LMFDB - Embedded newform 690.3.g.a.461.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(461,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("690.461");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.g (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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.5
Character	$\chi$	$=$	690.461
Dual form			690.3.g.a.461.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(-2.73248 - 1.23837i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-1.75132 + 3.86431i) q^{6} +4.14117 q^{7} +2.82843i q^{8} +(5.93289 + 6.76763i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(-2.73248 - 1.23837i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-1.75132 + 3.86431i) q^{6} +4.14117 q^{7} +2.82843i q^{8} +(5.93289 + 6.76763i) q^{9} +3.16228 q^{10} -18.2040i q^{11} +(5.46496 + 2.47674i) q^{12} -8.45273 q^{13} -5.85650i q^{14} +(2.76908 - 6.11001i) q^{15} +4.00000 q^{16} +14.2788i q^{17} +(9.57088 - 8.39037i) q^{18} -25.5703 q^{19} -4.47214i q^{20} +(-11.3157 - 5.12830i) q^{21} -25.7443 q^{22} -4.79583i q^{23} +(3.50263 - 7.72862i) q^{24} -5.00000 q^{25} +11.9540i q^{26} +(-7.83068 - 25.8395i) q^{27} -8.28235 q^{28} +30.0240i q^{29} +(-8.64086 - 3.91606i) q^{30} -20.5971 q^{31} -5.65685i q^{32} +(-22.5432 + 49.7420i) q^{33} +20.1932 q^{34} +9.25994i q^{35} +(-11.8658 - 13.5353i) q^{36} +58.2578 q^{37} +36.1618i q^{38} +(23.0969 + 10.4676i) q^{39} -6.32456 q^{40} +55.4616i q^{41} +(-7.25251 + 16.0028i) q^{42} -61.0293 q^{43} +36.4080i q^{44} +(-15.1329 + 13.2663i) q^{45} -6.78233 q^{46} +13.9735i q^{47} +(-10.9299 - 4.95347i) q^{48} -31.8507 q^{49} +7.07107i q^{50} +(17.6824 - 39.0165i) q^{51} +16.9055 q^{52} -25.4683i q^{53} +(-36.5426 + 11.0743i) q^{54} +40.7054 q^{55} +11.7130i q^{56} +(69.8702 + 31.6654i) q^{57} +42.4604 q^{58} +79.7148i q^{59} +(-5.53815 + 12.2200i) q^{60} +95.2262 q^{61} +29.1286i q^{62} +(24.5691 + 28.0259i) q^{63} -8.00000 q^{64} -18.9009i q^{65} +(70.3459 + 31.8810i) q^{66} +75.8720 q^{67} -28.5576i q^{68} +(-5.93901 + 13.1045i) q^{69} +13.0955 q^{70} +132.680i q^{71} +(-19.1418 + 16.7807i) q^{72} -73.4381 q^{73} -82.3890i q^{74} +(13.6624 + 6.19184i) q^{75} +51.1405 q^{76} -75.3859i q^{77} +(14.8034 - 32.6640i) q^{78} +23.5709 q^{79} +8.94427i q^{80} +(-10.6017 + 80.3032i) q^{81} +78.4345 q^{82} -134.121i q^{83} +(22.6313 + 10.2566i) q^{84} -31.9283 q^{85} +86.3084i q^{86} +(37.1808 - 82.0401i) q^{87} +51.4887 q^{88} +116.975i q^{89} +(18.7614 + 21.4011i) q^{90} -35.0042 q^{91} +9.59166i q^{92} +(56.2810 + 25.5067i) q^{93} +19.7615 q^{94} -57.1768i q^{95} +(-7.00527 + 15.4572i) q^{96} -82.3630 q^{97} +45.0437i q^{98} +(123.198 - 108.002i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7}+O(q^{10}) $ 56 * q - 8 * q^3 - 112 * q^4 + 16 * q^6 - 16 * q^7	$ 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7} + 16 q^{12} + 80 q^{13} - 40 q^{15} + 224 q^{16} - 32 q^{18} - 64 q^{19} + 56 q^{21} - 96 q^{22} - 32 q^{24} - 280 q^{25} + 40 q^{27} + 32 q^{28} - 80 q^{31} + 32 q^{33} + 192 q^{34} + 240 q^{37} - 56 q^{39} - 144 q^{43} - 32 q^{48} + 72 q^{49} - 24 q^{51} - 160 q^{52} + 16 q^{54} - 16 q^{57} + 80 q^{60} + 112 q^{61} - 64 q^{63} - 448 q^{64} + 160 q^{66} + 832 q^{67} + 64 q^{72} - 608 q^{73} + 40 q^{75} + 128 q^{76} - 320 q^{78} + 48 q^{79} - 32 q^{81} - 448 q^{82} - 112 q^{84} + 240 q^{85} + 200 q^{87} + 192 q^{88} + 80 q^{91} - 232 q^{93} + 160 q^{94} + 64 q^{96} - 448 q^{97} + 464 q^{99}+O(q^{100}) $ 56 * q - 8 * q^3 - 112 * q^4 + 16 * q^6 - 16 * q^7 + 16 * q^12 + 80 * q^13 - 40 * q^15 + 224 * q^16 - 32 * q^18 - 64 * q^19 + 56 * q^21 - 96 * q^22 - 32 * q^24 - 280 * q^25 + 40 * q^27 + 32 * q^28 - 80 * q^31 + 32 * q^33 + 192 * q^34 + 240 * q^37 - 56 * q^39 - 144 * q^43 - 32 * q^48 + 72 * q^49 - 24 * q^51 - 160 * q^52 + 16 * q^54 - 16 * q^57 + 80 * q^60 + 112 * q^61 - 64 * q^63 - 448 * q^64 + 160 * q^66 + 832 * q^67 + 64 * q^72 - 608 * q^73 + 40 * q^75 + 128 * q^76 - 320 * q^78 + 48 * q^79 - 32 * q^81 - 448 * q^82 - 112 * q^84 + 240 * q^85 + 200 * q^87 + 192 * q^88 + 80 * q^91 - 232 * q^93 + 160 * q^94 + 64 * q^96 - 448 * q^97 + 464 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	−2.73248	−	1.23837i	−0.910827	−	0.412789i
$3$	−2.73248	−	1.23837i	−0.910827	−	0.412789i
$4$	−2.00000			−0.500000
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$	−1.75132	+	3.86431i	−0.291886	+	0.644052i
$7$	4.14117			0.591596			0.295798	−	0.955250i	$-0.404414\pi$
$7$	4.14117			0.591596			0.295798	+	0.955250i	$0.404414\pi$
$8$			2.82843i			0.353553i
$9$	5.93289	+	6.76763i	0.659210	+	0.751959i
$10$	3.16228			0.316228
$11$		−	18.2040i		−	1.65491i	−0.561533	−	0.827454i	$-0.689788\pi$
$11$		−	18.2040i		−	1.65491i	0.561533	−	0.827454i	$-0.310212\pi$
$12$	5.46496	+	2.47674i	0.455413	+	0.206395i
$13$	−8.45273			−0.650210			−0.325105	−	0.945678i	$-0.605400\pi$
$13$	−8.45273			−0.650210			−0.325105	+	0.945678i	$0.605400\pi$
$14$		−	5.85650i		−	0.418322i
$15$	2.76908	−	6.11001i	0.184605	−	0.407334i
$16$	4.00000			0.250000
$17$			14.2788i			0.839928i	0.907541	+	0.419964i	$0.137957\pi$
$17$			14.2788i			0.839928i	−0.907541	+	0.419964i	$0.862043\pi$
$18$	9.57088	−	8.39037i	0.531715	−	0.466132i
$19$	−25.5703			−1.34580			−0.672901	−	0.739732i	$-0.734952\pi$
$19$	−25.5703			−1.34580			−0.672901	+	0.739732i	$0.734952\pi$
$20$		−	4.47214i		−	0.223607i
$21$	−11.3157	−	5.12830i	−0.538841	−	0.244205i
$22$	−25.7443			−1.17020
$23$		−	4.79583i		−	0.208514i
$23$		−	4.79583i		−	0.208514i
$24$	3.50263	−	7.72862i	0.145943	−	0.322026i
$25$	−5.00000			−0.200000
$26$			11.9540i			0.459768i
$27$	−7.83068	−	25.8395i	−0.290025	−	0.957019i
$28$	−8.28235			−0.295798
$29$			30.0240i			1.03531i	0.855589	+	0.517656i	$0.173195\pi$
$29$			30.0240i			1.03531i	−0.855589	+	0.517656i	$0.826805\pi$
$30$	−8.64086	−	3.91606i	−0.288029	−	0.130535i
$31$	−20.5971			−0.664421			−0.332211	−	0.943205i	$-0.607794\pi$
$31$	−20.5971			−0.664421			−0.332211	+	0.943205i	$0.607794\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−22.5432	+	49.7420i	−0.683129	+	1.50733i
$34$	20.1932			0.593919
$35$			9.25994i			0.264570i
$36$	−11.8658	−	13.5353i	−0.329605	−	0.375980i
$37$	58.2578			1.57453			0.787267	−	0.616612i	$-0.211495\pi$
$37$	58.2578			1.57453			0.787267	+	0.616612i	$0.211495\pi$
$38$			36.1618i			0.951626i
$39$	23.0969	+	10.4676i	0.592229	+	0.268400i
$40$	−6.32456			−0.158114
$41$			55.4616i			1.35272i	0.736571	+	0.676361i	$0.236444\pi$
$41$			55.4616i			1.35272i	−0.736571	+	0.676361i	$0.763556\pi$
$42$	−7.25251	+	16.0028i	−0.172679	+	0.381018i
$43$	−61.0293			−1.41929			−0.709643	−	0.704562i	$-0.751144\pi$
$43$	−61.0293			−1.41929			−0.709643	+	0.704562i	$0.751144\pi$
$44$			36.4080i			0.827454i
$45$	−15.1329	+	13.2663i	−0.336286	+	0.294808i
$46$	−6.78233			−0.147442
$47$			13.9735i			0.297308i	0.988889	+	0.148654i	$0.0474941\pi$
$47$			13.9735i			0.297308i	−0.988889	+	0.148654i	$0.952506\pi$
$48$	−10.9299	−	4.95347i	−0.227707	−	0.103197i
$49$	−31.8507			−0.650014
$50$			7.07107i			0.141421i
$51$	17.6824	−	39.0165i	0.346714	−	0.765029i
$52$	16.9055			0.325105
$53$		−	25.4683i		−	0.480533i	−0.970707	−	0.240267i	$-0.922765\pi$
$53$		−	25.4683i		−	0.480533i	0.970707	−	0.240267i	$-0.0772348\pi$
$54$	−36.5426	+	11.0743i	−0.676715	+	0.205079i
$55$	40.7054			0.740098
$56$			11.7130i			0.209161i
$57$	69.8702	+	31.6654i	1.22579	+	0.555533i
$58$	42.4604			0.732076
$59$			79.7148i			1.35110i	0.737315	+	0.675549i	$0.236093\pi$
