LMFDB - Embedded newform 210.3.c.a.29.12

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			29.12
Character	$\chi$	$=$	210.29
Dual form			210.3.c.a.29.11

$q$-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} +(11.3028 + 9.86135i) 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} +(-15.9846 - 13.9461i) 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} +(24.5068 + 37.7415i) 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} +(22.6056 + 19.7227i) 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} +(30.1366 + 68.6789i) 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} +(-34.6578 - 53.3745i) 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	$0.308890\pi$
$11$			18.1525i			1.65023i	−0.564965	+	0.825115i	$0.691110\pi$
$12$	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
$15$	11.3028	+	9.86135i	0.753522	+	0.657423i
$16$	4.00000			0.250000
$17$	0.457150			0.0268912			0.0134456	−	0.999910i	$-0.495720\pi$
$17$	0.457150			0.0268912			0.0134456	+	0.999910i	$0.495720\pi$
$18$	−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	$-0.413138\pi$
$23$	12.3975			0.539021			0.269510	+	0.962997i	$0.413138\pi$
$24$	−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	$-0.974138\pi$
$29$		−	4.70721i		−	0.162318i	0.996701	−	0.0811588i	$-0.0258621\pi$
$30$	−15.9846	−	13.9461i	−0.532820	−	0.464868i
$31$	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	$0.0902644\pi$
$41$			22.9427i			0.559578i	−0.960062	+	0.279789i	$0.909736\pi$
$42$	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
$45$	24.5068	+	37.7415i	0.544595	+	0.838699i
$46$	−17.5327			−0.381145
$47$	9.67333			0.205816			0.102908	−	0.994691i	$-0.467185\pi$
$47$	9.67333			0.205816			0.102908	+	0.994691i	$0.467185\pi$
$48$	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	$-0.517951\pi$
$53$	−5.97465			−0.112729			−0.0563646	+	0.998410i	$0.517951\pi$
$54$	−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	$-0.594407\pi$
$59$		−	112.848i		−	1.91268i	0.292259	−	0.956339i	$-0.405593\pi$
$60$	22.6056	+	19.7227i	0.376761	+	0.328712i
$61$	−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	$-0.952888\pi$
$71$		−	20.9402i		−	0.294932i	0.989067	−	0.147466i	$-0.0471117\pi$
$72$	−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
$75$	30.1366	+	68.6789i	0.401821	+	0.915718i
$76$	−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	$-0.762581\pi$
$83$	−121.926			−1.46899			−0.734496	+	0.678613i	$0.762581\pi$
$84$	−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	$-0.951865\pi$
$89$		−	26.8148i		−	0.301289i	0.988588	−	0.150645i	$-0.0481349\pi$
$90$	−34.6578	−	53.3745i	−0.385087	−	0.593050i
$91$	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	$0.0623611\pi$
$101$			39.3218i			0.389324i	−0.980870	+	0.194662i	$0.937639\pi$
$102$	−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
$105$	−26.0907	+	29.9045i	−0.248483	+	0.284804i
$106$	8.44943			0.0797116
$107$	86.0409			0.804121			0.402060	−	0.915613i	$-0.368294\pi$
$107$	86.0409			0.804121			0.402060	+	0.915613i	$0.368294\pi$
$108$	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	$-0.586652\pi$
$113$	−60.7659			−0.537752			−0.268876	+	0.963175i	$0.586652\pi$
$114$	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
$120$	−31.9692	−	27.8921i	−0.266410	−	0.232434i
$121$	−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	$-0.992746\pi$
$131$		−	5.97035i		−	0.0455752i	0.999740	−	0.0227876i	$-0.00725414\pi$
$132$	−29.8372	+	104.749i	−0.226039	+	0.793549i
$133$		−	79.8029i		−	0.600022i
$134$			94.9905i			0.708885i
$135$	39.6900	+	129.034i	0.294000	+	0.955805i
$136$	−1.29301			−0.00950746
$137$	−129.294			−0.943754			−0.471877	−	0.881664i	$-0.656423\pi$
$137$	−129.294			−0.943754			−0.471877	+	0.881664i	$0.656423\pi$
$138$	−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	$-0.894249\pi$
$149$		−	97.1922i		−	0.652297i	0.945319	−	0.326148i	$-0.105751\pi$
$150$	−42.6196	−	97.1266i	−0.284131	−	0.647510i
$151$	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
$165$	−179.008	+	205.175i	−1.08490	+	1.24348i
$166$	172.430			1.03873
