LMFDB - Embedded newform 690.3.g.a.461.10

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			461.10
Character	$\chi$	$=$	690.461
Dual form			690.3.g.a.461.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(2.16025 - 2.08166i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(2.94392 + 3.05506i) q^{6} +12.7530 q^{7} -2.82843i q^{8} +(0.333364 - 8.99382i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(2.16025 - 2.08166i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(2.94392 + 3.05506i) q^{6} +12.7530 q^{7} -2.82843i q^{8} +(0.333364 - 8.99382i) q^{9} +3.16228 q^{10} -10.4206i q^{11} +(-4.32050 + 4.16332i) q^{12} -10.0884 q^{13} +18.0355i q^{14} +(-4.65474 - 4.83047i) q^{15} +4.00000 q^{16} +0.278181i q^{17} +(12.7192 + 0.471449i) q^{18} +14.4422 q^{19} +4.47214i q^{20} +(27.5497 - 26.5474i) q^{21} +14.7369 q^{22} -4.79583i q^{23} +(-5.88783 - 6.11011i) q^{24} -5.00000 q^{25} -14.2672i q^{26} +(-18.0020 - 20.1229i) q^{27} -25.5060 q^{28} +1.71142i q^{29} +(6.83131 - 6.58279i) q^{30} -36.9908 q^{31} +5.65685i q^{32} +(-21.6921 - 22.5111i) q^{33} -0.393408 q^{34} -28.5166i q^{35} +(-0.666729 + 17.9876i) q^{36} +17.1960 q^{37} +20.4243i q^{38} +(-21.7936 + 21.0007i) q^{39} -6.32456 q^{40} +36.4515i q^{41} +(37.5437 + 38.9611i) q^{42} -41.5531 q^{43} +20.8412i q^{44} +(-20.1108 - 0.745426i) q^{45} +6.78233 q^{46} -73.4371i q^{47} +(8.64100 - 8.32665i) q^{48} +113.639 q^{49} -7.07107i q^{50} +(0.579080 + 0.600942i) q^{51} +20.1769 q^{52} +20.7239i q^{53} +(28.4580 - 25.4586i) q^{54} -23.3011 q^{55} -36.0709i q^{56} +(31.1987 - 30.0637i) q^{57} -2.42032 q^{58} -74.5843i q^{59} +(9.30948 + 9.66093i) q^{60} +77.3260 q^{61} -52.3129i q^{62} +(4.25139 - 114.698i) q^{63} -8.00000 q^{64} +22.5584i q^{65} +(31.8355 - 30.6773i) q^{66} +103.539 q^{67} -0.556363i q^{68} +(-9.98330 - 10.3602i) q^{69} +40.3285 q^{70} +56.8221i q^{71} +(-25.4384 - 0.942897i) q^{72} -39.9241 q^{73} +24.3188i q^{74} +(-10.8013 + 10.4083i) q^{75} -28.8843 q^{76} -132.894i q^{77} +(-29.6995 - 30.8207i) q^{78} +81.4578 q^{79} -8.94427i q^{80} +(-80.7777 - 5.99644i) q^{81} -51.5502 q^{82} -37.1864i q^{83} +(-55.0993 + 53.0949i) q^{84} +0.622033 q^{85} -58.7650i q^{86} +(3.56261 + 3.69711i) q^{87} -29.4739 q^{88} +129.429i q^{89} +(1.05419 - 28.4410i) q^{90} -128.658 q^{91} +9.59166i q^{92} +(-79.9094 + 77.0024i) q^{93} +103.856 q^{94} -32.2937i q^{95} +(11.7757 + 12.2202i) q^{96} +39.8372 q^{97} +160.710i q^{98} +(-93.7209 - 3.47385i) 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
$3$	2.16025	−	2.08166i	0.720084	−	0.693887i
$3$	2.16025	−	2.08166i	0.720084	−	0.693887i
