211	−	0.0746326i	$-0.0237784\pi$
$522$	31.5704	+	50.9203i	0.0604797	+	0.0975484i
$523$		−	781.844i		−	1.49492i	−0.664305	−	0.747461i	$-0.731273\pi$
$523$		−	781.844i		−	1.49492i	0.664305	−	0.747461i	$-0.268727\pi$
$524$			11.9407i			0.0227876i
$525$	112.419	−	163.515i	0.214131	−	0.311456i
$526$	−212.118			−0.403266
$527$	−20.6935			−0.0392666
$528$	59.6743	+	209.497i	0.113020	+	0.396775i
$529$	−375.303			−0.709457
$530$	−38.2250	−	17.9908i	−0.0721227	−	0.0339449i
$531$	535.175	+	863.190i	1.00786	+	1.62559i
$532$		−	159.606i		−	0.300011i
$533$	−517.312			−0.970566
$534$	−31.1659	−	109.413i	−0.0583631	−	0.204894i
$535$	389.247	+	183.201i	0.727565	+	0.342432i
$536$		−	189.981i		−	0.354442i
$537$	163.906	+	575.420i	0.305225	+	1.07155i
$538$			233.347i			0.433730i
$539$			127.068i			0.235747i
$540$	249.459	−	103.298i	0.461960	−	0.191292i
$541$	355.089			0.656356			0.328178	−	0.944616i	$-0.393565\pi$
$541$	355.089			0.656356			0.328178	+	0.944616i	$0.393565\pi$
$542$	−0.386122			−0.000712403
$543$	−121.890	+	34.7197i	−0.224474	+	0.0639405i
$544$	−2.58603			−0.00475373
$545$	−210.115	−	98.8918i	−0.385532	−	0.181453i
$546$	−243.418	+	69.3367i	−0.445821	+	0.126990i
$547$		−	883.402i		−	1.61499i	−0.589872	−	0.807497i	$-0.700822\pi$
$547$		−	883.402i		−	1.61499i	0.589872	−	0.807497i	$-0.299178\pi$
$548$	258.589			0.471877
$549$	−431.282	+	267.394i	−0.785578	+	0.487056i
$550$	494.568	−	409.018i	0.899214	−	0.743669i
$551$		−	141.982i		−	0.257680i
$552$	101.172	−	28.8183i	0.183282	−	0.0522071i
$553$		−	109.547i		−	0.198095i
$554$		−	122.266i		−	0.220697i
$555$	80.0091	−	488.325i	0.144161	−	0.879865i
$556$	472.921			0.850576
$557$	−76.6136			−0.137547			−0.0687735	−	0.997632i	$-0.521909\pi$
$557$	−76.6136			−0.137547			−0.0687735	+	0.997632i	$0.521909\pi$
$558$	489.670	−	303.593i	0.877544	−	0.544074i
$559$	457.042			0.817606
$560$	22.5337	−	47.8773i	0.0402387	−	0.0854951i
$561$	−6.82003	−	23.9429i	−0.0121569	−	0.0426789i
$562$		−	426.404i		−	0.758726i
$563$	361.800			0.642629			0.321314	−	0.946973i	$-0.395875\pi$
$563$	361.800			0.642629			0.321314	+	0.946973i	$0.395875\pi$
$564$	55.8196	−	15.9000i	0.0989710	−	0.0281915i
$565$	−274.904	−	129.385i	−0.486555	−	0.229000i
$566$		−	105.130i		−	0.185742i
$567$	191.952	+	95.2963i	0.338540	+	0.168071i
$568$			59.2277i			0.104274i
$569$			72.2936i			0.127054i	0.997980	+	0.0635269i	$0.0202349\pi$
$569$			72.2936i			0.127054i	−0.997980	+	0.0635269i	$0.979765\pi$
$570$	−631.427	−	103.455i	−1.10777	−	0.181501i
$571$	90.4610			0.158426			0.0792128	−	0.996858i	$-0.474759\pi$
$571$	90.4610			0.158426			0.0792128	+	0.996858i	$0.474759\pi$
$572$	−818.607			−1.43113
$573$	174.978	+	614.291i	0.305372	+	1.07206i
$574$	85.8437			0.149553
$575$	−197.526	−	238.840i	−0.343523	−	0.415374i
$576$	61.1931	−	37.9395i	0.106238	−	0.0658672i
$577$			456.970i			0.791976i	0.918256	+	0.395988i	$0.129598\pi$
$577$			456.970i			0.791976i	−0.918256	+	0.395988i	$0.870402\pi$
$578$	−408.412			−0.706595
$579$	−67.2286	−	236.018i	−0.116112	−	0.407630i
$580$	20.0455	−	42.5906i	0.0345612	−	0.0734321i
$581$			322.587i			0.555227i
$582$	176.098	+	618.221i	0.302573	+	1.06224i
$583$		−	108.455i		−	0.186029i
$584$		−	276.588i		−	0.473609i
$585$	116.525	+	1007.95i	0.199189	+	1.72299i
$586$	−501.308			−0.855474
$587$	−245.442			−0.418130			−0.209065	−	0.977902i	$-0.567042\pi$
$587$	−245.442			−0.418130			−0.209065	+	0.977902i	$0.567042\pi$
$588$	40.3933	−	11.5058i	0.0686960	−	0.0195678i
$589$	−1365.35			−2.31809
$590$	339.807	−	721.987i	0.575944	−	1.22371i
$591$	−406.492	+	115.787i	−0.687803	+	0.195918i
$592$		−	131.956i		−	0.222899i
$593$	−308.286			−0.519876			−0.259938	−	0.965625i	$-0.583702\pi$