$59$			79.7148i			1.35110i	−0.737315	+	0.675549i	$0.763907\pi$
$60$	−5.53815	+	12.2200i	−0.0923025	+	0.203667i
$61$	95.2262			1.56109			0.780543	−	0.625102i	$-0.214943\pi$
$61$	95.2262			1.56109			0.780543	+	0.625102i	$0.214943\pi$
$62$			29.1286i			0.469817i
$63$	24.5691	+	28.0259i	0.389986	+	0.444856i
$64$	−8.00000			−0.125000
$65$		−	18.9009i		−	0.290783i
$66$	70.3459	+	31.8810i	1.06585	+	0.483045i
$67$	75.8720			1.13242			0.566209	−	0.824262i	$-0.308410\pi$
$67$	75.8720			1.13242			0.566209	+	0.824262i	$0.308410\pi$
$68$		−	28.5576i		−	0.419964i
$69$	−5.93901	+	13.1045i	−0.0860725	+	0.189920i
$70$	13.0955			0.187079
$71$			132.680i			1.86873i	0.356317	+	0.934365i	$0.384032\pi$
$71$			132.680i			1.86873i	−0.356317	+	0.934365i	$0.615968\pi$
$72$	−19.1418	+	16.7807i	−0.265858	+	0.233066i
$73$	−73.4381			−1.00600			−0.503000	−	0.864286i	$-0.667771\pi$
$73$	−73.4381			−1.00600			−0.503000	+	0.864286i	$0.667771\pi$
$74$		−	82.3890i		−	1.11336i
$75$	13.6624	+	6.19184i	0.182165	+	0.0825579i
$76$	51.1405			0.672901
$77$		−	75.3859i		−	0.979038i
$78$	14.8034	−	32.6640i	0.189787	−	0.418769i
$79$	23.5709			0.298366			0.149183	−	0.988810i	$-0.452336\pi$
$79$	23.5709			0.298366			0.149183	+	0.988810i	$0.452336\pi$
$80$			8.94427i			0.111803i
$81$	−10.6017	+	80.3032i	−0.130885	+	0.991398i
$82$	78.4345			0.956518
$83$		−	134.121i		−	1.61591i	−0.589243	−	0.807956i	$-0.700574\pi$
$83$		−	134.121i		−	1.61591i	0.589243	−	0.807956i	$-0.299426\pi$
$84$	22.6313	+	10.2566i	0.269421	+	0.122102i
$85$	−31.9283			−0.375627
$86$			86.3084i			1.00359i
$87$	37.1808	−	82.0401i	0.427366	−	0.942989i
$88$	51.4887			0.585099
$89$			116.975i			1.31432i	0.753751	+	0.657161i	$0.228243\pi$
$89$			116.975i			1.31432i	−0.753751	+	0.657161i	$0.771757\pi$
$90$	18.7614	+	21.4011i	0.208460	+	0.237790i
$91$	−35.0042			−0.384662
$92$			9.59166i			0.104257i
$93$	56.2810	+	25.5067i	0.605172	+	0.274266i
$94$	19.7615			0.210229
$95$		−	57.1768i		−	0.601861i
$96$	−7.00527	+	15.4572i	−0.0729715	+	0.161013i
$97$	−82.3630			−0.849104			−0.424552	−	0.905404i	$-0.639568\pi$
$97$	−82.3630			−0.849104			−0.424552	+	0.905404i	$0.639568\pi$
$98$			45.0437i			0.459629i
$99$	123.198	−	108.002i	1.24442	−	1.09093i
$100$	10.0000			0.100000
$101$			133.725i			1.32401i	0.749501	+	0.662003i	$0.230294\pi$
$101$			133.725i			1.32401i	−0.749501	+	0.662003i	$0.769706\pi$
$102$	−55.1776	−	25.0067i	−0.540957	−	0.245163i
$103$	−157.226			−1.52647			−0.763233	−	0.646124i	$-0.776389\pi$
$103$	−157.226			−1.52647			−0.763233	+	0.646124i	$0.776389\pi$
$104$		−	23.9079i		−	0.229884i
$105$	11.4672	−	25.3026i	0.109212	−	0.240977i
$106$	−36.0175			−0.339788
$107$			68.1719i			0.637120i	0.947903	+	0.318560i	$0.103199\pi$
$107$			68.1719i			0.637120i	−0.947903	+	0.318560i	$0.896801\pi$
$108$	15.6614	+	51.6790i	0.145013	+	0.478510i
$109$	−3.60776			−0.0330987			−0.0165494	−	0.999863i	$-0.505268\pi$
$109$	−3.60776			−0.0330987			−0.0165494	+	0.999863i	$0.505268\pi$
$110$		−	57.5661i		−	0.523328i
$111$	−159.188	−	72.1446i	−1.43413	−	0.649951i
$112$	16.5647			0.147899
$113$			82.8721i			0.733382i	0.930343	+	0.366691i	$0.119509\pi$
$113$			82.8721i			0.733382i	−0.930343	+	0.366691i	$0.880491\pi$
$114$	44.7816	−	98.8114i	0.392821	−	0.866767i
$115$	10.7238			0.0932505
$116$		−	60.0481i		−	0.517656i
$117$	−50.1491	−	57.2050i	−0.428625	−	0.488932i
$118$	112.734			0.955371
$119$			59.1309i			0.496898i
$120$	17.2817	+	7.83213i	0.144014	+	0.0652677i
$121$	−210.385			−1.73872
$122$		−	134.670i		−	1.10385i
$123$	68.6818	−	151.548i	0.558389	−	1.23209i
$124$	41.1941			0.332211
$125$		−	11.1803i		−	0.0894427i
$126$	39.6347	−	34.7460i	0.314561	−	0.275762i
$127$	−12.8307			−0.101029			−0.0505145	−	0.998723i	$-0.516086\pi$
$127$	−12.8307			−0.101029			−0.0505145	+	0.998723i	$0.516086\pi$
$128$			11.3137i			0.0883883i
$129$	166.761	+	75.5767i	1.29272	+	0.585866i
$130$	−26.7299			−0.205615
$131$			260.678i			1.98991i	0.100330	+	0.994954i	$0.468010\pi$
$131$			260.678i			1.98991i	−0.100330	+	0.994954i	$0.531990\pi$
$132$	45.0865	−	99.4841i	0.341564	−	0.753667i
$133$	−105.891			−0.796172
$134$		−	107.299i		−	0.800740i
$135$	57.7789	−	17.5099i	0.427992	−	0.129703i
$136$	−40.3865			−0.296960
$137$		−	122.563i		−	0.894619i	−0.894379	−	0.447309i	$-0.852382\pi$
$137$		−	122.563i		−	0.894619i	0.894379	−	0.447309i	$-0.147618\pi$
$138$	18.5326	+	8.39902i	0.134294	+	0.0608625i
$139$	−79.5231			−0.572109			−0.286054	−	0.958213i	$-0.592344\pi$
$139$	−79.5231			−0.572109			−0.286054	+	0.958213i	$0.592344\pi$
$140$		−	18.5199i		−	0.132285i
$141$	17.3043	−	38.1822i	0.122726	−	0.270796i
$142$	187.638			1.32139
$143$			153.874i			1.07604i
$144$	23.7316	+	27.0705i	0.164802	+	0.187990i
$145$	−67.1358			−0.463006
$146$			103.857i			0.711350i
$147$	87.0314	+	39.4429i	0.592050	+	0.268319i
$148$	−116.516			−0.787267
$149$			14.2215i			0.0954460i	0.998861	+	0.0477230i	$0.0151965\pi$
$149$			14.2215i			0.0954460i	−0.998861	+	0.0477230i	$0.984804\pi$
$150$	8.75659	−	19.3215i	0.0583772	−	0.128810i
$151$	199.067			1.31832			0.659161	−	0.752002i	$-0.270912\pi$
$151$	199.067			1.31832			0.659161	+	0.752002i	$0.270912\pi$
$152$		−	72.3236i		−	0.475813i
$153$	−96.6335	+	84.7144i	−0.631592	+	0.553689i
$154$	−106.612			−0.692284
$155$		−	46.0564i		−	0.297138i
$156$	−46.1938	−	20.9352i	−0.296114	−	0.134200i
$157$	−150.983			−0.961676			−0.480838	−	0.876809i	$-0.659668\pi$
$157$	−150.983			−0.961676			−0.480838	+	0.876809i	$0.659668\pi$
$158$		−	33.3343i		−	0.210977i
$159$	−31.5391	+	69.5915i	−0.198359	+	0.437682i
$160$	12.6491			0.0790569
$161$		−	19.8604i		−	0.123356i
$162$	113.566	+	14.9930i	0.701024	+	0.0925495i
$163$	157.063			0.963577			0.481789	−	0.876287i	$-0.339987\pi$
$163$	157.063			0.963577			0.481789	+	0.876287i	$0.339987\pi$
$164$		−	110.923i		−	0.676361i
$165$	−111.227	−	50.4082i	−0.674101	−	0.305504i
$166$	−189.675			−1.14262
$167$			140.625i			0.842065i	0.907046	+	0.421032i	$0.138332\pi$
$167$			140.625i			0.842065i	−0.907046	+	0.421032i	$0.861668\pi$
$168$	14.5050	−	32.0055i	0.0863394	−	0.190509i
$169$	−97.5513			−0.577226
$170$			45.1535i			0.265609i
$171$	−151.705	−	173.050i	−0.887167	−	1.01199i
$172$	122.059			0.709643
$173$		−	129.805i		−	0.750317i	−0.926961	−	0.375158i	$-0.877588\pi$
$173$		−	129.805i		−	0.750317i	0.926961	−	0.375158i	$-0.122412\pi$
$174$	−116.022	−	52.5816i	−0.666794	−	0.302193i
$175$	−20.7059			−0.118319
$176$		−	72.8160i		−	0.413727i
$177$	98.7163	−	217.819i	0.557719	−	1.23062i
$178$	165.427			0.929365
$179$		−	277.661i		−	1.55118i	−0.631239	−	0.775588i	$-0.717453\pi$
$179$		−	277.661i		−	1.55118i	0.631239	−	0.775588i	$-0.282547\pi$
$180$	30.2658	−	26.5327i	0.168143	−	0.147404i
$181$	−248.306			−1.37185			−0.685927	−	0.727670i	$-0.740603\pi$
$181$	−248.306			−1.37185			−0.685927	+	0.727670i	$0.740603\pi$
$182$			49.5035i			0.271997i
$183$	−260.204	−	117.925i	−1.42188	−	0.644400i
$184$	13.5647			0.0737210
$185$			130.268i			0.704153i
$186$	36.0720	−	79.5934i	0.193935	−	0.427922i
$187$	259.931			1.39000
$188$		−	27.9470i		−	0.148654i
$189$	−32.4282	−	107.006i	−0.171578	−	0.566169i
$190$	−80.8602			−0.425580
$191$		−	114.375i		−	0.598820i	−0.954125	−	0.299410i	$-0.903210\pi$
$191$		−	114.375i		−	0.598820i	0.954125	−	0.299410i	$-0.0967898\pi$
$192$	21.8598	+	9.90695i	0.113853	+	0.0515987i
$193$	−224.783			−1.16468			−0.582341	−	0.812945i	$-0.697863\pi$
$193$	−224.783			−1.16468			−0.582341	+	0.812945i	$0.697863\pi$
$194$			116.479i			0.600407i