$4$	−2.00000			−0.500000
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	2.94392	+	3.05506i	0.490653	+	0.509176i
$7$	12.7530			1.82186			0.910928	−	0.412565i	$-0.135367\pi$
$7$	12.7530			1.82186			0.910928	+	0.412565i	$0.135367\pi$
$8$		−	2.82843i		−	0.353553i
$9$	0.333364	−	8.99382i	0.0370405	−	0.999314i
$10$	3.16228			0.316228
$11$		−	10.4206i		−	0.947326i	−0.880706	−	0.473663i	$-0.842931\pi$
$11$		−	10.4206i		−	0.947326i	0.880706	−	0.473663i	$-0.157069\pi$
$12$	−4.32050	+	4.16332i	−0.360042	+	0.346944i
$13$	−10.0884			−0.776034			−0.388017	−	0.921652i	$-0.626840\pi$
$13$	−10.0884			−0.776034			−0.388017	+	0.921652i	$0.626840\pi$
$14$			18.0355i			1.28825i
$15$	−4.65474	−	4.83047i	−0.310316	−	0.322031i
$16$	4.00000			0.250000
$17$			0.278181i			0.0163636i	0.999967	+	0.00818181i	$0.00260438\pi$
$17$			0.278181i			0.0163636i	−0.999967	+	0.00818181i	$0.997396\pi$
$18$	12.7192	+	0.471449i	0.706622	+	0.0261916i
$19$	14.4422			0.760114			0.380057	−	0.924963i	$-0.375904\pi$
$19$	14.4422			0.760114			0.380057	+	0.924963i	$0.375904\pi$
$20$			4.47214i			0.223607i
$21$	27.5497	−	26.5474i	1.31189	−	1.26416i
$22$	14.7369			0.669861
$23$		−	4.79583i		−	0.208514i
$23$		−	4.79583i		−	0.208514i
$24$	−5.88783	−	6.11011i	−0.245326	−	0.254588i
$25$	−5.00000			−0.200000
$26$		−	14.2672i		−	0.548739i
$27$	−18.0020	−	20.1229i	−0.666739	−	0.745291i
$28$	−25.5060			−0.910928
$29$			1.71142i			0.0590146i	0.999565	+	0.0295073i	$0.00939383\pi$
$29$			1.71142i			0.0590146i	−0.999565	+	0.0295073i	$0.990606\pi$
$30$	6.83131	−	6.58279i	0.227710	−	0.219426i
$31$	−36.9908			−1.19325			−0.596626	−	0.802520i	$-0.703492\pi$
$31$	−36.9908			−1.19325			−0.596626	+	0.802520i	$0.703492\pi$
$32$			5.65685i			0.176777i
$33$	−21.6921	−	22.5111i	−0.657338	−	0.682154i
$34$	−0.393408			−0.0115708
$35$		−	28.5166i		−	0.814759i
$36$	−0.666729	+	17.9876i	−0.0185202	+	0.499657i
$37$	17.1960			0.464756			0.232378	−	0.972626i	$-0.425349\pi$
$37$	17.1960			0.464756			0.232378	+	0.972626i	$0.425349\pi$
$38$			20.4243i			0.537482i
$39$	−21.7936	+	21.0007i	−0.558809	+	0.538480i
$40$	−6.32456			−0.158114
$41$			36.4515i			0.889062i	0.895764	+	0.444531i	$0.146630\pi$
$41$			36.4515i			0.889062i	−0.895764	+	0.444531i	$0.853370\pi$
$42$	37.5437	+	38.9611i	0.893898	+	0.927645i
$43$	−41.5531			−0.966352			−0.483176	−	0.875523i	$-0.660517\pi$
$43$	−41.5531			−0.966352			−0.483176	+	0.875523i	$0.660517\pi$
$44$			20.8412i			0.473663i
$45$	−20.1108	−	0.745426i	−0.446907	−	0.0165650i
$46$	6.78233			0.147442
$47$		−	73.4371i		−	1.56249i	−0.624224	−	0.781246i	$-0.714585\pi$