$167$	−189.086			−1.13225			−0.566125	−	0.824320i	$-0.691558\pi$
$167$	−189.086			−1.13225			−0.566125	+	0.824320i	$0.691558\pi$
$168$	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	$-0.820820\pi$
$173$	−292.614			−1.69141			−0.845706	+	0.533650i	$0.820820\pi$
$174$	−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	$0.188080\pi$
$179$			199.436i			1.11417i	−0.830456	+	0.557084i	$0.811920\pi$
$180$	49.0135	+	75.4829i	0.272297	+	0.419350i
$181$	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	$0.188183\pi$
$191$			212.909i			1.11471i	−0.830276	+	0.557353i	$0.811817\pi$
$192$	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
$195$	222.354	−	254.856i	1.14028	−	1.30695i
$196$	−14.0000			−0.0714286
$197$	−140.887			−0.715162			−0.357581	−	0.933882i	$-0.616398\pi$
$197$	−140.887			−0.715162			−0.357581	+	0.933882i	$0.616398\pi$
$198$	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
$210$	36.8978	−	42.2913i	0.175704	−	0.201387i
$211$	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
$225$	30.5076	+	222.922i	0.135590	+	0.990765i
$226$	85.9360			0.380248
$227$	104.070			0.458458			0.229229	−	0.973373i	$-0.426380\pi$
$227$	104.070			0.458458			0.229229	+	0.973373i	$0.426380\pi$
$228$	−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	$-0.549909\pi$
$233$	−72.7668			−0.312304			−0.156152	+	0.987733i	$0.549909\pi$
$234$	−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	$-0.791242\pi$
$239$		−	291.494i		−	1.21964i	0.792540	−	0.609819i	$-0.208758\pi$
$240$	45.2113	+	39.4454i	0.188380	+	0.164356i
$241$	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	$0.136952\pi$
$251$			209.382i			0.834193i	−0.908862	+	0.417096i	$0.863048\pi$
$252$	−25.0946	+	40.4754i	−0.0995818	+	0.160617i
$253$			225.045i			0.889508i
$254$		−	205.147i		−	0.807667i
$255$	5.16708	+	4.50811i	0.0202631	+	0.0176789i
$256$	16.0000			0.0625000
$257$	357.735			1.39197			0.695983	−	0.718058i	$-0.254969\pi$
$257$	357.735			1.39197			0.695983	+	0.718058i	$0.254969\pi$
$258$	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	$-0.407956\pi$
$263$	149.990			0.570304			0.285152	+	0.958482i	$0.407956\pi$
$264$	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	$-0.900777\pi$
$269$		−	165.001i		−	0.613386i	0.951808	−	0.306693i	$-0.0992225\pi$
$270$	−56.1302	−	182.481i	−0.207890	−	0.675856i
$271$	−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	$0.180254\pi$
$281$			301.513i			1.07300i	−0.843900	+	0.536500i	$0.819746\pi$
$282$	−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
$285$	−340.923	−	297.444i	−1.19622	−	1.04366i
$286$	−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	$-0.293209\pi$
$293$	354.478			1.20982			0.604911	+	0.796293i	$0.293209\pi$
$294$	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
$300$	60.2732	+	137.358i	0.200911	+	0.457859i
$301$	−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	$0.0796219\pi$
$311$			153.969i			0.495078i	−0.968878	+	0.247539i	$0.920378\pi$
$312$	−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
$315$	−99.8545	+	64.8388i	−0.316999	+	0.205837i
$316$	−82.8094			−0.262055
$317$	8.21324			0.0259093			0.0129546	−	0.999916i	$-0.495876\pi$
$317$	8.21324			0.0259093			0.0129546	+	0.999916i	$0.495876\pi$
$318$	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
$330$	253.156	−	290.161i	0.767139	−	0.879276i
$331$	−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
$345$	140.127	+	122.256i	0.406164	+	0.354365i
$346$	413.819			1.19601
$347$	466.444			1.34422			0.672110	−	0.740452i	$-0.265388\pi$
$347$	466.444			1.34422			0.672110	+	0.740452i	$0.265388\pi$
$348$	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	$-0.609266\pi$
$353$	−237.617			−0.673137			−0.336568	+	0.941659i	$0.609266\pi$
$354$	−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	$0.143536\pi$
$359$			312.908i			0.871610i	−0.900041	+	0.435805i	$0.856464\pi$
$360$	−69.3156	−	106.749i	−0.192543	−	0.296525i
$361$	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
$375$	−9.89602	+	374.869i	−0.0263894	+	0.999652i
$376$	−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	$-0.601787\pi$