$195$	−23.4063	+	51.6463i	−0.120032	+	0.264853i
$196$	63.7014			0.325007
$197$			237.189i			1.20401i	0.798493	+	0.602004i	$0.205631\pi$
$197$			237.189i			1.20401i	−0.798493	+	0.602004i	$0.794369\pi$
$198$	−152.738	−	174.228i	−0.771406	−	0.879940i
$199$	−200.271			−1.00639			−0.503194	−	0.864174i	$-0.667842\pi$
$199$	−200.271			−1.00639			−0.503194	+	0.864174i	$0.667842\pi$
$200$		−	14.1421i		−	0.0707107i
$201$	−207.319	−	93.9574i	−1.03144	−	0.467450i
$202$	189.115			0.936214
$203$			124.335i			0.612486i
$204$	−35.3648	+	78.0330i	−0.173357	+	0.382515i
$205$	−124.016			−0.604955
$206$			222.351i			1.07937i
$207$	32.4564	−	28.4531i	0.156794	−	0.137455i
$208$	−33.8109			−0.162553
$209$			465.481i			2.22718i
$210$	−35.7833	−	16.2171i	−0.170397	−	0.0772243i
$211$	−199.810			−0.946967			−0.473483	−	0.880803i	$-0.657004\pi$
$211$	−199.810			−0.946967			−0.473483	+	0.880803i	$0.657004\pi$
$212$			50.9365i			0.240267i
$213$	164.307	−	362.545i	0.771392	−	1.70209i
$214$	96.4096			0.450512
$215$		−	136.466i		−	0.634724i
$216$	73.0852	−	22.1485i	0.338357	−	0.102539i
$217$	−85.2960			−0.393069
$218$			5.10215i			0.0234043i
$219$	200.668	+	90.9434i	0.916292	+	0.415266i
$220$	−81.4107			−0.370049
$221$		−	120.695i		−	0.546130i
$222$	−102.028	+	225.126i	−0.459585	+	1.01408i
$223$	251.698			1.12869			0.564345	−	0.825539i	$-0.309129\pi$
$223$	251.698			1.12869			0.564345	+	0.825539i	$0.309129\pi$
$224$		−	23.4260i		−	0.104580i
$225$	−29.6644	−	33.8382i	−0.131842	−	0.150392i
$226$	117.199			0.518579
$227$		−	209.743i		−	0.923977i	−0.886886	−	0.461988i	$-0.847136\pi$
$227$		−	209.743i		−	0.923977i	0.886886	−	0.461988i	$-0.152864\pi$
$228$	−139.740	−	63.3308i	−0.612896	−	0.277767i
$229$	310.423			1.35556			0.677781	−	0.735264i	$-0.262942\pi$
$229$	310.423			1.35556			0.677781	+	0.735264i	$0.262942\pi$
$230$		−	15.1658i		−	0.0659380i
$231$	−93.3555	+	205.990i	−0.404136	+	0.891733i
$232$	−84.9208			−0.366038
$233$		−	13.5244i		−	0.0580446i	−0.999579	−	0.0290223i	$-0.990761\pi$
$233$		−	13.5244i		−	0.0580446i	0.999579	−	0.0290223i	$-0.00923938\pi$
$234$	−80.9001	+	70.9216i	−0.345727	+	0.303084i
$235$	−31.2457			−0.132960
$236$		−	159.430i		−	0.675549i
$237$	−64.4070	−	29.1895i	−0.271760	−	0.123162i
$238$	83.6237			0.351360
$239$		−	162.359i		−	0.679328i	−0.940547	−	0.339664i	$-0.889687\pi$
$239$		−	162.359i		−	0.679328i	0.940547	−	0.339664i	$-0.110313\pi$
$240$	11.0763	−	24.4400i	0.0461513	−	0.101833i
$241$	114.412			0.474740			0.237370	−	0.971419i	$-0.423715\pi$
$241$	114.412			0.474740			0.237370	+	0.971419i	$0.423715\pi$
$242$			297.530i			1.22946i
$243$	128.414	−	206.298i	0.528452	−	0.848963i
$244$	−190.452			−0.780543
$245$		−	71.2203i		−	0.290695i
$246$	−214.321	−	97.1308i	−0.871222	−	0.394841i
$247$	216.139			0.875055
$248$		−	58.2573i		−	0.234908i
$249$	−166.091	+	366.482i	−0.667031	+	1.47181i
$250$	−15.8114			−0.0632456
$251$			77.7456i			0.309743i	0.987935	+	0.154872i	$0.0494964\pi$
$251$			77.7456i			0.309743i	−0.987935	+	0.154872i	$0.950504\pi$
$252$	−49.1382	−	56.0519i	−0.194993	−	0.222428i
$253$	−87.3033			−0.345072
$254$			18.1453i			0.0714383i
$255$	87.2435	+	39.5390i	0.342131	+	0.155055i
$256$	16.0000			0.0625000
$257$		−	252.344i		−	0.981883i	−0.871193	−	0.490941i	$-0.836653\pi$
$257$		−	252.344i		−	0.981883i	0.871193	−	0.490941i	$-0.163347\pi$
$258$	106.882	−	235.836i	0.414270	−	0.914093i
$259$	241.256			0.931489
$260$			37.8018i			0.145391i
$261$	−203.192	+	178.129i	−0.778512	+	0.682488i
$262$	368.654			1.40708
$263$			192.257i			0.731016i	0.930808	+	0.365508i	$0.119105\pi$
$263$			192.257i			0.731016i	−0.930808	+	0.365508i	$0.880895\pi$
$264$	−140.692	−	63.7619i	−0.532923	−	0.241522i
$265$	56.9487			0.214901
$266$			149.752i			0.562978i
$267$	144.858	−	319.631i	0.542538	−	1.19712i
$268$	−151.744			−0.566209
$269$		−	334.333i		−	1.24287i	−0.783464	−	0.621437i	$-0.786549\pi$
$269$		−	334.333i		−	1.24287i	0.783464	−	0.621437i	$-0.213451\pi$
$270$	−24.7628	−	81.7117i	−0.0917140	−	0.302636i
$271$	−415.940			−1.53483			−0.767416	−	0.641149i	$-0.778458\pi$
$271$	−415.940			−1.53483			−0.767416	+	0.641149i	$0.778458\pi$
$272$			57.1151i			0.209982i
$273$	95.6484	+	43.3481i	0.350360	+	0.158784i
$274$	−173.330			−0.632591
$275$			91.0200i			0.330982i
$276$	11.8780	−	26.2090i	0.0430363	−	0.0949602i
$277$	95.1282			0.343423			0.171712	−	0.985147i	$-0.445070\pi$
$277$	95.1282			0.343423			0.171712	+	0.985147i	$0.445070\pi$
$278$			112.463i			0.404542i
$279$	−122.200	−	139.393i	−0.437993	−	0.499617i
$280$	−26.1911			−0.0935396
$281$			62.8658i			0.223722i	0.993724	+	0.111861i	$0.0356811\pi$
$281$			62.8658i			0.223722i	−0.993724	+	0.111861i	$0.964319\pi$
$282$	−53.9979	−	24.4720i	−0.191482	−	0.0867801i
$283$	469.458			1.65886			0.829431	−	0.558609i	$-0.188665\pi$
$283$	469.458			1.65886			0.829431	+	0.558609i	$0.188665\pi$
$284$		−	265.360i		−	0.934365i
$285$	−70.8060	+	156.235i	−0.248442	+	0.548191i
$286$	217.610			0.760874
$287$			229.676i			0.800265i
$288$	38.2835	−	33.5615i	0.132929	−	0.116533i
$289$	85.1164			0.294520
$290$			94.9444i			0.327394i
$291$	225.055	+	101.996i	0.773386	+	0.350501i
$292$	146.876			0.503000
$293$		−	288.659i		−	0.985184i	−0.870260	−	0.492592i	$-0.836049\pi$
$293$		−	288.659i		−	0.985184i	0.870260	−	0.492592i	$-0.163951\pi$
$294$	55.7807	−	123.081i	0.189730	−	0.418643i
$295$	−178.248			−0.604229
$296$			164.778i			0.556682i
$297$	−470.382	+	142.550i	−1.58378	+	0.479965i
$298$	20.1122			0.0674905
$299$			40.5379i			0.135578i
$300$	−27.3248	−	12.3837i	−0.0910827	−	0.0412789i
$301$	−252.733			−0.839644
$302$		−	281.523i		−	0.932194i
$303$	165.600	−	365.400i	0.546536	−	1.20594i
$304$	−102.281			−0.336451
$305$			212.932i			0.698139i
$306$	119.804	+	136.660i	0.391517	+	0.446603i
$307$	−453.095			−1.47588			−0.737940	−	0.674867i	$-0.764201\pi$
$307$	−453.095			−1.47588			−0.737940	+	0.674867i	$0.764201\pi$
$308$			150.772i			0.489519i
$309$	429.617	+	194.704i	1.39035	+	0.630109i
$310$	−65.1336			−0.210108
$311$		−	445.022i		−	1.43094i	−0.698644	−	0.715470i	$-0.746213\pi$
$311$		−	445.022i		−	1.43094i	0.698644	−	0.715470i	$-0.253787\pi$
$312$	−29.6068	+	65.3280i	−0.0948937	+	0.209385i
$313$	−548.133			−1.75122			−0.875612	−	0.483016i	$-0.839541\pi$
$313$	−548.133			−1.75122			−0.875612	+	0.483016i	$0.839541\pi$
$314$			213.522i			0.680008i
$315$	−62.6679	+	54.9382i	−0.198946	+	0.174407i
$316$	−47.1418			−0.149183
$317$		−	1.18880i		−	0.00375016i	−0.999998	−	0.00187508i	$-0.999403\pi$
$317$		−	1.18880i		−	0.00375016i	0.999998	−	0.00187508i	$-0.000596858\pi$
$318$	98.4172	+	44.6030i	0.309488	+	0.140261i
$319$	546.558			1.71335
$320$		−	17.8885i		−	0.0559017i
$321$	84.4219	−	186.278i	0.262996	−	0.580306i
$322$	−28.0868			−0.0872261
$323$		−	365.112i		−	1.13038i
$324$	21.2033	−	160.606i	0.0654424	−	0.495699i
$325$	42.2637			0.130042
$326$		−	222.121i		−	0.681352i
$327$	9.85814	+	4.46774i	0.0301472	+	0.0136628i
$328$	−156.869			−0.478259
$329$			57.8666i			0.175886i
$330$	−71.2880	+	157.298i	−0.216024	+	0.476661i
$331$	−84.6998			−0.255891			−0.127945	−	0.991781i	$-0.540838\pi$
$331$	−84.6998			−0.255891			−0.127945	+	0.991781i	$0.540838\pi$
$332$			268.241i			0.807956i
$333$	345.637	+	394.267i	1.03795	+	1.18399i
$334$	198.874			0.595430
$335$			169.655i			0.506432i
$336$	−45.2627	−	20.5132i	−0.134710	−	0.0610511i
$337$	301.194			0.893752			0.446876	−	0.894596i	$-0.352537\pi$
$337$	301.194			0.893752			0.446876	+	0.894596i	$0.352537\pi$
$338$			137.958i			0.408161i