$47$		−	73.4371i		−	1.56249i	0.624224	−	0.781246i	$-0.285415\pi$
$48$	8.64100	−	8.32665i	0.180021	−	0.173472i
$49$	113.639			2.31916
$50$		−	7.07107i		−	0.141421i
$51$	0.579080	+	0.600942i	0.0113545	+	0.0117832i
$52$	20.1769			0.388017
$53$			20.7239i			0.391017i	0.980702	+	0.195509i	$0.0626358\pi$
$53$			20.7239i			0.391017i	−0.980702	+	0.195509i	$0.937364\pi$
$54$	28.4580	−	25.4586i	0.527001	−	0.471456i
$55$	−23.3011			−0.423657
$56$		−	36.0709i		−	0.644123i
$57$	31.1987	−	30.0637i	0.547346	−	0.527434i
$58$	−2.42032			−0.0417297
$59$		−	74.5843i		−	1.26414i	−0.774911	−	0.632070i	$-0.782206\pi$
$59$		−	74.5843i		−	1.26414i	0.774911	−	0.632070i	$-0.217794\pi$
$60$	9.30948	+	9.66093i	0.155158	+	0.161016i
$61$	77.3260			1.26764			0.633820	−	0.773481i	$-0.281486\pi$
$61$	77.3260			1.26764			0.633820	+	0.773481i	$0.281486\pi$
$62$		−	52.3129i		−	0.843756i
$63$	4.25139	−	114.698i	0.0674825	−	1.82061i
$64$	−8.00000			−0.125000
$65$			22.5584i			0.347053i
$66$	31.8355	−	30.6773i	0.482356	−	0.464808i
$67$	103.539			1.54536			0.772679	−	0.634796i	$-0.218916\pi$
$67$	103.539			1.54536			0.772679	+	0.634796i	$0.218916\pi$
$68$		−	0.556363i		−	0.00818181i
$69$	−9.98330	−	10.3602i	−0.144686	−	0.150148i
$70$	40.3285			0.576122
$71$			56.8221i			0.800311i	0.916447	+	0.400156i	$0.131044\pi$
$71$			56.8221i			0.800311i	−0.916447	+	0.400156i	$0.868956\pi$
$72$	−25.4384	−	0.942897i	−0.353311	−	0.0130958i
$73$	−39.9241			−0.546905			−0.273453	−	0.961886i	$-0.588166\pi$
$73$	−39.9241			−0.546905			−0.273453	+	0.961886i	$0.588166\pi$
$74$			24.3188i			0.328632i
$75$	−10.8013	+	10.4083i	−0.144017	+	0.138777i
$76$	−28.8843			−0.380057
$77$		−	132.894i		−	1.72589i
$78$	−29.6995	−	30.8207i	−0.380763	−	0.395138i
$79$	81.4578			1.03111			0.515556	−	0.856856i	$-0.327586\pi$
$79$	81.4578			1.03111			0.515556	+	0.856856i	$0.327586\pi$
$80$		−	8.94427i		−	0.111803i
$81$	−80.7777	−	5.99644i	−0.997256	−	0.0740302i
$82$	−51.5502			−0.628662
$83$		−	37.1864i		−	0.448029i	−0.974586	−	0.224014i	$-0.928084\pi$
$83$		−	37.1864i		−	0.448029i	0.974586	−	0.224014i	$-0.0719162\pi$
$84$	−55.0993	+	53.0949i	−0.655944	+	0.632082i
$85$	0.622033			0.00731803
$86$		−	58.7650i		−	0.683314i
$87$	3.56261	+	3.69711i	0.0409495	+	0.0424955i
$88$	−29.4739			−0.334930
$89$			129.429i			1.45426i	0.686498	+	0.727132i	$0.259147\pi$
$89$			129.429i			1.45426i	−0.686498	+	0.727132i	$0.740853\pi$
$90$	1.05419	−	28.4410i	0.0117132	−	0.316011i
$91$	−128.658			−1.41382
$92$			9.59166i			0.104257i
$93$	−79.9094	+	77.0024i	−0.859241	+	0.827982i
$94$	103.856			1.10485
$95$		−	32.2937i		−	0.339933i