$593$	−308.286			−0.519876			−0.259938	+	0.965625i	$0.583702\pi$
$594$	512.647	+	466.503i	0.863041	+	0.785359i
$595$	−2.57532	+	5.47177i	−0.00432827	+	0.00919625i
$596$			194.384i			0.326148i
$597$	344.491	−	98.1267i	0.577036	−	0.164366i
$598$			395.327i			0.661082i
$599$		−	171.484i		−	0.286283i	−0.989702	−	0.143142i	$-0.954280\pi$
$599$		−	171.484i		−	0.286283i	0.989702	−	0.143142i	$-0.0457205\pi$
$600$	−174.804	−	120.181i	−0.291341	−	0.200301i
$601$	−507.061			−0.843695			−0.421848	−	0.906667i	$-0.638618\pi$
$601$	−507.061			−0.843695			−0.421848	+	0.906667i	$0.638618\pi$
$602$	−75.8424			−0.125984
$603$	−318.542	−	513.781i	−0.528262	−	0.852041i
$604$	248.264			0.411033
$605$	943.313	+	443.975i	1.55919	+	0.733843i
$606$	45.7024	+	160.446i	0.0754164	+	0.264762i
$607$		−	86.8260i		−	0.143041i	−0.997439	−	0.0715206i	$-0.977215\pi$
$607$		−	86.8260i		−	0.143041i	0.997439	−	0.0715206i	$-0.0227852\pi$
$608$	−170.626			−0.280634
$609$	35.9330	−	10.2354i	0.0590033	−	0.0168068i
$610$	360.732	+	169.780i	0.591364	+	0.278329i
$611$			218.114i			0.356979i
$612$	−6.99360	+	4.33601i	−0.0114275	+	0.00708498i
$613$			1109.19i			1.80945i	0.425996	+	0.904725i	$0.359924\pi$
$613$			1109.19i			1.80945i	−0.425996	+	0.904725i	$0.640076\pi$
$614$			549.920i			0.895635i
$615$	55.6433	−	339.612i	0.0904770	−	0.552215i
$616$	135.841			0.220521
$617$	572.163			0.927331			0.463665	−	0.886010i	$-0.346534\pi$
$617$	572.163			0.927331			0.463665	+	0.886010i	$0.346534\pi$
$618$	−81.6028	−	286.481i	−0.132043	−	0.463561i
$619$	−535.523			−0.865143			−0.432571	−	0.901600i	$-0.642394\pi$
$619$	−535.523			−0.865143			−0.432571	+	0.901600i	$0.642394\pi$
$620$	−409.568	−	192.765i	−0.660594	−	0.310912i
$621$	225.287	−	247.571i	0.362781	−	0.398665i
$622$		−	217.746i		−	0.350073i
$623$	−70.9452			−0.113877
$624$	74.1240	+	260.225i	0.118788	+	0.417027i
$625$	−117.296	+	613.895i	−0.187674	+	0.982231i
$626$		−	162.486i		−	0.259562i
$627$	−449.984	−	1579.75i	−0.717678	−	2.51953i
$628$		−	100.823i		−	0.160547i
$629$			15.0810i			0.0239761i
$630$	−19.3364	−	167.261i	−0.0306927	−	0.265493i
$631$	308.871			0.489495			0.244747	−	0.969587i	$-0.421295\pi$
$631$	308.871			0.489495			0.244747	+	0.969587i	$0.421295\pi$
$632$	−117.110			−0.185301
$633$	−48.1146	+	13.7052i	−0.0760104	+	0.0216512i
$634$	−11.6153			−0.0183206
$635$	308.869	−	656.253i	0.486408	−	1.03347i
$636$	−34.4765	+	9.82049i	−0.0542084	+	0.0154410i
$637$			157.836i			0.247780i
$638$	120.841			0.189406
$639$	99.3074	+	160.174i	0.155411	+	0.250664i
$640$	−51.1830	−	24.0895i	−0.0799734	−	0.0376399i
$641$		−	795.563i		−	1.24113i	−0.784156	−	0.620564i	$-0.786904\pi$
$641$		−	795.563i		−	1.24113i	0.784156	−	0.620564i	$-0.213096\pi$
$642$	351.076	−	100.002i	0.546847	−	0.155767i
$643$			567.428i			0.882469i	0.897392	+	0.441234i	$0.145459\pi$
$643$			567.428i			0.882469i	−0.897392	+	0.441234i	$0.854541\pi$
$644$		−	65.6013i		−	0.101865i
$645$	−49.1606	+	300.045i	−0.0762179	+	0.465186i
$646$	19.5004			0.0301863
$647$	−482.089			−0.745114			−0.372557	−	0.928009i	$-0.621519\pi$
$647$	−482.089			−0.745114			−0.372557	+	0.928009i	$0.621519\pi$
$648$	101.876	−	205.205i	0.157216	−	0.316675i
$649$	2048.48			3.15636
$650$	614.323	−	508.058i	0.945112	−	0.781628i
$651$	−98.4273	−	345.546i	−0.151194	−	0.530792i
$652$		−	263.603i		−	0.404300i
$653$	1072.96			1.64313			0.821565	−	0.570114i	$-0.193101\pi$
$653$	1072.96			1.64313			0.821565	+	0.570114i	$0.193101\pi$
$654$	−189.510	+	53.9812i	−0.289771	+	0.0825401i
$655$	12.7123	−	27.0097i	0.0194080	−	0.0412362i
$656$		−	91.7707i		−	0.139894i
$657$	−463.756	−	747.998i	−0.705869	−	1.13851i
$658$		−	36.1943i		−	0.0550065i