$383$	−240.793			−0.628702			−0.314351	+	0.949307i	$0.601787\pi$
$384$	−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	$-0.933767\pi$
$389$		−	160.718i		−	0.413157i	0.978430	−	0.206579i	$-0.0662329\pi$
$390$	−314.456	+	360.421i	−0.806297	+	0.924157i
$391$	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	$0.0779476\pi$
$401$			194.436i			0.484879i	−0.970167	+	0.242439i	$0.922052\pi$
$402$	−78.0676	+	274.070i	−0.194198	+	0.681766i
$403$		−	1020.67i		−	2.53267i
$404$			78.6435i			0.194662i
$405$	8.46910	+	404.911i	0.0209114	+	0.999781i
$406$	−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	$0.264174\pi$
$419$			618.346i			1.47577i	−0.674929	+	0.737883i	$0.735826\pi$
$420$	−52.1813	+	59.8089i	−0.124241	+	0.142402i
$421$	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	$-0.932871\pi$
$431$		−	180.443i		−	0.418662i	0.977845	−	0.209331i	$-0.0671287\pi$
$432$	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
$435$	46.4194	−	53.2047i	0.106711	−	0.122310i
$436$	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	$-0.700308\pi$
$443$	−521.471			−1.17714			−0.588568	+	0.808448i	$0.700308\pi$
$444$	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	$0.231072\pi$
$449$			596.122i			1.32767i	−0.747880	+	0.663833i	$0.768928\pi$
$450$	−43.1443	−	315.260i	−0.0958763	−	0.700577i
$451$	−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	$-0.950803\pi$
$461$		−	141.935i		−	0.307885i	0.988080	−	0.153943i	$-0.0491971\pi$
$462$	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
$465$	511.638	+	446.388i	1.10030	+	0.959973i
$466$	102.908			0.220832
$467$	−388.847			−0.832649			−0.416325	−	0.909216i	$-0.636682\pi$
$467$	−388.847			−0.832649			−0.416325	+	0.909216i	$0.636682\pi$
$468$	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	$0.380745\pi$
$479$			891.549i			1.86127i	−0.365946	+	0.930636i	$0.619255\pi$
$480$	−63.9384	−	55.7842i	−0.133205	−	0.116217i
$481$	−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	$-0.891270\pi$
$491$		−	328.951i		−	0.669960i	0.942225	−	0.334980i	$-0.108730\pi$
$492$	−37.7107	+	132.390i	−0.0766478	+	0.269085i
$493$		−	2.15190i		−	0.00436491i
$494$		−	961.818i		−	1.94700i
$495$	−685.103	+	444.860i	−1.38405	+	0.898706i
$496$	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	$-0.385607\pi$
$503$	353.801			0.703381			0.351691	+	0.936116i	$0.385607\pi$
$504$	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	$-0.648526\pi$
$509$		−	909.175i		−	1.78620i	0.449859	−	0.893099i	$-0.351474\pi$
$510$	−7.30736	−	6.37543i	−0.0143282	−	0.0125009i
$511$	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	$0.0237784\pi$
$521$			77.7672i			0.149265i	−0.997211	+	0.0746326i	$0.976222\pi$
$522$	−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
$525$	−181.707	+	79.7340i	−0.346109	+	0.151874i
$526$	−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
$540$	79.3801	+	258.067i	0.147000	+	0.477903i
$541$	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
$555$	325.317	−	372.870i	0.586157	−	0.671838i
$556$	472.921			0.850576
$557$	76.6136			0.137547			0.0687735	−	0.997632i	$-0.478091\pi$
$557$	76.6136			0.137547			0.0687735	+	0.997632i	$0.478091\pi$
$558$	−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	$-0.604125\pi$
$563$	−361.800			−0.642629			−0.321314	+	0.946973i	$0.604125\pi$
$564$	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	$-0.979765\pi$
$569$		−	72.2936i		−	0.127054i	0.997980	−	0.0635269i	$-0.0202349\pi$
$570$	482.138	+	420.650i	0.845856	+	0.737982i
$571$	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
$585$	850.995	−	552.579i	1.45469	−	0.944579i
$586$	−501.308			−0.855474
$587$	245.442			0.418130			0.209065	−	0.977902i	$-0.432958\pi$
$587$	245.442			0.418130			0.209065	+	0.977902i	$0.432958\pi$
$588$	−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	$-0.416298\pi$
$593$	308.286			0.519876			0.259938	+	0.965625i	$0.416298\pi$
$594$	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	$0.0457205\pi$
$599$			171.484i			0.286283i	−0.989702	+	0.143142i	$0.954280\pi$
$600$	−85.2392	−	194.253i	−0.142065	−	0.323755i