$339$	102.626	−	226.446i	0.302732	−	0.667983i
$340$	63.8567			0.187814
$341$			374.949i			1.09956i
$342$	−244.730	+	214.544i	−0.715584	+	0.627321i
$343$	−334.817			−0.976142
$344$		−	172.617i		−	0.501793i
$345$	−29.3026	−	13.2800i	−0.0849350	−	0.0384928i
$346$	−183.572			−0.530554
$347$		−	74.3987i		−	0.214405i	−0.994237	−	0.107203i	$-0.965811\pi$
$347$		−	74.3987i		−	0.214405i	0.994237	−	0.107203i	$-0.0341894\pi$
$348$	−74.3616	+	164.080i	−0.213683	+	0.471495i
$349$	122.217			0.350193			0.175096	−	0.984551i	$-0.443976\pi$
$349$	122.217			0.350193			0.175096	+	0.984551i	$0.443976\pi$
$350$			29.2825i			0.0836643i
$351$	66.1906	+	218.415i	0.188577	+	0.622264i
$352$	−102.977			−0.292549
$353$			257.047i			0.728179i	0.931364	+	0.364089i	$0.118620\pi$
$353$			257.047i			0.728179i	−0.931364	+	0.364089i	$0.881380\pi$
$354$	−308.043	−	139.606i	−0.870177	−	0.394367i
$355$	−296.681			−0.835722
$356$		−	233.949i		−	0.657161i
$357$	73.2258	−	161.574i	0.205114	−	0.452588i
$358$	−392.671			−1.09685
$359$		−	411.848i		−	1.14721i	−0.819133	−	0.573604i	$-0.805545\pi$
$359$		−	411.848i		−	1.14721i	0.819133	−	0.573604i	$-0.194455\pi$
$360$	−37.5229	−	42.8023i	−0.104230	−	0.118895i
$361$	292.838			0.811185
$362$			351.157i			0.970047i
$363$	574.874	+	260.535i	1.58368	+	0.717726i
$364$	70.0085			0.192331
$365$		−	164.213i		−	0.449897i
$366$	−166.771	+	367.984i	−0.455659	+	1.00542i
$367$	390.609			1.06433			0.532165	−	0.846640i	$-0.321378\pi$
$367$	390.609			1.06433			0.532165	+	0.846640i	$0.321378\pi$
$368$		−	19.1833i		−	0.0521286i
$369$	−375.343	+	329.047i	−1.01719	+	0.891727i
$370$	184.227			0.497912
$371$		−	105.468i		−	0.284281i
$372$	−112.562	−	51.0135i	−0.302586	−	0.137133i
$373$	−358.049			−0.959916			−0.479958	−	0.877292i	$-0.659348\pi$
$373$	−358.049			−0.959916			−0.479958	+	0.877292i	$0.659348\pi$
$374$		−	367.598i		−	0.982882i
$375$	−13.8454	+	30.5500i	−0.0369210	+	0.0814668i
$376$	−39.5230			−0.105114
$377$		−	253.785i		−	0.673170i
$378$	−151.329	+	45.8604i	−0.400342	+	0.121324i
$379$	−292.500			−0.771769			−0.385884	−	0.922547i	$-0.626104\pi$
$379$	−292.500			−0.771769			−0.385884	+	0.922547i	$0.626104\pi$
$380$			114.354i			0.300931i
$381$	35.0596	+	15.8891i	0.0920199	+	0.0417037i
$382$	−161.750			−0.423430
$383$		−	67.9007i		−	0.177286i	−0.996063	−	0.0886432i	$-0.971747\pi$
$383$		−	67.9007i		−	0.177286i	0.996063	−	0.0886432i	$-0.0282531\pi$
$384$	14.0105	−	30.9145i	0.0364858	−	0.0805064i
$385$	168.568			0.437839
$386$			317.892i			0.823554i
$387$	−362.080	−	413.024i	−0.935607	−	1.06724i
$388$	164.726			0.424552
$389$		−	332.519i		−	0.854806i	−0.904061	−	0.427403i	$-0.859429\pi$
$389$		−	332.519i		−	0.854806i	0.904061	−	0.427403i	$-0.140571\pi$
$390$	73.0389	+	33.1015i	0.187279	+	0.0848755i
$391$	68.4786			0.175137
$392$		−	90.0874i		−	0.229815i
$393$	322.815	−	712.297i	0.821413	−	1.81246i
$394$	335.437			0.851362
$395$			52.7061i			0.133433i
$396$	−246.396	+	216.005i	−0.622212	+	0.545466i
$397$	185.010			0.466020			0.233010	−	0.972474i	$-0.425142\pi$
$397$	185.010			0.466020			0.233010	+	0.972474i	$0.425142\pi$
$398$			283.226i			0.711624i
$399$	289.345	+	131.132i	0.725174	+	0.328651i
$400$	−20.0000			−0.0500000
$401$			28.7486i			0.0716924i	0.999357	+	0.0358462i	$0.0114126\pi$
$401$			28.7486i			0.0716924i	−0.999357	+	0.0358462i	$0.988587\pi$
$402$	−132.876	+	293.193i	−0.330537	+	0.729335i
$403$	174.101			0.432014
$404$		−	267.449i		−	0.662003i
$405$	−179.563	−	23.7060i	−0.443366	−	0.0585334i
$406$	175.836			0.433093
$407$		−	1060.52i		−	2.60571i
$408$	110.355	+	50.0134i	0.270479	+	0.122582i
$409$	307.733			0.752402			0.376201	−	0.926538i	$-0.377230\pi$
$409$	307.733			0.752402			0.376201	+	0.926538i	$0.377230\pi$
$410$			175.385i			0.427768i
$411$	−151.778	+	334.900i	−0.369289	+	0.814842i
$412$	314.452			0.763233
$413$			330.113i			0.799304i
$414$	−40.2388	−	45.9003i	−0.0971952	−	0.110870i
$415$	299.903			0.722657
$416$			47.8159i			0.114942i
$417$	217.295	+	98.4789i	0.521092	+	0.236161i
$418$	658.289			1.57485
$419$			346.936i			0.828010i	0.910275	+	0.414005i	$0.135870\pi$
$419$			346.936i			0.828010i	−0.910275	+	0.414005i	$0.864130\pi$
$420$	−22.9344	+	50.6052i	−0.0546058	+	0.120489i
$421$	216.953			0.515329			0.257664	−	0.966234i	$-0.417047\pi$
$421$	216.953			0.515329			0.257664	+	0.966234i	$0.417047\pi$
$422$			282.574i			0.669607i
$423$	−94.5674	+	82.9031i	−0.223563	+	0.195988i
$424$	72.0351			0.169894
$425$		−	71.3939i		−	0.167986i
$426$	−512.716	−	232.364i	−1.20356	−	0.545457i
$427$	394.348			0.923532
$428$		−	136.344i		−	0.318560i
$429$	190.552	−	420.456i	0.444177	−	0.980085i
$430$	−192.991			−0.448817
$431$			595.252i			1.38109i	0.723287	+	0.690547i	$0.242630\pi$
$431$			595.252i			1.38109i	−0.723287	+	0.690547i	$0.757370\pi$
$432$	−31.3227	−	103.358i	−0.0725063	−	0.239255i
$433$	−162.757			−0.375882			−0.187941	−	0.982180i	$-0.560181\pi$
$433$	−162.757			−0.375882			−0.187941	+	0.982180i	$0.560181\pi$
$434$			120.627i			0.277942i
$435$	183.447	+	83.1388i	0.421718	+	0.191124i
$436$	7.21553			0.0165494
$437$			122.631i			0.280619i
$438$	128.613	−	283.787i	0.293638	−	0.647916i
$439$	−137.285			−0.312721			−0.156361	−	0.987700i	$-0.549976\pi$
$439$	−137.285			−0.312721			−0.156361	+	0.987700i	$0.549976\pi$
$440$			115.132i			0.261664i
$441$	−188.967	−	215.554i	−0.428496	−	0.488784i
$442$	−170.688			−0.386172
$443$			309.185i			0.697935i	0.937135	+	0.348967i	$0.113468\pi$
$443$			309.185i			0.697935i	−0.937135	+	0.348967i	$0.886532\pi$
$444$	318.376	+	144.289i	0.717064	+	0.324976i
$445$	−261.563			−0.587782
$446$		−	355.954i		−	0.798104i
$447$	17.6114	−	38.8598i	0.0393991	−	0.0869348i
$448$	−33.1294			−0.0739495
$449$		−	61.1567i		−	0.136206i	−0.997678	−	0.0681032i	$-0.978305\pi$
$449$		−	61.1567i		−	0.136206i	0.997678	−	0.0681032i	$-0.0216947\pi$
$450$	−47.8544	+	41.9519i	−0.106343	+	0.0932264i
$451$	1009.62			2.23863
$452$		−	165.744i		−	0.366691i
$453$	−543.945	−	246.518i	−1.20076	−	0.544189i
$454$	−296.621			−0.653350
$455$		−	78.2718i		−	0.172026i
$456$	−89.5632	+	197.623i	−0.196411	+	0.433383i
$457$	325.253			0.711714			0.355857	−	0.934540i	$-0.384189\pi$
$457$	325.253			0.711714			0.355857	+	0.934540i	$0.384189\pi$
$458$		−	439.005i		−	0.958526i
$459$	368.957	−	111.813i	0.803827	−	0.243600i
$460$	−21.4476			−0.0466252
$461$			178.646i			0.387518i	0.981049	+	0.193759i	$0.0620679\pi$
$461$			178.646i			0.387518i	−0.981049	+	0.193759i	$0.937932\pi$
$462$	291.314	+	132.025i	0.630551	+	0.285768i
$463$	753.662			1.62778			0.813890	−	0.581019i	$-0.197346\pi$
$463$	753.662			1.62778			0.813890	+	0.581019i	$0.197346\pi$
$464$			120.096i			0.258828i
$465$	−57.0348	+	125.848i	−0.122655	+	0.270641i
$466$	−19.1264			−0.0410437
$467$		−	341.612i		−	0.731504i	−0.930712	−	0.365752i	$-0.880812\pi$
$467$		−	341.612i		−	0.731504i	0.930712	−	0.365752i	$-0.119188\pi$
$468$	100.298	+	114.410i	0.214313	+	0.244466i
$469$	314.199			0.669934
$470$			44.1880i			0.0940171i
$471$	412.558	+	186.973i	0.875920	+	0.396970i
$472$	−225.467			−0.477685
$473$			1110.98i			2.34879i
$474$	−41.2801	+	91.0853i	−0.0870889	+	0.192163i
$475$	127.851			0.269161
$476$		−	118.262i		−	0.248449i
$477$	172.360	−	151.100i	0.361341	−	0.316772i
$478$	−229.611			−0.480358
$479$			129.264i			0.269862i	0.990855	+	0.134931i	$0.0430813\pi$
$479$			129.264i			0.269862i	−0.990855	+	0.134931i	$0.956919\pi$
$480$	−34.5634	−	15.6643i	−0.0720072	−	0.0326339i
$481$	−492.438			−1.02378
$482$		−	161.803i		−	0.335692i