$659$		−	653.498i		−	0.991651i	−0.868422	−	0.495825i	$-0.834866\pi$
$659$		−	653.498i		−	0.991651i	0.868422	−	0.495825i	$-0.165134\pi$
$660$	88.0514	−	537.410i	0.133411	−	0.814258i
$661$	1085.85			1.64274			0.821372	−	0.570392i	$-0.193209\pi$
$661$	1085.85			1.64274			0.821372	+	0.570392i	$0.193209\pi$
$662$	−881.393			−1.33141
$663$	−8.47144	−	29.7405i	−0.0127774	−	0.0448574i
$664$	344.860			0.519367
$665$	−169.919	+	361.026i	−0.255517	+	0.542897i
$666$	−221.252	−	356.860i	−0.332210	−	0.535826i
$667$		−	58.3575i		−	0.0874925i
$668$	378.171			0.566125
$669$	−59.3657	−	208.413i	−0.0887379	−	0.311530i
$670$	−202.257	+	429.735i	−0.301876	+	0.641395i
$671$			1023.50i			1.52533i
$672$	−12.3003	−	43.1822i	−0.0183040	−	0.0642592i
$673$			199.268i			0.296089i	0.988981	+	0.148044i	$0.0472979\pi$
$673$			199.268i			0.296089i	−0.988981	+	0.148044i	$0.952702\pi$
$674$			395.826i			0.587279i
$675$	−674.245	−	31.9192i	−0.998881	−	0.0472877i
$676$	−678.826			−1.00418
$677$	409.731			0.605216			0.302608	−	0.953115i	$-0.402143\pi$
$677$	409.731			0.605216			0.302608	+	0.953115i	$0.402143\pi$
$678$	−247.945	+	70.6262i	−0.365701	+	0.104168i
$679$	400.864			0.590374
$680$	5.84957	+	2.75313i	0.00860231	+	0.00404872i
$681$	300.266	−	85.5295i	0.440919	−	0.125594i
$682$		−	1162.06i		−	1.70390i
$683$	−204.910			−0.300015			−0.150008	−	0.988685i	$-0.547930\pi$
$683$	−204.910			−0.300015			−0.150008	+	0.988685i	$0.547930\pi$
$684$	−461.436	+	286.089i	−0.674615	+	0.418259i
$685$	−584.925	−	275.298i	−0.853905	−	0.401895i
$686$		−	26.1916i		−	0.0381802i
$687$	−951.264	+	270.964i	−1.38466	+	0.394416i
$688$			81.0789i			0.117847i
$689$		−	134.717i		−	0.195525i
$690$	−259.530	−	42.5224i	−0.376130	−	0.0616266i
$691$	−437.098			−0.632558			−0.316279	−	0.948666i	$-0.602434\pi$
$691$	−437.098			−0.632558			−0.316279	+	0.948666i	$0.602434\pi$
$692$	585.228			0.845706
$693$	367.366	−	227.765i	0.530109	−	0.328666i
$694$	−659.652			−0.950507
$695$	−1069.74	−	503.479i	−1.53920	−	0.724430i
$696$	−10.9421	−	38.4140i	−0.0157213	−	0.0551925i
$697$			10.4882i			0.0150477i
$698$	−79.7561			−0.114264
$699$	−209.949	+	59.8032i	−0.300357	+	0.0855553i
$700$	−101.942	+	84.3081i	−0.145631	+	0.120440i
$701$			969.784i			1.38343i	0.722171	+	0.691715i	$0.243145\pi$
$701$			969.784i			1.38343i	−0.722171	+	0.691715i	$0.756855\pi$
$702$	636.780	+	579.463i	0.907094	+	0.825446i
$703$			995.038i			1.41542i
$704$		−	145.220i		−	0.206279i
$705$	−143.191	−	23.4609i	−0.203107	−	0.0332779i
$706$	336.042			0.475980
$707$	104.036			0.147151
$708$	−185.487	−	651.186i	−0.261988	−	0.919754i
$709$	−575.519			−0.811733			−0.405866	−	0.913932i	$-0.633030\pi$
$709$	−575.519			−0.811733			−0.405866	+	0.913932i	$0.633030\pi$
$710$	63.0548	−	133.972i	0.0888096	−	0.188694i
$711$	−316.710	+	196.359i	−0.445443	+	0.276173i
$712$			75.8436i			0.106522i
$713$	−561.189			−0.787081
$714$	1.40577	+	4.93518i	0.00196886	+	0.00691202i
$715$	1851.68	+	871.502i	2.58976	+	1.21888i
$716$		−	398.872i		−	0.557084i
$717$	−239.563	−	841.027i	−0.334119	−	1.17298i
$718$		−	442.519i		−	0.616321i
$719$		−	1327.86i		−	1.84681i	−0.383825	−	0.923406i	$-0.625393\pi$
$719$		−	1327.86i		−	1.84681i	0.383825	−	0.923406i	$-0.374607\pi$
$720$	−178.809	+	20.6715i	−0.248346	+	0.0287104i
$721$	−185.758			−0.257640
$722$	776.100			1.07493
$723$	−812.721	+	231.500i	−1.12409	+	0.320194i
$724$	84.4920			0.116702
$725$	−90.6853	+	74.9987i	−0.125083	+	0.103446i
$726$	850.807	−	242.349i	1.17191	−	0.333814i
$727$			136.854i			0.188245i	0.995561	+	0.0941226i	$0.0300046\pi$
$727$			136.854i			0.188245i	−0.995561	+	0.0941226i	$0.969995\pi$
$728$	168.734			0.231777