$96$	11.7757	+	12.2202i	0.122663	+	0.127294i
$97$	39.8372			0.410693			0.205346	−	0.978689i	$-0.434168\pi$
$97$	39.8372			0.410693			0.205346	+	0.978689i	$0.434168\pi$
$98$			160.710i			1.63989i
$99$	−93.7209	−	3.47385i	−0.946676	−	0.0350894i
$100$	10.0000			0.100000
$101$		−	104.192i		−	1.03161i	−0.856707	−	0.515804i	$-0.827493\pi$
$101$		−	104.192i		−	1.03161i	0.856707	−	0.515804i	$-0.172507\pi$
$102$	−0.849860	+	0.818942i	−0.00833196	+	0.00802885i
$103$	26.0419			0.252834			0.126417	−	0.991977i	$-0.459652\pi$
$103$	26.0419			0.252834			0.126417	+	0.991977i	$0.459652\pi$
$104$			28.5344i			0.274369i
$105$	−59.3618	−	61.6029i	−0.565351	−	0.586694i
$106$	−29.3080			−0.276491
$107$			28.1668i			0.263241i	0.991300	+	0.131621i	$0.0420181\pi$
$107$			28.1668i			0.263241i	−0.991300	+	0.131621i	$0.957982\pi$
$108$	36.0039	+	40.2457i	0.333370	+	0.372646i
$109$	138.704			1.27251			0.636257	−	0.771477i	$-0.280482\pi$
$109$	138.704			1.27251			0.636257	+	0.771477i	$0.280482\pi$
$110$		−	32.9528i		−	0.299571i
$111$	37.1476	−	35.7962i	0.334663	−	0.322488i
$112$	51.0120			0.455464
$113$			59.4090i			0.525743i	0.964831	+	0.262871i	$0.0846695\pi$
$113$			59.4090i			0.525743i	−0.964831	+	0.262871i	$0.915330\pi$
$114$	42.5165	+	44.1216i	0.372952	+	0.387032i
$115$	−10.7238			−0.0932505
$116$		−	3.42285i		−	0.0295073i
$117$	−3.36313	+	90.7336i	−0.0287447	+	0.775501i
$118$	105.478			0.893882
$119$			3.54765i			0.0298122i
$120$	−13.6626	+	13.1656i	−0.113855	+	0.109713i
$121$	12.4114			0.102573
$122$			109.355i			0.896356i
$123$	75.8798	+	78.7444i	0.616909	+	0.640199i
$124$	73.9816			0.596626
$125$			11.1803i			0.0894427i
$126$	162.208	+	6.01238i	1.28736	+	0.0477173i
$127$	−127.559			−1.00440			−0.502201	−	0.864751i	$-0.667476\pi$
$127$	−127.559			−1.00440			−0.502201	+	0.864751i	$0.667476\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	−89.7652	+	86.4996i	−0.695854	+	0.670539i
$130$	−31.9024			−0.245403
$131$			24.8275i			0.189523i	0.995500	+	0.0947616i	$0.0302089\pi$
$131$			24.8275i			0.189523i	−0.995500	+	0.0947616i	$0.969791\pi$
$132$	43.3843	+	45.0222i	0.328669	+	0.341077i
$133$	184.181			1.38482
$134$			146.426i			1.09273i
$135$	−44.9961	+	40.2536i	−0.333304	+	0.298175i
$136$	0.786816			0.00578541
$137$		−	48.0916i		−	0.351033i	−0.984476	−	0.175517i	$-0.943840\pi$
$137$		−	48.0916i		−	0.351033i	0.984476	−	0.175517i	$-0.0561596\pi$
$138$	14.6515	−	14.1185i	0.106171	−	0.102308i
$139$	−243.193			−1.74959			−0.874795	−	0.484494i	$-0.839004\pi$
$139$	−243.193			−1.74959			−0.874795	+	0.484494i	$0.839004\pi$
$140$			57.0331i			0.407379i