$483$	−24.5944	+	54.2680i	−0.0509202	+	0.112356i
$484$	420.771			0.869362
$485$		−	184.169i		−	0.379731i
$486$	−291.750	−	181.604i	−0.600308	−	0.373672i
$487$	−356.900			−0.732855			−0.366428	−	0.930447i	$-0.619419\pi$
$487$	−356.900			−0.732855			−0.366428	+	0.930447i	$0.619419\pi$
$488$			269.340i			0.551927i
$489$	−429.172	−	194.502i	−0.877652	−	0.397755i
$490$	−100.721			−0.205552
$491$			576.525i			1.17419i	0.809520	+	0.587093i	$0.199728\pi$
$491$			576.525i			1.17419i	−0.809520	+	0.587093i	$0.800272\pi$
$492$	−137.364	+	303.095i	−0.279194	+	0.616047i
$493$	−428.707			−0.869588
$494$		−	305.666i		−	0.618757i
$495$	241.500	+	275.479i	0.487880	+	0.556523i
$496$	−82.3882			−0.166105
$497$			549.450i			1.10553i
$498$	518.284	+	234.888i	1.04073	+	0.471662i
$499$	−622.821			−1.24814			−0.624069	−	0.781369i	$-0.714522\pi$
$499$	−622.821			−1.24814			−0.624069	+	0.781369i	$0.714522\pi$
$500$			22.3607i			0.0447214i
$501$	174.145	−	384.255i	0.347595	−	0.766975i
$502$	109.949			0.219022
$503$			407.531i			0.810200i	0.914272	+	0.405100i	$0.132763\pi$
$503$			407.531i			0.810200i	−0.914272	+	0.405100i	$0.867237\pi$
$504$	−79.2693	+	69.4920i	−0.157280	+	0.137881i
$505$	−299.018			−0.592114
$506$			123.466i			0.244003i
$507$	266.557	+	120.804i	0.525753	+	0.238273i
$508$	25.6614			0.0505145
$509$			274.372i			0.539041i	0.962995	+	0.269520i	$0.0868651\pi$
$509$			274.372i			0.539041i	−0.962995	+	0.269520i	$0.913135\pi$
$510$	55.9166	−	123.381i	0.109640	−	0.241923i
$511$	−304.120			−0.595146
$512$		−	22.6274i		−	0.0441942i
$513$	200.232	+	660.723i	0.390317	+	1.28796i
$514$	−356.868			−0.694296
$515$		−	351.568i		−	0.682656i
$516$	−333.522	−	151.153i	−0.646361	−	0.292933i
$517$	254.373			0.492018
$518$		−	341.187i		−	0.658662i
$519$	−160.746	+	354.689i	−0.309723	+	0.683409i
$520$	53.4598			0.102807
$521$			227.719i			0.437080i	0.975828	+	0.218540i	$0.0701295\pi$
$521$			227.719i			0.437080i	−0.975828	+	0.218540i	$0.929871\pi$
$522$	251.913	+	287.356i	0.482592	+	0.550491i
$523$	178.583			0.341460			0.170730	−	0.985318i	$-0.445387\pi$
$523$	178.583			0.341460			0.170730	+	0.985318i	$0.445387\pi$
$524$		−	521.356i		−	0.994954i
$525$	56.5783	+	25.6415i	0.107768	+	0.0488409i
$526$	271.893			0.516907
$527$		−	294.101i		−	0.558066i
$528$	−90.1730	+	198.968i	−0.170782	+	0.376834i
$529$	−23.0000			−0.0434783
$530$		−	80.5377i		−	0.151958i
$531$	−539.480	+	472.939i	−1.01597	+	0.890657i
$532$	211.782			0.398086
$533$		−	468.802i		−	0.879553i
$534$	−452.026	−	204.860i	−0.846491	−	0.383632i
$535$	−152.437			−0.284929
$536$			214.598i			0.400370i
$537$	−343.846	+	758.702i	−0.640309	+	1.41285i
$538$	−472.818			−0.878845
$539$			579.810i			1.07571i
$540$	−115.558	+	35.0199i	−0.213996	+	0.0648516i
$541$	−406.572			−0.751519			−0.375760	−	0.926717i	$-0.622618\pi$
$541$	−406.572			−0.751519			−0.375760	+	0.926717i	$0.622618\pi$
$542$			588.228i			1.08529i
$543$	678.490	+	307.494i	1.24952	+	0.566287i
$544$	80.7730			0.148480
$545$		−	8.06720i		−	0.0148022i
$546$	61.3035	−	135.267i	0.112277	−	0.247742i
$547$	−762.540			−1.39404			−0.697020	−	0.717051i	$-0.745491\pi$
$547$	−762.540			−1.39404			−0.697020	+	0.717051i	$0.745491\pi$
$548$			245.126i			0.447309i
$549$	564.967	+	644.456i	1.02908	+	1.17387i
$550$	128.722			0.234039
$551$		−	767.722i		−	1.39333i
$552$	−37.0652	−	16.7980i	−0.0671470	−	0.0304312i
$553$	97.6112			0.176512
$554$		−	134.532i		−	0.242837i
$555$	161.320	−	355.956i	0.290667	−	0.641362i
$556$	159.046			0.286054
$557$			868.898i			1.55996i	0.625804	+	0.779980i	$0.284771\pi$
$557$			868.898i			1.55996i	−0.625804	+	0.779980i	$0.715229\pi$
$558$	−197.132	+	172.817i	−0.353283	+	0.309708i
$559$	515.864			0.922834
$560$			37.0398i			0.0661425i
$561$	−710.256	−	321.890i	−1.26605	−	0.573779i
$562$	88.9056			0.158195
$563$			703.584i			1.24971i	0.780743	+	0.624853i	$0.214841\pi$
$563$			703.584i			1.24971i	−0.780743	+	0.624853i	$0.785159\pi$
$564$	−34.6086	+	76.3645i	−0.0613628	+	0.135398i
$565$	−185.308			−0.327978
$566$		−	663.914i		−	1.17299i
$567$	−43.9033	+	332.549i	−0.0774309	+	0.586507i
$568$	−375.275			−0.660696
$569$		−	594.365i		−	1.04458i	−0.852768	−	0.522289i	$-0.825078\pi$
$569$		−	594.365i		−	1.04458i	0.852768	−	0.522289i	$-0.174922\pi$
$570$	220.949	+	100.135i	0.387630	+	0.175675i
$571$	526.041			0.921263			0.460631	−	0.887592i	$-0.347623\pi$
$571$	526.041			0.921263			0.460631	+	0.887592i	$0.347623\pi$
$572$		−	307.747i		−	0.538019i
$573$	−141.638	+	312.526i	−0.247186	+	0.545421i
$574$	324.811			0.565872
$575$			23.9792i			0.0417029i
$576$	−47.4631	−	54.1410i	−0.0824012	−	0.0939949i
$577$	−146.152			−0.253296			−0.126648	−	0.991948i	$-0.540422\pi$
$577$	−146.152			−0.253296			−0.126648	+	0.991948i	$0.540422\pi$
$578$		−	120.373i		−	0.208257i
$579$	614.216	+	278.365i	1.06082	+	0.480768i
$580$	134.272			0.231503
$581$		−	555.417i		−	0.955967i
$582$	144.244	−	318.276i	0.247842	−	0.546866i
$583$	−463.624			−0.795238
$584$		−	207.714i		−	0.355675i
$585$	127.914	−	112.137i	0.218657	−	0.191687i
$586$	−408.226			−0.696631
$587$			478.018i			0.814340i	0.913352	+	0.407170i	$0.133484\pi$
$587$			478.018i			0.814340i	−0.913352	+	0.407170i	$0.866516\pi$
$588$	−174.063	−	78.8858i	−0.296025	−	0.134159i
$589$	526.672			0.894180
$590$			252.080i			0.427255i
$591$	293.728	−	648.115i	0.497002	−	1.09664i
$592$	233.031			0.393634
$593$		−	793.839i		−	1.33868i	−0.742955	−	0.669341i	$-0.766576\pi$
$593$		−	793.839i		−	1.33868i	0.742955	−	0.669341i	$-0.233424\pi$
$594$	201.596	+	665.221i	0.339387	+	1.11990i
$595$	−132.221			−0.222220
$596$		−	28.4429i		−	0.0477230i
$597$	547.237	+	248.009i	0.916645	+	0.415426i
$598$	57.3292			0.0958683
$599$		−	329.048i		−	0.549329i	−0.961540	−	0.274664i	$-0.911433\pi$
$599$		−	329.048i		−	0.549329i	0.961540	−	0.274664i	$-0.0885667\pi$
$600$	−17.5132	+	38.6431i	−0.0291886	+	0.0644052i
$601$	−98.7656			−0.164335			−0.0821677	−	0.996619i	$-0.526184\pi$
$601$	−98.7656			−0.164335			−0.0821677	+	0.996619i	$0.526184\pi$
$602$			357.418i			0.593718i
$603$	450.140	+	513.473i	0.746501	+	0.851531i
$604$	−398.133			−0.659161
$605$		−	470.436i		−	0.777581i
$606$	−516.754	−	234.194i	−0.852729	−	0.386459i
$607$	131.584			0.216777			0.108389	−	0.994109i	$-0.465431\pi$
$607$	131.584			0.216777			0.108389	+	0.994109i	$0.465431\pi$
$608$			144.647i			0.237907i
$609$	153.972	−	339.742i	0.252828	−	0.557869i
$610$	301.132			0.493659
$611$		−	118.114i		−	0.193313i
$612$	193.267	−	169.429i	0.315796	−	0.276845i
$613$	537.185			0.876322			0.438161	−	0.898897i	$-0.355630\pi$
$613$	537.185			0.876322			0.438161	+	0.898897i	$0.355630\pi$
$614$			640.773i			1.04360i
$615$	338.871	+	153.577i	0.551009	+	0.249719i
$616$	213.224			0.346142
$617$		−	997.204i		−	1.61621i	−0.589036	−	0.808107i	$-0.700492\pi$
$617$		−	997.204i		−	1.61621i	0.589036	−	0.808107i	$-0.299508\pi$
$618$	275.352	−	607.570i	0.445554	−	0.983123i
$619$	−146.256			−0.236277			−0.118139	−	0.992997i	$-0.537693\pi$
$619$	−146.256			−0.236277			−0.118139	+	0.992997i	$0.537693\pi$
$620$			92.1128i			0.148569i
$621$	−123.922	+	37.5546i	−0.199552	+	0.0604744i
$622$	−629.356			−1.01183
$623$			484.412i			0.777547i
$624$	92.3877	+	41.8704i	0.148057	+	0.0671000i
$625$	25.0000			0.0400000
$626$			775.177i			1.23830i
$627$	576.437	−	1271.92i	0.919357	−	2.02858i
$628$	301.966			0.480838
$629$			831.850i			1.32250i
$630$	77.6944	+	88.6258i	0.123324	+	0.140676i
$631$	−520.059			−0.824182			−0.412091	−	0.911143i	$-0.635201\pi$