$601$	−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
$615$	−226.246	+	259.317i	−0.367879	+	0.421654i
$616$	135.841			0.220521
$617$	−572.163			−0.927331			−0.463665	−	0.886010i	$-0.653466\pi$
$617$	−572.163			−0.927331			−0.463665	+	0.886010i	$0.653466\pi$
$618$	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
$630$	141.216	−	91.6959i	0.224152	−	0.145549i
$631$	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	$0.213096\pi$
$641$			795.563i			1.24113i	−0.784156	+	0.620564i	$0.786904\pi$
$642$	−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
$645$	−199.887	+	229.105i	−0.309902	+	0.355202i
$646$	19.5004			0.0301863
$647$	482.089			0.745114			0.372557	−	0.928009i	$-0.378481\pi$
$647$	482.089			0.745114			0.372557	+	0.928009i	$0.378481\pi$
$648$	−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	$-0.806899\pi$
$653$	−1072.96			−1.64313			−0.821565	+	0.570114i	$0.806899\pi$
$654$	−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	$0.165134\pi$
$659$			653.498i			0.991651i	−0.868422	+	0.495825i	$0.834866\pi$
$660$	−358.017	+	410.350i	−0.542449	+	0.621742i
$661$	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
$675$	−95.1861	+	668.255i	−0.141016	+	0.990007i
$676$	−678.826			−1.00418
$677$	−409.731			−0.605216			−0.302608	−	0.953115i	$-0.597857\pi$
$677$	−409.731			−0.605216			−0.302608	+	0.953115i	$0.597857\pi$
$678$	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	$-0.452070\pi$
$683$	204.910			0.300015			0.150008	+	0.988685i	$0.452070\pi$
$684$	−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
$690$	−198.169	−	172.896i	−0.287201	−	0.250574i
$691$	−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	$-0.756855\pi$
$701$		−	969.784i		−	1.38343i	0.722171	−	0.691715i	$-0.243145\pi$
$702$	−636.780	+	579.463i	−0.907094	+	0.825446i
$703$			995.038i			1.41542i
$704$			145.220i			0.206279i
$705$	109.336	+	95.3921i	0.155086	+	0.135308i
$706$	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	$0.374607\pi$
$719$			1327.86i			1.84681i	−0.383825	+	0.923406i	$0.625393\pi$
$720$	98.0271	+	150.966i	0.136149	+	0.209675i
$721$	−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
$735$	−79.1198	−	69.0294i	−0.107646	−	0.0939176i
$736$	−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	$-0.518446\pi$
$743$	−86.0672			−0.115837			−0.0579187	+	0.998321i	$0.518446\pi$
$744$	−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
$750$	13.9951	−	530.145i	0.0186601	−	0.706861i
$751$	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	$-0.710044\pi$
$761$		−	1202.49i		−	1.58014i	0.613017	−	0.790069i	$-0.289956\pi$
$762$	168.600	−	591.898i	0.221259	−	0.776769i
$763$			122.881i			0.161050i
$764$			425.817i			0.557353i
$765$	11.2033	+	17.2535i	0.0146448	+	0.0225536i
$766$	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	$-0.315346\pi$
$773$	847.386			1.09623			0.548115	+	0.836403i	$0.315346\pi$
$774$	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
$780$	444.708	−	509.712i	0.570138	−	0.653477i
$781$	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
$795$	−67.5304	−	58.9181i	−0.0849439	−	0.0741108i
$796$	−238.796			−0.299995
$797$	−65.3181			−0.0819550			−0.0409775	−	0.999160i	$-0.513047\pi$
$797$	−65.3181			−0.0819550			−0.0409775	+	0.999160i	$0.513047\pi$
$798$	−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	$0.208293\pi$
$809$			984.812i			1.21732i	−0.793431	+	0.608660i	$0.791707\pi$
$810$	−11.9771	−	572.631i	−0.0147866	−	0.706952i
$811$	−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	$0.0617295\pi$
$821$			316.439i			0.385431i	−0.981255	+	0.192716i	$0.938271\pi$
$822$	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
$825$	−1246.69	+	547.055i	−1.51114	+	0.663097i
$826$	−422.239			−0.511185
$827$	−1321.39			−1.59781			−0.798907	−	0.601455i	$-0.794588\pi$
$827$	−1321.39			−1.59781			−0.798907	+	0.601455i	$0.794588\pi$
$828$	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	$-0.815263\pi$
$839$		−	920.100i		−	1.09666i	0.836261	−	0.548331i	$-0.184737\pi$
$840$	73.7956	−	84.5826i	0.0878519	−	0.100694i
$841$	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