$141$	−152.871	−	158.642i	−1.08419	−	1.12512i
$142$	−80.3586			−0.565906
$143$			105.127i			0.735157i
$144$	1.33346	−	35.9753i	0.00926012	−	0.249828i
$145$	3.82686			0.0263921
$146$		−	56.4612i		−	0.386720i
$147$	245.488	−	236.558i	1.66999	−	1.60924i
$148$	−34.3920			−0.232378
$149$			168.605i			1.13158i	0.824551	+	0.565788i	$0.191428\pi$
$149$			168.605i			1.13158i	−0.824551	+	0.565788i	$0.808572\pi$
$150$	−14.7196	−	15.2753i	−0.0981305	−	0.101835i
$151$	−64.6419			−0.428092			−0.214046	−	0.976824i	$-0.568664\pi$
$151$	−64.6419			−0.428092			−0.214046	+	0.976824i	$0.568664\pi$
$152$		−	40.8486i		−	0.268741i
$153$	2.50191	+	0.0927358i	0.0163524	+	0.000606116i
$154$	187.940			1.22039
$155$			82.7139i			0.533638i
$156$	43.5871	−	42.0014i	0.279404	−	0.269240i
$157$	101.508			0.646547			0.323274	−	0.946306i	$-0.395217\pi$
$157$	101.508			0.646547			0.323274	+	0.946306i	$0.395217\pi$
$158$			115.199i			0.729106i
$159$	43.1402	+	44.7689i	0.271322	+	0.281565i
$160$	12.6491			0.0790569
$161$		−	61.1612i		−	0.379883i
$162$	8.48025	−	114.237i	0.0523472	−	0.705166i
$163$	138.601			0.850310			0.425155	−	0.905120i	$-0.360220\pi$
$163$	138.601			0.850310			0.425155	+	0.905120i	$0.360220\pi$
$164$		−	72.9031i		−	0.444531i
$165$	−50.3363	+	48.5051i	−0.305069	+	0.293970i
$166$	52.5895			0.316804
$167$			293.071i			1.75492i	0.479651	+	0.877459i	$0.340763\pi$
$167$			293.071i			1.75492i	−0.479651	+	0.877459i	$0.659237\pi$
$168$	−75.0875	−	77.9222i	−0.446949	−	0.463823i
$169$	−67.2234			−0.397772
$170$			0.879687i			0.00517463i
$171$	4.81451	−	129.890i	0.0281550	−	0.759593i
$172$	83.1063			0.483176
$173$			139.905i			0.808698i	0.914605	+	0.404349i	$0.132502\pi$
$173$			139.905i			0.808698i	−0.914605	+	0.404349i	$0.867498\pi$
$174$	−5.22850	+	5.03829i	−0.0300488	+	0.0289557i
$175$	−63.7650			−0.364371
$176$		−	41.6823i		−	0.236832i
$177$	−155.259	−	161.121i	−0.877171	−	0.910286i
$178$	−183.041			−1.02832
$179$			77.8984i			0.435187i	0.976040	+	0.217593i	$0.0698206\pi$
$179$			77.8984i			0.435187i	−0.976040	+	0.217593i	$0.930179\pi$
$180$	40.2216	+	1.49085i	0.223453	+	0.00828251i
$181$	−39.3128			−0.217198			−0.108599	−	0.994086i	$-0.534636\pi$
$181$	−39.3128			−0.217198			−0.108599	+	0.994086i	$0.534636\pi$
$182$		−	181.950i		−	0.999723i
$183$	167.044	−	160.967i	0.912806	−	0.879599i
$184$	−13.5647			−0.0737210
$185$		−	38.4514i		−	0.207845i
$186$	−108.898	−	113.009i	−0.585472	−	0.607575i
$187$	2.89881			0.0155017
$188$			146.874i			0.781246i
$189$	−229.579	−	256.627i	−1.21470	−	1.35781i
$190$	45.6702			0.240369
$191$		−	112.583i		−	0.589440i	−0.955584	−	0.294720i	$-0.904774\pi$