$631$	−520.059			−0.824182			−0.412091	+	0.911143i	$0.635201\pi$
$632$			66.6686i			0.105488i
$633$	545.977	+	247.438i	0.862522	+	0.390898i
$634$	−1.68122			−0.00265177
$635$		−	28.6903i		−	0.0451815i
$636$	63.0781	−	139.183i	0.0991795	−	0.218841i
$637$	269.225			0.422646
$638$		−	772.949i		−	1.21152i
$639$	−897.928	+	787.175i	−1.40521	+	1.23189i
$640$	−25.2982			−0.0395285
$641$			343.613i			0.536058i	0.963411	+	0.268029i	$0.0863723\pi$
$641$			343.613i			0.536058i	−0.963411	+	0.268029i	$0.913628\pi$
$642$	−263.437	−	119.391i	−0.410338	−	0.185967i
$643$	−972.075			−1.51178			−0.755890	−	0.654698i	$-0.772796\pi$
$643$	−972.075			−1.51178			−0.755890	+	0.654698i	$0.772796\pi$
$644$			39.7207i			0.0616782i
$645$	−168.995	+	372.889i	−0.262007	+	0.578123i
$646$	−516.347			−0.799298
$647$			356.832i			0.551518i	0.961227	+	0.275759i	$0.0889292\pi$
$647$			356.832i			0.551518i	−0.961227	+	0.275759i	$0.911071\pi$
$648$	−227.132	−	29.9860i	−0.350512	−	0.0462747i
$649$	1451.13			2.23594
$650$		−	59.7699i		−	0.0919536i
$651$	233.069	+	105.628i	0.358018	+	0.162255i
$652$	−314.126			−0.481789
$653$		−	374.245i		−	0.573116i	−0.958063	−	0.286558i	$-0.907489\pi$
$653$		−	374.245i		−	0.573116i	0.958063	−	0.286558i	$-0.0925111\pi$
$654$	6.31834	−	13.9415i	0.00966107	−	0.0213173i
$655$	−582.894			−0.889914
$656$			221.846i			0.338180i
$657$	−435.700	−	497.002i	−0.663166	−	0.756471i
$658$	81.8357			0.124370
$659$			30.2813i			0.0459504i	0.999736	+	0.0229752i	$0.00731387\pi$
$659$			30.2813i			0.0459504i	−0.999736	+	0.0229752i	$0.992686\pi$
$660$	222.453	+	100.816i	0.337050	+	0.152752i
$661$	−1230.40			−1.86143			−0.930714	−	0.365749i	$-0.880813\pi$
$661$	−1230.40			−1.86143			−0.930714	+	0.365749i	$0.880813\pi$
$662$			119.784i			0.180942i
$663$	−149.465	+	329.796i	−0.225437	+	0.497430i
$664$	379.350			0.571311
$665$		−	236.779i		−	0.356059i
$666$	557.578	−	488.805i	0.837204	−	0.733941i
$667$	143.990			0.215877
$668$		−	281.250i		−	0.421032i
$669$	−687.759	−	311.695i	−1.02804	−	0.465911i
$670$	239.928			0.358102
$671$		−	1733.50i		−	2.58345i
$672$	−29.0100	+	64.0111i	−0.0431697	+	0.0952546i
$673$	746.022			1.10850			0.554251	−	0.832350i	$-0.313005\pi$
$673$	746.022			1.10850			0.554251	+	0.832350i	$0.313005\pi$
$674$		−	425.953i		−	0.631978i
$675$	39.1534	+	129.198i	0.0580050	+	0.191404i
$676$	195.103			0.288613
$677$		−	491.931i		−	0.726634i	−0.931666	−	0.363317i	$-0.881644\pi$
$677$		−	491.931i		−	0.726634i	0.931666	−	0.363317i	$-0.118356\pi$
$678$	−320.243	−	145.135i	−0.472336	−	0.214064i
$679$	−341.080			−0.502326
$680$		−	90.3070i		−	0.132804i
$681$	−259.739	+	573.118i	−0.381408	+	0.841583i
$682$	530.258			0.777504
$683$			399.771i			0.585316i	0.956217	+	0.292658i	$0.0945397\pi$
$683$			399.771i			0.585316i	−0.956217	+	0.292658i	$0.905460\pi$
$684$	303.411	+	346.100i	0.443583	+	0.505994i
$685$	274.059			0.400086
$686$			473.502i			0.690237i
$687$	−848.226	−	384.419i	−1.23468	−	0.559561i
$688$	−244.117			−0.354821
$689$			215.276i			0.312448i
$690$	−18.7808	+	41.4401i	−0.0272185	+	0.0600581i
$691$	205.782			0.297804			0.148902	−	0.988852i	$-0.452426\pi$
$691$	205.782			0.297804			0.148902	+	0.988852i	$0.452426\pi$
$692$			259.610i			0.375158i
$693$	510.184	−	447.256i	0.736196	−	0.645391i
$694$	−105.216			−0.151608
$695$		−	177.819i		−	0.255855i
$696$	232.044	+	105.163i	0.333397	+	0.151097i
$697$	−791.924			−1.13619
$698$		−	172.841i		−	0.247624i
$699$	−16.7482	+	36.9551i	−0.0239602	+	0.0528686i
$700$	41.4117			0.0591596
$701$			95.2339i			0.135854i	0.997690	+	0.0679272i	$0.0216385\pi$
$701$			95.2339i			0.135854i	−0.997690	+	0.0679272i	$0.978361\pi$
$702$	308.885	−	93.6077i	0.440007	−	0.133344i
$703$	−1489.67			−2.11901
$704$			145.632i			0.206864i
$705$	85.3781	+	38.6936i	0.121104	+	0.0548846i
$706$	363.519			0.514900
$707$			553.777i			0.783277i
$708$	−197.433	+	435.638i	−0.278859	+	0.615308i
$709$	−1225.99			−1.72918			−0.864589	−	0.502479i	$-0.832421\pi$
$709$	−1225.99			−1.72918			−0.864589	+	0.502479i	$0.832421\pi$
$710$			419.571i			0.590944i
$711$	139.844	+	159.519i	0.196686	+	0.224359i
$712$	−330.854			−0.464683
$713$			98.7800i			0.138541i
$714$	−228.500	−	103.557i	−0.320028	−	0.145038i
$715$	−344.072			−0.481219
$716$			555.321i			0.775588i
$717$	−201.061	+	443.644i	−0.280420	+	0.618750i
$718$	−582.441			−0.811199
$719$		−	1015.78i		−	1.41277i	−0.707826	−	0.706387i	$-0.750324\pi$
$719$		−	1015.78i		−	1.41277i	0.707826	−	0.706387i	$-0.249676\pi$
$720$	−60.5315	+	53.0654i	−0.0840716	+	0.0737019i
$721$	−651.100			−0.903051
$722$		−	414.135i		−	0.573595i
$723$	−312.629	−	141.685i	−0.432406	−	0.195968i
$724$	496.611			0.685927
$725$		−	150.120i		−	0.207062i
$726$	368.452	−	812.995i	0.507509	−	1.11983i
$727$	−794.186			−1.09242			−0.546208	−	0.837650i	$-0.683929\pi$
$727$	−794.186			−1.09242			−0.546208	+	0.837650i	$0.683929\pi$
$728$		−	99.0069i		−	0.135999i
$729$	−606.361	+	404.682i	−0.831771	+	0.555119i
$730$	−232.232			−0.318125
$731$		−	871.424i		−	1.19210i
$732$	520.407	+	235.850i	0.710939	+	0.322200i
$733$	502.321			0.685295			0.342648	−	0.939464i	$-0.388676\pi$
$733$	502.321			0.685295			0.342648	+	0.939464i	$0.388676\pi$
$734$		−	552.405i		−	0.752595i
$735$	−88.1970	+	194.608i	−0.119996	+	0.264773i
$736$	−27.1293			−0.0368605
$737$		−	1381.17i		−	1.87405i
$738$	465.343	+	530.816i	0.630546	+	0.719263i
$739$	505.526			0.684067			0.342034	−	0.939688i	$-0.388884\pi$
$739$	505.526			0.684067			0.342034	+	0.939688i	$0.388884\pi$
$740$		−	260.537i		−	0.352077i
$741$	−590.594	−	267.659i	−0.797023	−	0.361213i
$742$	−149.155			−0.201017
$743$		−	345.072i		−	0.464430i	−0.972664	−	0.232215i	$-0.925403\pi$
$743$		−	345.072i		−	0.464430i	0.972664	−	0.232215i	$-0.0745973\pi$
$744$	−72.1439	+	159.187i	−0.0969677	+	0.213961i
$745$	−31.8001			−0.0426848
$746$			506.357i			0.678763i
$747$	907.679	−	795.723i	1.21510	−	1.06522i
$748$	−519.862			−0.695002
$749$			282.311i			0.376918i
$750$	43.2043	+	19.5803i	0.0576057	+	0.0261071i
$751$	691.345			0.920566			0.460283	−	0.887772i	$-0.347748\pi$
$751$	691.345			0.920566			0.460283	+	0.887772i	$0.347748\pi$
$752$			55.8939i			0.0743270i
$753$	96.2776	−	212.438i	0.127859	−	0.282122i
$754$	−358.907			−0.476003
$755$			445.126i			0.589571i
$756$	64.8564	+	214.012i	0.0857889	+	0.283084i
$757$	−127.590			−0.168546			−0.0842732	−	0.996443i	$-0.526857\pi$
$757$	−127.590			−0.168546			−0.0842732	+	0.996443i	$0.526857\pi$
$758$			413.658i			0.545723i
$759$	238.554	+	108.114i	0.314301	+	0.142442i
$760$	161.720			0.212790
$761$		−	183.936i		−	0.241703i	−0.992671	−	0.120852i	$-0.961438\pi$
$761$		−	183.936i		−	0.241703i	0.992671	−	0.120852i	$-0.0385625\pi$
$762$	22.4706	−	49.5817i	0.0294890	−	0.0650679i
$763$	−14.9404			−0.0195811
$764$			228.749i			0.299410i
$765$	−189.427	−	216.079i	−0.247617	−	0.282456i
$766$	−96.0261			−0.125360
$767$		−	673.808i		−	0.878498i
$768$	−43.7197	−	19.8139i	−0.0569267	−	0.0257993i
$769$	−1436.65			−1.86821			−0.934104	−	0.357002i	$-0.883799\pi$
$769$	−1436.65			−1.86821			−0.934104	+	0.357002i	$0.883799\pi$
$770$		−	238.391i		−	0.309599i
$771$	−312.495	+	689.524i	−0.405311	+	0.894325i
$772$	449.567			0.582341
$773$		−	666.904i		−	0.862748i	−0.902173	−	0.431374i	$-0.858029\pi$
$773$		−	666.904i		−	0.862748i	0.902173	−	0.431374i	$-0.141971\pi$
$774$	−584.103	+	512.058i	−0.754656	+	0.661574i
$775$	102.985			0.132884
$776$		−	232.958i		−	0.300203i
$777$	−659.226	−	298.763i	−0.848425	−	0.384509i
$778$	−470.254			−0.604439