$855$	−739.189	−	1138.38i	−0.864549	−	1.33144i
$856$	−243.361			−0.284300
$857$	948.093			1.10629			0.553147	−	0.833084i	$-0.313427\pi$
$857$	948.093			1.10629			0.553147	+	0.833084i	$0.313427\pi$
$858$	−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	$-0.856578\pi$
$863$	−1553.74			−1.80040			−0.900198	+	0.435482i	$0.856578\pi$
$864$	−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
$870$	−65.6470	+	75.2429i	−0.0754563	+	0.0864861i
$871$	−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	$0.0431450\pi$
$881$			238.098i			0.270259i	−0.990828	+	0.135129i	$0.956855\pi$
$882$	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
$885$	1112.83	−	1275.50i	1.25744	−	1.44124i
$886$	737.471			0.832361
$887$	186.566			0.210333			0.105167	−	0.994455i	$-0.466462\pi$
$887$	186.566			0.210333			0.105167	+	0.994455i	$0.466462\pi$
$888$	−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
$900$	61.0153	+	445.844i	0.0677948	+	0.495383i
$901$	−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	$-0.753382\pi$
$911$		−	1274.59i		−	1.39911i	0.714580	−	0.699554i	$-0.246618\pi$
$912$	−348.105	−	99.1563i	−0.381694	−	0.108724i
$913$		−	2213.27i		−	2.42417i
$914$			452.873i			0.495484i
$915$	−637.289	−	556.014i	−0.696491	−	0.607665i
$916$	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	$-0.975887\pi$
$929$		−	140.614i		−	0.151361i	0.997132	−	0.0756803i	$-0.0241129\pi$
$930$	−723.565	−	631.287i	−0.778027	−	0.678804i
$931$	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	$0.00102674\pi$
$941$			6.07056i			0.00645118i	−0.999995	+	0.00322559i	$0.998973\pi$
$942$	−58.5918	+	205.696i	−0.0621993	+	0.218361i
$943$			284.431i			0.301624i
$944$		−	451.392i		−	0.478170i
$945$	−341.391	+	105.010i	−0.361260	+	0.111122i
$946$	520.355			0.550058
$947$	1311.95			1.38538			0.692688	−	0.721237i	$-0.256426\pi$
$947$	1311.95			1.38538			0.692688	+	0.721237i	$0.256426\pi$
$948$	−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	$-0.666688\pi$
$953$	−953.113			−1.00012			−0.500059	+	0.865991i	$0.666688\pi$
$954$	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
$960$	90.4226	+	78.8908i	0.0941902	+	0.0821779i
$961$	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	$-0.831142\pi$
$971$		−	982.557i		−	1.01190i	0.862562	−	0.505951i	$-0.168858\pi$
$972$	88.5924	+	477.857i	0.0911444	+	0.491623i
$973$			625.615i			0.642975i
$974$		−	323.738i		−	0.332380i
$975$	1548.57	−	679.520i	1.58828	−	0.696944i
$976$	−225.533			−0.231079
$977$	−1520.84			−1.55664			−0.778320	−	0.627868i	$-0.783928\pi$
$977$	−1520.84			−1.55664			−0.778320	+	0.627868i	$0.783928\pi$
$978$	−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	$-0.440300\pi$
$983$	366.574			0.372914			0.186457	+	0.982463i	$0.440300\pi$
$984$	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
$990$	968.882	−	629.126i	0.978668	−	0.635481i
$991$	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.29.12	yes	24
3.2	odd	2	inner	210.3.c.a.29.14	yes	24
5.2	odd	4		1050.3.e.e.701.22		24
5.3	odd	4		1050.3.e.e.701.23		24
5.4	even	2	inner	210.3.c.a.29.13	yes	24
15.2	even	4		1050.3.e.e.701.24		24
15.8	even	4		1050.3.e.e.701.21		24
15.14	odd	2	inner	210.3.c.a.29.11	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.c.a.29.11	✓	24	15.14	odd	2	inner
210.3.c.a.29.12	yes	24	1.1	even	1	trivial
210.3.c.a.29.13	yes	24	5.4	even	2	inner
210.3.c.a.29.14	yes	24	3.2	odd	2	inner
1050.3.e.e.701.21		24	15.8	even	4
1050.3.e.e.701.22		24	5.2	odd	4
1050.3.e.e.701.23		24	5.3	odd	4
1050.3.e.e.701.24		24	15.2	even	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} +(11.3028 + 9.86135i) 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} +(-15.9846 - 13.9461i) 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} +(24.5068 + 37.7415i) 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} +(22.6056 + 19.7227i) 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} +(30.1366 + 68.6789i) 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} +(-34.6578 - 53.3745i) 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

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