$191$		−	112.583i		−	0.589440i	0.955584	−	0.294720i	$-0.0952263\pi$
$192$	−17.2820	+	16.6533i	−0.0900104	+	0.0867359i
$193$	−325.616			−1.68713			−0.843564	−	0.537029i	$-0.819547\pi$
$193$	−325.616			−1.68713			−0.843564	+	0.537029i	$0.819547\pi$
$194$			56.3383i			0.290404i
$195$	46.9590	+	48.7319i	0.240816	+	0.249907i
$196$	−227.278			−1.15958
$197$			232.078i			1.17806i	0.808111	+	0.589031i	$0.200490\pi$
$197$			232.078i			1.17806i	−0.808111	+	0.589031i	$0.799510\pi$
$198$	4.91277	−	132.541i	0.0248120	−	0.669401i
$199$	144.995			0.728620			0.364310	−	0.931278i	$-0.381305\pi$
$199$	144.995			0.728620			0.364310	+	0.931278i	$0.381305\pi$
$200$			14.1421i			0.0707107i
$201$	223.670	−	215.533i	1.11279	−	1.07230i
$202$	147.350			0.729457
$203$			21.8258i			0.107516i
$204$	−1.15816	−	1.20188i	−0.00567725	−	0.00589158i
$205$	81.5081			0.397600
$206$			36.8288i			0.178780i
$207$	−43.1329	−	1.59876i	−0.208371	−	0.00772348i
$208$	−40.3537			−0.194008
$209$		−	150.496i		−	0.720076i
$210$	87.1197	−	83.9503i	0.414856	−	0.399763i
$211$	152.832			0.724321			0.362160	−	0.932116i	$-0.382039\pi$
$211$	152.832			0.724321			0.362160	+	0.932116i	$0.382039\pi$
$212$		−	41.4478i		−	0.195509i
$213$	118.284	+	122.750i	0.555326	+	0.576291i
$214$	−39.8339			−0.186140
$215$			92.9156i			0.432166i
$216$	−56.9161	+	50.9172i	−0.263500	+	0.235728i
$217$	−471.743			−2.17393
$218$			196.157i			0.899803i
$219$	−86.2460	+	83.1084i	−0.393817	+	0.379491i
$220$	46.6023			0.211829
$221$		−	2.80642i		−	0.0126987i
$222$	50.6235	+	52.5347i	0.228034	+	0.236643i
$223$	275.685			1.23625			0.618127	−	0.786078i	$-0.287892\pi$
$223$	275.685			1.23625			0.618127	+	0.786078i	$0.287892\pi$
$224$			72.1418i			0.322062i
$225$	−1.66682	+	44.9691i	−0.00740810	+	0.199863i
$226$	−84.0169			−0.371756
$227$			372.107i			1.63924i	0.572909	+	0.819619i	$0.305815\pi$
$227$			372.107i			1.63924i	−0.572909	+	0.819619i	$0.694185\pi$
$228$	−62.3974	+	60.1274i	−0.273673	+	0.263717i
$229$	−193.596			−0.845397			−0.422699	−	0.906270i	$-0.638917\pi$
$229$	−193.596			−0.845397			−0.422699	+	0.906270i	$0.638917\pi$
$230$		−	15.1658i		−	0.0659380i
$231$	−276.640	−	287.084i	−1.19757	−	1.24279i
$232$	4.84064			0.0208648
$233$			339.560i			1.45734i	0.684866	+	0.728669i	$0.259861\pi$
$233$			339.560i			1.45734i	−0.684866	+	0.728669i	$0.740139\pi$
$234$	−128.317	−	4.75618i	−0.548362	−	0.0203255i
$235$	−164.210			−0.698767
$236$			149.169i			0.632070i
$237$	175.969	−	169.568i	0.742486	−	0.715475i
$238$	−5.01713			−0.0210804
$239$		−	190.187i		−	0.795764i	−0.917437	−	0.397882i	$-0.869745\pi$