$729$	−68.5577	−	725.769i	−0.0940435	−	0.995568i
$730$	−294.460	+	625.638i	−0.403370	+	0.857039i
$731$		−	9.26630i		−	0.0126762i
$732$	325.357	−	92.6766i	0.444477	−	0.126607i
$733$			345.348i			0.471143i	0.971857	+	0.235572i	$0.0756963\pi$
$733$			345.348i			0.471143i	−0.971857	+	0.235572i	$0.924304\pi$
$734$			82.1996i			0.111989i
$735$	−103.618	−	16.9772i	−0.140977	−	0.0230983i
$736$	−70.1307			−0.0952863
$737$	−1219.28			−1.65438
$738$	−153.872	−	248.183i	−0.208499	−	0.336291i
$739$	−91.4827			−0.123793			−0.0618963	−	0.998083i	$-0.519715\pi$
$739$	−91.4827			−0.123793			−0.0618963	+	0.998083i	$0.519715\pi$
$740$	−140.483	+	298.484i	−0.189842	+	0.403356i
$741$	−558.944	−	1962.27i	−0.754311	−	2.64814i
$742$			22.3551i			0.0301282i
$743$	86.0672			0.115837			0.0579187	−	0.998321i	$-0.481554\pi$
$743$	86.0672			0.115837			0.0579187	+	0.998321i	$0.481554\pi$
$744$	−369.404	+	105.223i	−0.496511	+	0.141429i
$745$	206.945	−	439.695i	0.277778	−	0.590195i
$746$			616.388i			0.826258i
$747$	932.631	−	578.228i	1.24850	−	0.774067i
$748$			16.5968i			0.0221883i
$749$		−	227.643i		−	0.303929i
$750$	267.459	+	457.947i	0.356612	+	0.610596i
$751$	107.700			0.143408			0.0717042	−	0.997426i	$-0.477156\pi$
$751$	107.700			0.143408			0.0717042	+	0.997426i	$0.477156\pi$
$752$	−38.6933			−0.0514539
$753$	172.080	+	604.117i	0.228526	+	0.802280i
$754$	150.102			0.199074
$755$	−561.570	−	264.306i	−0.743801	−	0.350074i
$756$	−105.668	−	96.1571i	−0.139773	−	0.127192i
$757$			485.286i			0.641065i	0.947238	+	0.320532i	$0.103862\pi$
$757$			485.286i			0.641065i	−0.947238	+	0.320532i	$0.896138\pi$
$758$	−904.238			−1.19293
$759$	−184.953	−	649.309i	−0.243680	−	0.855479i
$760$	385.953	+	181.651i	0.507833	+	0.239014i
$761$			1202.49i			1.58014i	0.613017	+	0.790069i	$0.289956\pi$
$761$			1202.49i			1.58014i	−0.613017	+	0.790069i	$0.710044\pi$
$762$	−168.600	−	591.898i	−0.221259	−	0.776769i
$763$			122.881i			0.161050i
$764$		−	425.817i		−	0.557353i
$765$	20.4356	−	2.36249i	0.0267132	−	0.00308823i
$766$	340.532			0.444559
$767$	2544.50			3.31747
$768$	−46.1637	+	13.1495i	−0.0601090	+	0.0171218i
$769$	1020.23			1.32670			0.663351	−	0.748308i	$-0.269133\pi$
$769$	1020.23			1.32670			0.663351	+	0.748308i	$0.269133\pi$
$770$	−307.271	−	144.619i	−0.399053	−	0.187816i
$771$	1032.15	−	294.004i	1.33872	−	0.381328i
$772$			163.604i			0.211922i
$773$	−847.386			−1.09623			−0.548115	−	0.836403i	$-0.684654\pi$
$773$	−847.386			−1.09623			−0.548115	+	0.836403i	$0.684654\pi$
$774$	135.945	+	219.268i	0.175640	+	0.283292i
$775$	721.217	+	872.066i	0.930603	+	1.12525i
$776$		−	428.542i		−	0.552244i
$777$	−251.826	+	71.7315i	−0.324100	+	0.0923185i
$778$			227.290i			0.292146i
$779$			692.012i			0.888334i
$780$	109.372	−	667.540i	0.140221	−	0.855820i
$781$	380.117			0.486705
$782$	8.01506			0.0102494
$783$	−94.0004	−	85.5393i	−0.120052	−	0.109246i
$784$	−28.0000			−0.0357143
$785$	−107.338	+	228.061i	−0.136737	+	0.290524i
$786$	−6.93913	−	24.3610i	−0.00882841	−	0.0309937i
$787$		−	515.749i		−	0.655336i	−0.944793	−	0.327668i	$-0.893737\pi$
$787$		−	515.749i		−	0.655336i	0.944793	−	0.327668i	$-0.106263\pi$
$788$	281.774			0.357581
$789$	432.756	−	123.269i	0.548487	−	0.156234i
$790$	264.902	+	124.677i	0.335319	+	0.157820i
$791$			160.772i			0.203251i
$792$	−243.491	−	392.730i	−0.307439	−	0.495872i
$793$			1271.33i			1.60319i
$794$			300.293i			0.378203i
$795$	88.4405	+	14.4904i	0.111246	+	0.0182270i
$796$	−238.796			−0.299995
$797$	65.3181			0.0819550			0.0409775	−	0.999160i	$-0.486953\pi$
$797$	65.3181			0.0819550			0.0409775	+	0.999160i	$0.486953\pi$
$798$	92.7522	+	325.622i	0.116231	+	0.408048i
$799$	4.42216			0.00553462