$779$		−	1418.17i		−	1.82050i
$780$	46.8125	−	103.293i	0.0600161	−	0.132426i
$781$	2415.30			3.09258
$782$		−	96.8434i		−	0.123841i
$783$	775.807	−	235.109i	0.990813	−	0.300266i
$784$	−127.403			−0.162504
$785$		−	337.609i		−	0.430075i
$786$	−1007.34	−	456.530i	−1.28160	−	0.580827i
$787$	375.910			0.477649			0.238825	−	0.971063i	$-0.423238\pi$
$787$	375.910			0.477649			0.238825	+	0.971063i	$0.423238\pi$
$788$		−	474.379i		−	0.602004i
$789$	238.085	−	525.339i	0.301756	−	0.665829i
$790$	74.5377			0.0943516
$791$			343.188i			0.433866i
$792$	305.477	+	348.456i	0.385703	+	0.439970i
$793$	−804.922			−1.01503
$794$		−	261.644i		−	0.329526i
$795$	−155.611	−	70.5235i	−0.195737	−	0.0887088i
$796$	400.542			0.503194
$797$		−	735.801i		−	0.923213i	−0.887085	−	0.461607i	$-0.847273\pi$
$797$		−	735.801i		−	0.923213i	0.887085	−	0.461607i	$-0.152727\pi$
$798$	185.448	−	409.195i	0.232392	−	0.512776i
$799$	−199.524			−0.249717
$800$			28.2843i			0.0353553i
$801$	−791.641	+	693.997i	−0.988316	+	0.866413i
$802$	40.6567			0.0506942
$803$			1336.87i			1.66484i
$804$	414.637	+	187.915i	0.515718	+	0.233725i
$805$	44.4091			0.0551666
$806$		−	246.217i		−	0.305480i
$807$	−414.027	+	913.558i	−0.513045	+	1.13204i
$808$	−378.231			−0.468107
$809$			792.628i			0.979762i	0.871789	+	0.489881i	$0.162960\pi$
$809$			792.628i			0.979762i	−0.871789	+	0.489881i	$0.837040\pi$
$810$	−33.5254	+	253.941i	−0.0413894	+	0.313507i
$811$	1358.33			1.67489			0.837444	−	0.546523i	$-0.184049\pi$
$811$	1358.33			1.67489			0.837444	+	0.546523i	$0.184049\pi$
$812$		−	248.669i		−	0.306243i
$813$	1136.55	+	515.086i	1.39797	+	0.633563i
$814$	−1499.81			−1.84252
$815$			351.204i			0.430925i
$816$	70.7296	−	156.066i	0.0866784	−	0.191257i
$817$	1560.53			1.91008
$818$		−	435.200i		−	0.532029i
$819$	−207.676	−	236.896i	−0.253573	−	0.289250i
$820$	248.032			0.302478
$821$		−	86.1260i		−	0.104904i	−0.998623	−	0.0524519i	$-0.983296\pi$
$821$		−	86.1260i		−	0.104904i	0.998623	−	0.0524519i	$-0.0167036\pi$
$822$	473.620	+	214.646i	0.576181	+	0.261127i
$823$	901.372			1.09523			0.547613	−	0.836732i	$-0.315537\pi$
$823$	901.372			1.09523			0.547613	+	0.836732i	$0.315537\pi$
$824$		−	444.702i		−	0.539687i
$825$	112.716	−	248.710i	0.136626	−	0.301467i
$826$	466.850			0.565194
$827$		−	873.842i		−	1.05664i	−0.849045	−	0.528321i	$-0.822822\pi$
$827$		−	873.842i		−	1.05664i	0.849045	−	0.528321i	$-0.177178\pi$
$828$	−64.9128	+	56.9063i	−0.0783971	+	0.0687274i
$829$	998.270			1.20419			0.602093	−	0.798426i	$-0.294334\pi$
$829$	998.270			1.20419			0.602093	+	0.798426i	$0.294334\pi$
$830$		−	424.127i		−	0.510996i
$831$	−259.936	−	117.804i	−0.312799	−	0.141761i
$832$	67.6219			0.0812763
$833$		−	454.789i		−	0.545965i
$834$	139.270	−	307.302i	0.166991	−	0.368468i
$835$	−314.447			−0.376583
$836$		−	930.962i		−	1.11359i
$837$	161.289	+	532.218i	0.192699	+	0.635864i
$838$	490.642			0.585491
$839$			602.116i			0.717659i	0.933403	+	0.358830i	$0.116824\pi$
$839$			602.116i			0.717659i	−0.933403	+	0.358830i	$0.883176\pi$
$840$	71.5666	+	32.4342i	0.0851983	+	0.0386121i
$841$	−60.4431			−0.0718705
$842$		−	306.819i		−	0.364393i
$843$	77.8510	−	171.779i	0.0923499	−	0.203772i
$844$	399.620			0.473483
$845$		−	218.131i		−	0.258144i
$846$	117.243	+	133.738i	0.138585	+	0.158083i
$847$	−871.243			−1.02862
$848$		−	101.873i		−	0.120133i
$849$	−1282.78	−	581.362i	−1.51094	−	0.684761i
$850$	−100.966			−0.118784
$851$		−	279.395i		−	0.328313i
$852$	−328.613	+	725.090i	−0.385696	+	0.851045i
$853$	1007.76			1.18143			0.590716	−	0.806880i	$-0.298846\pi$
$853$	1007.76			1.18143			0.590716	+	0.806880i	$0.298846\pi$
$854$		−	557.693i		−	0.653036i
$855$	386.952	−	339.224i	0.452575	−	0.396753i
$856$	−192.819			−0.225256
$857$			954.087i			1.11329i	0.830751	+	0.556644i	$0.187911\pi$
$857$			954.087i			1.11329i	−0.830751	+	0.556644i	$0.812089\pi$
$858$	−594.615	−	269.481i	−0.693025	−	0.314081i
$859$	−1402.10			−1.63224			−0.816122	−	0.577879i	$-0.803881\pi$
$859$	−1402.10			−1.63224			−0.816122	+	0.577879i	$0.803881\pi$
$860$			272.931i			0.317362i
$861$	284.423	−	627.585i	0.330341	−	0.728902i
$862$	841.813			0.976581
$863$			380.578i			0.440994i	0.975388	+	0.220497i	$0.0707679\pi$
$863$			380.578i			0.440994i	−0.975388	+	0.220497i	$0.929232\pi$
$864$	−146.170	+	44.2970i	−0.169179	+	0.0512697i
$865$	290.252			0.335552
$866$			230.173i			0.265788i
$867$	−232.579	−	105.405i	−0.268257	−	0.121575i
$868$	170.592			0.196534
$869$		−	429.085i		−	0.493768i
$870$	117.576	−	259.434i	0.135145	−	0.298199i
$871$	−641.326			−0.736310
$872$		−	10.2043i		−	0.0117022i
$873$	−488.651	−	557.403i	−0.559737	−	0.638491i
$874$	173.426			0.198428
$875$		−	46.2997i		−	0.0529140i
$876$	−401.336	−	181.887i	−0.458146	−	0.207633i
$877$	−601.540			−0.685907			−0.342953	−	0.939352i	$-0.611427\pi$
$877$	−601.540			−0.685907			−0.342953	+	0.939352i	$0.611427\pi$
$878$			194.150i			0.221127i
$879$	−357.466	+	788.755i	−0.406674	+	0.897332i
$880$	162.821			0.185024
$881$		−	525.320i		−	0.596277i	−0.954523	−	0.298138i	$-0.903634\pi$
$881$		−	525.320i		−	0.596277i	0.954523	−	0.298138i	$-0.0963657\pi$
$882$	−304.839	+	267.239i	−0.345622	+	0.302992i
$883$	−1483.40			−1.67996			−0.839980	−	0.542618i	$-0.817433\pi$
$883$	−1483.40			−1.67996			−0.839980	+	0.542618i	$0.817433\pi$
$884$			241.390i			0.273065i
$885$	487.058	+	220.736i	0.550348	+	0.249419i
$886$	437.254			0.493514
$887$		−	658.597i		−	0.742499i	−0.928533	−	0.371249i	$-0.878929\pi$
$887$		−	658.597i		−	0.742499i	0.928533	−	0.371249i	$-0.121071\pi$
$888$	204.056	−	450.252i	0.229792	−	0.507041i
$889$	−53.1341			−0.0597684
$890$			369.906i			0.415625i
$891$	1461.84	+	192.993i	1.64067	+	0.216602i
$892$	−503.396			−0.564345
$893$		−	357.305i		−	0.400118i
$894$	−54.9561	−	24.9063i	−0.0614722	−	0.0278594i
$895$	620.868			0.693707
$896$			46.8520i			0.0522902i
$897$	50.2008	−	110.769i	0.0559653	−	0.123488i
$898$	−86.4887			−0.0963125
$899$		−	618.407i		−	0.687883i
$900$	59.3289	+	67.6763i	0.0659210	+	0.0751959i
$901$	363.656			0.403613
$902$		−	1427.82i		−	1.58295i
$903$	690.587	+	312.976i	0.764770	+	0.346596i
$904$	−234.398			−0.259290
$905$		−	555.228i		−	0.613512i
$906$	−348.629	+	769.255i	−0.384800	+	0.849067i
$907$	−618.860			−0.682315			−0.341158	−	0.940006i	$-0.610819\pi$
$907$	−618.860			−0.682315			−0.341158	+	0.940006i	$0.610819\pi$
$908$			419.486i			0.461988i
$909$	−904.999	+	793.374i	−0.995599	+	0.872798i
$910$	−110.693			−0.121641
$911$			1335.14i			1.46558i	0.680456	+	0.732789i	$0.261782\pi$
$911$			1335.14i			1.46558i	−0.680456	+	0.732789i	$0.738218\pi$
$912$	279.481	+	126.662i	0.306448	+	0.138883i
$913$	−2441.53			−2.67419
$914$		−	459.978i		−	0.503258i
$915$	263.689	−	581.833i	0.288184	−	0.635883i
$916$	−620.847			−0.677781
$917$			1079.51i			1.17722i
$918$	−158.127	−	521.784i	−0.172251	−	0.568392i
$919$	−712.731			−0.775551			−0.387775	−	0.921754i	$-0.626756\pi$
$919$	−712.731			−0.775551			−0.387775	+	0.921754i	$0.626756\pi$
$920$			30.3315i			0.0329690i
$921$	1238.07	+	561.098i	1.34427	+	0.609227i
$922$	252.643			0.274016
$923$		−	1121.51i		−	1.21507i
$924$	186.711	−	411.981i	0.202068	−	0.445867i
$925$	−291.289			−0.314907
$926$		−	1065.84i		−	1.15101i
$927$	−932.804	−	1064.05i	−1.00626	−	1.14784i
$928$	169.842			0.183019
$929$			589.860i			0.634941i	0.948268	+	0.317471i	$0.102833\pi$
$929$			589.860i			0.634941i	−0.948268	+	0.317471i	$0.897167\pi$
$930$	177.976	+	80.6594i	0.191372	+	0.0867305i
$931$	814.430			0.874791