$800$	90.1291	+	108.980i	0.112661	+	0.136226i
$801$	127.167	+	205.110i	0.158761	+	0.256067i
$802$		−	274.975i		−	0.342861i
$803$	−1775.11			−2.21060
$804$	110.404	+	387.593i	0.137319	+	0.482081i
$805$	−69.8402	+	148.389i	−0.0867580	+	0.184335i
$806$		−	1443.44i		−	1.79087i
$807$	−135.605	−	476.066i	−0.168036	−	0.589921i
$808$		−	111.219i		−	0.137647i
$809$		−	984.812i		−	1.21732i	−0.793431	−	0.608660i	$-0.791707\pi$
$809$		−	984.812i		−	1.21732i	0.793431	−	0.608660i	$-0.208293\pi$
$810$	−448.907	+	355.714i	−0.554207	+	0.439153i
$811$	−1043.21			−1.28632			−0.643162	−	0.765730i	$-0.722378\pi$
$811$	−1043.21			−1.28632			−0.643162	+	0.765730i	$0.722378\pi$
$812$	−24.9082			−0.0306751
$813$	0.787755	−	0.224389i	0.000968948	−	0.000276001i
$814$	−846.881			−1.04039
$815$	−280.636	+	596.268i	−0.344339	+	0.731617i
$816$	5.27593	−	1.50283i	0.00646561	−	0.00184170i
$817$		−	611.389i		−	0.748334i
$818$	417.124			0.509931
$819$	456.320	−	282.917i	0.557168	−	0.345442i
$820$	−97.7006	+	207.584i	−0.119147	+	0.253152i
$821$		−	316.439i		−	0.385431i	−0.981255	−	0.192716i	$-0.938271\pi$
$821$		−	316.439i		−	0.385431i	0.981255	−	0.192716i	$-0.0617295\pi$
$822$	−527.564	+	150.274i	−0.641806	+	0.182816i
$823$			770.671i			0.936417i	0.883618	+	0.468209i	$0.155100\pi$
$823$			770.671i			0.936417i	−0.883618	+	0.468209i	$0.844900\pi$
$824$			198.584i			0.241000i
$825$	−771.307	+	1121.87i	−0.934917	+	1.35985i
$826$	−422.239			−0.511185
$827$	1321.39			1.59781			0.798907	−	0.601455i	$-0.205412\pi$
$827$	1321.39			1.59781			0.798907	+	0.601455i	$0.205412\pi$
$828$	−189.660	+	117.588i	−0.229058	+	0.142015i
$829$	476.736			0.575074			0.287537	−	0.957770i	$-0.407164\pi$
$829$	476.736			0.575074			0.287537	+	0.957770i	$0.407164\pi$
$830$	−780.069	−	367.143i	−0.939842	−	0.442341i
$831$	71.0530	+	249.444i	0.0855030	+	0.300173i
$832$		−	180.384i		−	0.216808i
$833$	3.20005			0.00384160
$834$	−964.837	+	274.830i	−1.15688	+	0.329532i
$835$	−855.419	−	402.607i	−1.02445	−	0.482165i
$836$			1095.06i			1.30988i
$837$	−822.580	+	903.945i	−0.982772	+	1.07998i
$838$		−	874.473i		−	1.04352i
$839$			920.100i			1.09666i	0.836261	+	0.548331i	$0.184737\pi$
$839$			920.100i			1.09666i	−0.836261	+	0.548331i	$0.815263\pi$
$840$	−18.1494	+	110.773i	−0.0216065	+	0.131872i
$841$	818.842			0.973653
$842$	243.960			0.289739
$843$	247.797	+	869.935i	0.293947	+	1.03195i
$844$	33.3523			0.0395169
$845$	1535.50	+	722.689i	1.81715	+	0.855253i
$846$	−104.641	+	64.8773i	−0.123690	+	0.0766871i
$847$		−	551.676i		−	0.651330i
$848$	23.8986			0.0281823
$849$	61.0944	+	214.483i	0.0719605	+	0.252630i
$850$	−10.3006	−	12.4551i	−0.0121184	−	0.0146531i
$851$			408.981i			0.480589i
$852$	−34.4192	−	120.835i	−0.0403981	−	0.141825i
$853$			148.026i			0.173536i	0.996229	+	0.0867681i	$0.0276539\pi$
$853$			148.026i			0.173536i	−0.996229	+	0.0867681i	$0.972346\pi$
$854$		−	210.966i		−	0.247033i
$855$	1348.34	−	155.877i	1.57700	−	0.182312i
$856$	−243.361			−0.284300
$857$	−948.093			−1.10629			−0.553147	−	0.833084i	$-0.686573\pi$
$857$	−948.093			−1.10629			−0.553147	+	0.833084i	$0.686573\pi$
$858$	1670.09	−	475.719i	1.94650	−	0.554452i
$859$	−264.436			−0.307842			−0.153921	−	0.988083i	$-0.549190\pi$
$859$	−264.436			−0.307842			−0.153921	+	0.988083i	$0.549190\pi$
$860$	86.3179	−	183.400i	0.100370	−	0.213255i
$861$	−175.135	+	49.8866i	−0.203409	+	0.0579403i
$862$			255.186i			0.296039i
$863$	1553.74			1.80040			0.900198	−	0.435482i	$-0.143422\pi$
$863$	1553.74			1.80040			0.900198	+	0.435482i	$0.143422\pi$
$864$	−102.796	+	112.964i	−0.118977	+	0.130746i
$865$	−1323.78	−	623.044i	−1.53038	−	0.720282i
$866$		−	622.389i		−	0.718694i
$867$	833.229	−	237.342i	0.961049	−	0.273751i
$868$			239.527i			0.275953i
$869$			751.600i			0.864902i
$870$	−16.1453	+	98.5411i	−0.0185579	+	0.113266i
$871$	−1514.51			−1.73882
$872$	131.366			0.150649
$873$	−718.537	−	1158.94i	−0.823067	−	1.32754i
$874$	528.832			0.605071
$875$	320.347	−	82.1749i	0.366111	−	0.0939142i
$876$	160.734	+	564.285i	0.183487	+	0.644161i
$877$		−	1187.32i		−	1.35385i	−0.736053	−	0.676924i	$-0.763313\pi$
$877$		−	1187.32i		−	1.35385i	0.736053	−	0.676924i	$-0.236687\pi$
$878$	550.619			0.627128
$879$	1022.75	−	291.327i	1.16354	−	0.331429i
$880$	−154.604	+	328.486i	−0.175686	+	0.373280i
$881$		−	238.098i		−	0.270259i	−0.990828	−	0.135129i	$-0.956855\pi$
$881$		−	238.098i		−	0.270259i	0.990828	−	0.135129i	$-0.0431450\pi$
$882$	−75.7226	+	46.9477i	−0.0858533	+	0.0532287i
$883$		−	1720.86i		−	1.94888i	−0.224648	−	0.974440i	$-0.572123\pi$
$883$		−	1720.86i		−	1.94888i	0.224648	−	0.974440i	$-0.427877\pi$
$884$			20.6156i			0.0233209i
$885$	−273.693	+	1670.45i	−0.309257	+	1.88751i
$886$	737.471			0.832361
$887$	−186.566			−0.210333			−0.105167	−	0.994455i	$-0.533538\pi$
$887$	−186.566			−0.210333			−0.105167	+	0.994455i	$0.533538\pi$
$888$	76.6842	+	269.213i	0.0863561	+	0.303168i
$889$	−383.796			−0.431716
$890$	80.7443	−	171.557i	0.0907240	−	0.192761i
$891$	−1316.99	−	653.828i	−1.47810	−	0.733814i
$892$			144.469i			0.161961i
$893$	291.773			0.326734
$894$	−112.963	−	396.577i	−0.126357	−	0.443598i
$895$	−424.646	+	902.245i	−0.474465	+	1.00809i
$896$			29.9333i			0.0334077i
$897$	−229.738	−	806.534i	−0.256118	−	0.899146i
$898$		−	843.044i		−	0.938802i
$899$			213.078i			0.237017i
$900$	426.471	+	143.604i	0.473857	+	0.159560i
$901$	−2.73131			−0.00303142
$902$	−588.974			−0.652965
$903$	154.731	−	44.0745i	0.171352	−	0.0488090i
$904$	171.872			0.190124
$905$	−191.120	−	89.9516i	−0.211182	−	0.0993940i
$906$	−506.500	+	144.274i	−0.559051	+	0.159243i
$907$			1079.22i			1.18988i	0.803771	+	0.594939i	$0.202824\pi$
$907$			1079.22i			1.18988i	−0.803771	+	0.594939i	$0.797176\pi$
$908$	−208.140			−0.229229
$909$	−186.481	−	300.778i	−0.205150	−	0.330888i
$910$	−381.674	−	179.637i	−0.419422	−	0.197403i
$911$			1274.59i			1.39911i	0.714580	+	0.699554i	$0.246618\pi$
$911$			1274.59i			1.39911i	−0.714580	+	0.699554i	$0.753382\pi$
$912$	348.105	−	99.1563i	0.381694	−	0.108724i
$913$		−	2213.27i		−	2.42417i
$914$		−	452.873i		−	0.495484i
$915$	−834.619	−	136.747i	−0.912152	−	0.149450i
$916$	659.402			0.719871
$917$	−15.7961			−0.0172258
$918$	11.7483	−	12.9104i	0.0127977	−	0.0140636i
$919$	1110.91			1.20882			0.604412	−	0.796672i	$-0.293408\pi$
$919$	1110.91			1.20882			0.604412	+	0.796672i	$0.293408\pi$
$920$	158.635	+	74.6623i	0.172429	+	0.0811547i
$921$	−319.577	−	1121.93i	−0.346989	−	1.21816i
$922$			200.726i			0.217708i
$923$	472.159			0.511548
$924$	−277.138	+	78.9417i	−0.299933	+	0.0854348i
$925$	635.541	−	525.606i	0.687072	−	0.568223i
$926$			330.068i			0.356445i
$927$	332.967	+	537.047i	0.359188	+	0.579338i
$928$			26.6280i			0.0286940i
$929$			140.614i			0.151361i	0.997132	+	0.0756803i	$0.0241129\pi$
$929$			140.614i			0.151361i	−0.997132	+	0.0756803i	$0.975887\pi$
$930$	947.610	+	155.260i	1.01894	+	0.166946i
$931$	211.139			0.226787
$932$	145.534			0.156152
$933$	126.539	+	444.237i	0.135626	+	0.476139i
$934$	549.913			0.588772
$935$	17.6693	−	37.5419i	0.0188976	−	0.0401517i
$936$	−302.451	−	487.827i	−0.323131	−	0.521183i
$937$			1469.08i			1.56785i	0.620853	+	0.783927i	$0.286786\pi$
$937$			1469.08i			1.56785i	−0.620853	+	0.783927i	$0.713214\pi$
$938$	251.321			0.267933
$939$	94.4259	+	331.498i	0.100560	+	0.353033i
$940$	87.5238	+	41.1936i	0.0931105	+	0.0438229i