$932$			27.0488i			0.0290223i
$933$	−551.101	+	1216.01i	−0.590677	+	1.30334i
$934$	−483.113			−0.517251
$935$			581.223i			0.621629i
$936$	161.800	−	141.843i	0.172863	−	0.151542i
$937$	1588.05			1.69483			0.847413	−	0.530934i	$-0.178159\pi$
$937$	1588.05			1.69483			0.847413	+	0.530934i	$0.178159\pi$
$938$		−	444.344i		−	0.473715i
$939$	1497.76	+	678.790i	1.59506	+	0.722886i
$940$	62.4913			0.0664801
$941$		−	1060.18i		−	1.12666i	−0.826233	−	0.563329i	$-0.809520\pi$
$941$		−	1060.18i		−	1.12666i	0.826233	−	0.563329i	$-0.190480\pi$
$942$	264.419	−	583.446i	0.280700	−	0.619369i
$943$	265.984			0.282062
$944$			318.859i			0.337775i
$945$	239.272	−	72.5116i	0.253198	−	0.0767319i
$946$	1571.16			1.66084
$947$		−	1776.50i		−	1.87592i	−0.346744	−	0.937960i	$-0.612713\pi$
$947$		−	1776.50i		−	1.87592i	0.346744	−	0.937960i	$-0.387287\pi$
$948$	128.814	+	58.3789i	0.135880	+	0.0615811i
$949$	620.752			0.654112
$950$		−	180.809i		−	0.190325i
$951$	−1.47217	+	3.24838i	−0.00154803	+	0.00341575i
$952$	−167.247			−0.175680
$953$			456.158i			0.478655i	0.970939	+	0.239327i	$0.0769269\pi$
$953$			456.158i			0.478655i	−0.970939	+	0.239327i	$0.923073\pi$
$954$	−213.688	−	243.753i	−0.223992	−	0.255507i
$955$	255.749			0.267800
$956$			324.719i			0.339664i
$957$	−1493.46	−	676.839i	−1.56056	−	0.707251i
$958$	182.807			0.190822
$959$		−	507.554i		−	0.529253i
$960$	−22.1526	+	48.8801i	−0.0230756	+	0.0509167i
$961$	−536.761			−0.558545
$962$			696.412i			0.723921i
$963$	−461.362	+	404.456i	−0.479088	+	0.419996i
$964$	−228.825			−0.237370
$965$		−	502.631i		−	0.520861i
$966$	76.7466	+	34.7818i	0.0794478	+	0.0360060i
$967$	−266.946			−0.276056			−0.138028	−	0.990428i	$-0.544076\pi$
$967$	−266.946			−0.276056			−0.138028	+	0.990428i	$0.544076\pi$
$968$		−	595.060i		−	0.614731i
$969$	−452.143	+	997.661i	−0.466608	+	1.02958i
$970$	−260.455			−0.268510
$971$		−	624.625i		−	0.643280i	−0.946862	−	0.321640i	$-0.895766\pi$
$971$		−	624.625i		−	0.643280i	0.946862	−	0.321640i	$-0.104234\pi$
$972$	−256.828	+	412.596i	−0.264226	+	0.424482i
$973$	−329.319			−0.338457
$974$			504.733i			0.518207i
$975$	−115.485	−	52.3380i	−0.118446	−	0.0536800i
$976$	380.905			0.390271
$977$			631.153i			0.646011i	0.946397	+	0.323006i	$0.104693\pi$
$977$			631.153i			0.646011i	−0.946397	+	0.323006i	$0.895307\pi$
$978$	−275.067	+	606.941i	−0.281255	+	0.620594i
$979$	2129.40			2.17508
$980$			142.441i			0.145348i
$981$	−21.4045	−	24.4160i	−0.0218190	−	0.0248889i
$982$	815.329			0.830274
$983$		−	33.7587i		−	0.0343426i	−0.999853	−	0.0171713i	$-0.994534\pi$
$983$		−	33.7587i		−	0.0343426i	0.999853	−	0.0171713i	$-0.00546606\pi$
$984$	428.641	+	194.262i	0.435611	+	0.197420i
$985$	−530.372			−0.538449
$986$			606.283i			0.614891i
$987$	71.6601	−	158.119i	0.0726040	−	0.160202i
$988$	−432.277			−0.437528
$989$			292.686i			0.295941i
$990$	389.586	−	341.533i	0.393521	−	0.344983i
$991$	1329.87			1.34195			0.670976	−	0.741479i	$-0.265875\pi$
$991$	1329.87			1.34195			0.670976	+	0.741479i	$0.265875\pi$
$992$			116.515i			0.117454i
$993$	231.441	+	104.890i	0.233072	+	0.105629i
$994$	777.040			0.781730
$995$		−	447.820i		−	0.450070i
$996$	332.181	−	732.964i	0.333516	−	0.735907i
$997$	−1108.24			−1.11158			−0.555789	−	0.831323i	$-0.687584\pi$
$997$	−1108.24			−1.11158			−0.555789	+	0.831323i	$0.687584\pi$
$998$			880.802i			0.882567i
$999$	−456.198	−	1505.35i	−0.456655	−	1.50686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.g.a.461.5	✓	56
3.2	odd	2	inner	690.3.g.a.461.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.g.a.461.5	✓	56	1.1	even	1	trivial
690.3.g.a.461.6	yes	56	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-2.73248 - 1.23837i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-1.75132 + 3.86431i) q^{6} +4.14117 q^{7} +2.82843i q^{8} +(5.93289 + 6.76763i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(-2.73248 - 1.23837i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-1.75132 + 3.86431i) q^{6} +4.14117 q^{7} +2.82843i q^{8} +(5.93289 + 6.76763i) q^{9} +3.16228 q^{10} -18.2040i q^{11} +(5.46496 + 2.47674i) q^{12} -8.45273 q^{13} -5.85650i q^{14} +(2.76908 - 6.11001i) q^{15} +4.00000 q^{16} +14.2788i q^{17} +(9.57088 - 8.39037i) q^{18} -25.5703 q^{19} -4.47214i q^{20} +(-11.3157 - 5.12830i) q^{21} -25.7443 q^{22} -4.79583i q^{23} +(3.50263 - 7.72862i) q^{24} -5.00000 q^{25} +11.9540i q^{26} +(-7.83068 - 25.8395i) q^{27} -8.28235 q^{28} +30.0240i q^{29} +(-8.64086 - 3.91606i) q^{30} -20.5971 q^{31} -5.65685i q^{32} +(-22.5432 + 49.7420i) q^{33} +20.1932 q^{34} +9.25994i q^{35} +(-11.8658 - 13.5353i) q^{36} +58.2578 q^{37} +36.1618i q^{38} +(23.0969 + 10.4676i) q^{39} -6.32456 q^{40} +55.4616i q^{41} +(-7.25251 + 16.0028i) q^{42} -61.0293 q^{43} +36.4080i q^{44} +(-15.1329 + 13.2663i) q^{45} -6.78233 q^{46} +13.9735i q^{47} +(-10.9299 - 4.95347i) q^{48} -31.8507 q^{49} +7.07107i q^{50} +(17.6824 - 39.0165i) q^{51} +16.9055 q^{52} -25.4683i q^{53} +(-36.5426 + 11.0743i) q^{54} +40.7054 q^{55} +11.7130i q^{56} +(69.8702 + 31.6654i) q^{57} +42.4604 q^{58} +79.7148i q^{59} +(-5.53815 + 12.2200i) q^{60} +95.2262 q^{61} +29.1286i q^{62} +(24.5691 + 28.0259i) q^{63} -8.00000 q^{64} -18.9009i q^{65} +(70.3459 + 31.8810i) q^{66} +75.8720 q^{67} -28.5576i q^{68} +(-5.93901 + 13.1045i) q^{69} +13.0955 q^{70} +132.680i q^{71} +(-19.1418 + 16.7807i) q^{72} -73.4381 q^{73} -82.3890i q^{74} +(13.6624 + 6.19184i) q^{75} +51.1405 q^{76} -75.3859i q^{77} +(14.8034 - 32.6640i) q^{78} +23.5709 q^{79} +8.94427i q^{80} +(-10.6017 + 80.3032i) q^{81} +78.4345 q^{82} -134.121i q^{83} +(22.6313 + 10.2566i) q^{84} -31.9283 q^{85} +86.3084i q^{86} +(37.1808 - 82.0401i) q^{87} +51.4887 q^{88} +116.975i q^{89} +(18.7614 + 21.4011i) q^{90} -35.0042 q^{91} +9.59166i q^{92} +(56.2810 + 25.5067i) q^{93} +19.7615 q^{94} -57.1768i q^{95} +(-7.00527 + 15.4572i) q^{96} -82.3630 q^{97} +45.0437i q^{98} +(123.198 - 108.002i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7}+O(q^{10}) \) 56 * q - 8 * q^3 - 112 * q^4 + 16 * q^6 - 16 * q^7	\( 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7} + 16 q^{12} + 80 q^{13} - 40 q^{15} + 224 q^{16} - 32 q^{18} - 64 q^{19} + 56 q^{21} - 96 q^{22} - 32 q^{24} - 280 q^{25} + 40 q^{27} + 32 q^{28} - 80 q^{31} + 32 q^{33} + 192 q^{34} + 240 q^{37} - 56 q^{39} - 144 q^{43} - 32 q^{48} + 72 q^{49} - 24 q^{51} - 160 q^{52} + 16 q^{54} - 16 q^{57} + 80 q^{60} + 112 q^{61} - 64 q^{63} - 448 q^{64} + 160 q^{66} + 832 q^{67} + 64 q^{72} - 608 q^{73} + 40 q^{75} + 128 q^{76} - 320 q^{78} + 48 q^{79} - 32 q^{81} - 448 q^{82} - 112 q^{84} + 240 q^{85} + 200 q^{87} + 192 q^{88} + 80 q^{91} - 232 q^{93} + 160 q^{94} + 64 q^{96} - 448 q^{97} + 464 q^{99}+O(q^{100}) \) 56 * q - 8 * q^3 - 112 * q^4 + 16 * q^6 - 16 * q^7 + 16 * q^12 + 80 * q^13 - 40 * q^15 + 224 * q^16 - 32 * q^18 - 64 * q^19 + 56 * q^21 - 96 * q^22 - 32 * q^24 - 280 * q^25 + 40 * q^27 + 32 * q^28 - 80 * q^31 + 32 * q^33 + 192 * q^34 + 240 * q^37 - 56 * q^39 - 144 * q^43 - 32 * q^48 + 72 * q^49 - 24 * q^51 - 160 * q^52 + 16 * q^54 - 16 * q^57 + 80 * q^60 + 112 * q^61 - 64 * q^63 - 448 * q^64 + 160 * q^66 + 832 * q^67 + 64 * q^72 - 608 * q^73 + 40 * q^75 + 128 * q^76 - 320 * q^78 + 48 * q^79 - 32 * q^81 - 448 * q^82 - 112 * q^84 + 240 * q^85 + 200 * q^87 + 192 * q^88 + 80 * q^91 - 232 * q^93 + 160 * q^94 + 64 * q^96 - 448 * q^97 + 464 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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