$941$		−	6.07056i		−	0.00645118i	−0.999995	−	0.00322559i	$-0.998973\pi$
$941$		−	6.07056i		−	0.00645118i	0.999995	−	0.00322559i	$-0.00102674\pi$
$942$	58.5918	+	205.696i	0.0621993	+	0.218361i
$943$			284.431i			0.301624i
$944$			451.392i			0.478170i
$945$	136.650	+	330.003i	0.144603	+	0.349209i
$946$	520.355			0.550058
$947$	−1311.95			−1.38538			−0.692688	−	0.721237i	$-0.743574\pi$
$947$	−1311.95			−1.38538			−0.692688	+	0.721237i	$0.743574\pi$
$948$	238.924	−	68.0566i	0.252030	−	0.0717897i
$949$	−2204.94			−2.32343
$950$	−679.633	−	821.785i	−0.715404	−	0.865037i
$951$	23.6971	−	6.75002i	0.0249181	−	0.00709781i
$952$		−	3.42100i		−	0.00359348i
$953$	953.113			1.00012			0.500059	−	0.865991i	$-0.333312\pi$
$953$	953.113			1.00012			0.500059	+	0.865991i	$0.333312\pi$
$954$	64.6309	−	40.0709i	0.0677472	−	0.0420030i
$955$	−453.332	+	963.194i	−0.474694	+	1.00858i
$956$			582.987i			0.609819i
$957$	−246.537	+	70.2249i	−0.257614	+	0.0733802i
$958$		−	1260.84i		−	1.31612i
$959$			342.081i			0.356706i
$960$	118.421	+	19.4026i	0.123355	+	0.0202110i
$961$	1088.05			1.13220
$962$	−1051.95			−1.09350
$963$	−658.139	+	408.044i	−0.683426	+	0.423721i
$964$	563.366			0.584404
$965$	174.175	−	370.070i	0.180493	−	0.383492i
$966$	38.1231	+	133.838i	0.0394649	+	0.138548i
$967$		−	624.295i		−	0.645600i	−0.946467	−	0.322800i	$-0.895376\pi$
$967$		−	624.295i		−	0.645600i	0.946467	−	0.322800i	$-0.104624\pi$
$968$	−589.767			−0.609263
$969$	−39.7840	+	11.3323i	−0.0410568	+	0.0116949i
$970$	−456.232	+	969.356i	−0.470343	+	0.999336i
$971$			982.557i			1.01190i	0.862562	+	0.505951i	$0.168858\pi$
$971$			982.557i			1.01190i	−0.862562	+	0.505951i	$0.831142\pi$
$972$	−88.5924	+	477.857i	−0.0911444	+	0.491623i
$973$			625.615i			0.642975i
$974$			323.738i			0.332380i
$975$	−958.073	+	1393.53i	−0.982639	+	1.42926i
$976$	−225.533			−0.231079
$977$	1520.84			1.55664			0.778320	−	0.627868i	$-0.216072\pi$
$977$	1520.84			1.55664			0.778320	+	0.627868i	$0.216072\pi$
$978$	153.189	+	537.795i	0.156635	+	0.549893i
$979$	486.755			0.497197
$980$	63.3357	+	29.8093i	0.0646282	+	0.0304176i
$981$	355.262	−	220.261i	0.362143	−	0.224527i
$982$			465.206i			0.473734i
$983$	−366.574			−0.372914			−0.186457	−	0.982463i	$-0.559700\pi$
$983$	−366.574			−0.372914			−0.186457	+	0.982463i	$0.559700\pi$
$984$	53.3310	+	187.228i	0.0541982	+	0.190272i
$985$	−637.369	−	299.981i	−0.647075	−	0.304549i
$986$		−	3.04325i		−	0.00308646i
$987$	21.0337	+	73.8424i	0.0213107	+	0.0748150i
$988$			1360.22i			1.37674i
$989$		−	251.293i		−	0.254088i
$990$	132.667	+	1147.58i	0.134007	+	1.15917i
$991$	1204.07			1.21501			0.607505	−	0.794316i	$-0.292171\pi$
$991$	1204.07			1.21501			0.607505	+	0.794316i	$0.292171\pi$
$992$	256.065			0.258130
$993$	1798.19	−	512.207i	1.81087	−	0.515817i
$994$	−78.3509			−0.0788239
$995$	540.153	+	254.226i	0.542867	+	0.255503i
$996$	−703.572	+	200.409i	−0.706397	+	0.201214i
$997$			861.399i			0.863991i	0.901876	+	0.431995i	$0.142190\pi$
$997$			861.399i			0.863991i	−0.901876	+	0.431995i	$0.857810\pi$
$998$	239.925			0.240406
$999$	658.774	+	599.477i	0.659433	+	0.600077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.c.a.29.14	yes	24
3.2	odd	2	inner	210.3.c.a.29.12	yes	24
5.2	odd	4		1050.3.e.e.701.24		24
5.3	odd	4		1050.3.e.e.701.21		24
5.4	even	2	inner	210.3.c.a.29.11	✓	24
15.2	even	4		1050.3.e.e.701.22		24
15.8	even	4		1050.3.e.e.701.23		24
15.14	odd	2	inner	210.3.c.a.29.13	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.c.a.29.11	✓	24	5.4	even	2	inner
210.3.c.a.29.12	yes	24	3.2	odd	2	inner
210.3.c.a.29.13	yes	24	15.14	odd	2	inner
210.3.c.a.29.14	yes	24	1.1	even	1	trivial
1050.3.e.e.701.21		24	5.3	odd	4
1050.3.e.e.701.22		24	15.2	even	4
1050.3.e.e.701.23		24	15.8	even	4
1050.3.e.e.701.24		24	5.2	odd	4

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(-2.88523 + 0.821846i) q^{3} +2.00000 q^{4} +(-4.52398 - 2.12923i) q^{5} +(-4.08034 + 1.16227i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(7.64914 - 4.74244i) q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(-2.88523 + 0.821846i) q^{3} +2.00000 q^{4} +(-4.52398 - 2.12923i) q^{5} +(-4.08034 + 1.16227i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(7.64914 - 4.74244i) q^{9} +(-6.39787 - 3.01119i) q^{10} -18.1525i q^{11} +(-5.77047 + 1.64369i) q^{12} -22.5480i q^{13} +3.74166i q^{14} +(14.8026 + 2.42532i) q^{15} +4.00000 q^{16} -0.457150 q^{17} +(10.8175 - 6.70682i) q^{18} -30.1627 q^{19} +(-9.04795 - 4.25847i) q^{20} +(-2.17440 - 7.63361i) q^{21} -25.6715i q^{22} -12.3975 q^{23} +(-8.16067 + 2.32453i) q^{24} +(15.9327 + 19.2652i) q^{25} -31.8877i q^{26} +(-18.1720 + 19.9694i) q^{27} +5.29150i q^{28} +4.70721i q^{29} +(20.9341 + 3.42992i) q^{30} +45.2664 q^{31} +5.65685 q^{32} +(14.9186 + 52.3743i) q^{33} -0.646507 q^{34} +(5.63342 - 11.9693i) q^{35} +(15.2983 - 9.48487i) q^{36} -32.9891i q^{37} -42.6564 q^{38} +(18.5310 + 65.0563i) q^{39} +(-12.7957 - 6.02238i) q^{40} -22.9427i q^{41} +(-3.07507 - 10.7956i) q^{42} +20.2697i q^{43} -36.3050i q^{44} +(-44.7023 + 5.16787i) q^{45} -17.5327 q^{46} -9.67333 q^{47} +(-11.5409 + 3.28739i) q^{48} -7.00000 q^{49} +(22.5323 + 27.2451i) q^{50} +(1.31898 - 0.375707i) q^{51} -45.0960i q^{52} +5.97465 q^{53} +(-25.6991 + 28.2411i) q^{54} +(-38.6510 + 82.1216i) q^{55} +7.48331i q^{56} +(87.0263 - 24.7891i) q^{57} +6.65700i q^{58} +112.848i q^{59} +(29.6053 + 4.85064i) q^{60} -56.3832 q^{61} +64.0163 q^{62} +(12.5473 + 20.2377i) q^{63} +8.00000 q^{64} +(-48.0100 + 102.007i) q^{65} +(21.0981 + 74.0684i) q^{66} -67.1684i q^{67} -0.914300 q^{68} +(35.7696 - 10.1888i) q^{69} +(7.96686 - 16.9272i) q^{70} +20.9402i q^{71} +(21.6350 - 13.4136i) q^{72} -97.7885i q^{73} -46.6536i q^{74} +(-61.8027 - 42.4903i) q^{75} -60.3253 q^{76} +48.0271 q^{77} +(26.2068 + 92.0034i) q^{78} -41.4047 q^{79} +(-18.0959 - 8.51693i) q^{80} +(36.0186 - 72.5511i) q^{81} -32.4459i q^{82} +121.926 q^{83} +(-4.34880 - 15.2672i) q^{84} +(2.06814 + 0.973379i) q^{85} +28.6657i q^{86} +(-3.86860 - 13.5814i) q^{87} -51.3431i q^{88} +26.8148i q^{89} +(-63.2186 + 7.30848i) q^{90} +59.6564 q^{91} -24.7950 q^{92} +(-130.604 + 37.2020i) q^{93} -13.6802 q^{94} +(136.455 + 64.2233i) q^{95} +(-16.3213 + 4.64907i) q^{96} -151.512i q^{97} -9.89949 q^{98} +(-86.0872 - 138.851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 48 q^{4} + 44 q^{9}+O(q^{10}) \) 24 * q + 48 * q^4 + 44 * q^9	\( 24 q + 48 q^{4} + 44 q^{9} + 16 q^{10} + 4 q^{15} + 96 q^{16} - 80 q^{19} - 28 q^{21} + 48 q^{25} - 56 q^{30} + 224 q^{31} + 128 q^{34} + 88 q^{36} - 92 q^{39} + 32 q^{40} - 72 q^{45} - 144 q^{46} - 168 q^{49} - 284 q^{51} - 144 q^{54} - 320 q^{55} + 8 q^{60} + 192 q^{64} + 224 q^{66} - 152 q^{69} - 56 q^{70} + 48 q^{75} - 160 q^{76} - 72 q^{79} - 212 q^{81} - 56 q^{84} - 64 q^{85} - 240 q^{90} + 168 q^{91} - 128 q^{94} - 876 q^{99}+O(q^{100}) \) 24 * q + 48 * q^4 + 44 * q^9 + 16 * q^10 + 4 * q^15 + 96 * q^16 - 80 * q^19 - 28 * q^21 + 48 * q^25 - 56 * q^30 + 224 * q^31 + 128 * q^34 + 88 * q^36 - 92 * q^39 + 32 * q^40 - 72 * q^45 - 144 * q^46 - 168 * q^49 - 284 * q^51 - 144 * q^54 - 320 * q^55 + 8 * q^60 + 192 * q^64 + 224 * q^66 - 152 * q^69 - 56 * q^70 + 48 * q^75 - 160 * q^76 - 72 * q^79 - 212 * q^81 - 56 * q^84 - 64 * q^85 - 240 * q^90 + 168 * q^91 - 128 * q^94 - 876 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more