$239$		−	190.187i		−	0.795764i	0.917437	−	0.397882i	$-0.130255\pi$
$240$	−18.6190	−	19.3219i	−0.0775790	−	0.0805078i
$241$	−4.45865			−0.0185006			−0.00925031	−	0.999957i	$-0.502945\pi$
$241$	−4.45865			−0.0185006			−0.00925031	+	0.999957i	$0.502945\pi$
$242$			17.5523i			0.0725302i
$243$	−186.983	+	155.198i	−0.769476	+	0.638676i
$244$	−154.652			−0.633820
$245$		−	254.104i		−	1.03716i
$246$	−111.361	+	107.310i	−0.452689	+	0.436220i
$247$	−145.699			−0.589874
$248$			104.626i			0.421878i
$249$	−77.4095	−	80.3319i	−0.310881	−	0.322618i
$250$	−15.8114			−0.0632456
$251$		−	32.2001i		−	0.128287i	−0.997941	−	0.0641437i	$-0.979568\pi$
$251$		−	32.2001i		−	0.128287i	0.997941	−	0.0641437i	$-0.0204316\pi$
$252$	−8.50279	+	229.396i	−0.0337412	+	0.910303i
$253$	−49.9754			−0.197531
$254$		−	180.396i		−	0.710220i
$255$	1.34375	−	1.29486i	0.00526959	−	0.00507789i
$256$	16.0000			0.0625000
$257$			454.545i			1.76866i	0.466863	+	0.884329i	$0.345384\pi$
$257$			454.545i			1.76866i	−0.466863	+	0.884329i	$0.654616\pi$
$258$	−122.329	−	126.947i	−0.474143	−	0.492043i
$259$	219.300			0.846719
$260$		−	45.1169i		−	0.173526i
$261$	15.3923	+	0.570528i	0.0589741	+	0.00218593i
$262$	−35.1114			−0.134013
$263$		−	328.977i		−	1.25086i	−0.780279	−	0.625432i	$-0.784923\pi$
$263$		−	328.977i		−	1.25086i	0.780279	−	0.625432i	$-0.215077\pi$
$264$	−63.6709	+	61.3546i	−0.241178	+	0.232404i
$265$	46.3401			0.174868
$266$			260.471i			0.979215i
$267$	269.428	+	279.600i	1.00910	+	1.04719i
$268$	−207.078			−0.772679
$269$			35.5555i			0.132177i	0.997814	+	0.0660883i	$0.0210519\pi$
$269$			35.5555i			0.132177i	−0.997814	+	0.0660883i	$0.978948\pi$
$270$	−56.9272	−	63.6341i	−0.210841	−	0.235682i
$271$	−253.129			−0.934054			−0.467027	−	0.884243i	$-0.654675\pi$
$271$	−253.129			−0.934054			−0.467027	+	0.884243i	$0.654675\pi$
$272$			1.11273i			0.00409090i
$273$	−277.933	+	267.822i	−1.01807	+	0.981033i
$274$	68.0118			0.248218
$275$			52.1029i			0.189465i
$276$	19.9666	+	20.7204i	0.0723428	+	0.0750739i
$277$	−330.147			−1.19187			−0.595933	−	0.803034i	$-0.703218\pi$
$277$	−330.147			−1.19187			−0.595933	+	0.803034i	$0.703218\pi$
$278$		−	343.927i		−	1.23715i
$279$	−12.3314	+	332.689i	−0.0441986	+	1.19243i
$280$	−80.6570			−0.288061
$281$		−	151.413i		−	0.538838i	−0.963023	−	0.269419i	$-0.913168\pi$
$281$		−	151.413i		−	0.538838i	0.963023	−	0.269419i	$-0.0868316\pi$
$282$	224.354	−	216.193i	0.795583	−	0.766640i
$283$	−214.644			−0.758458			−0.379229	−	0.925303i	$-0.623811\pi$
$283$	−214.644			−0.758458			−0.379229	+	0.925303i	$0.623811\pi$
$284$		−	113.644i		−	0.400156i
$285$	−67.2245	−	69.7624i	−0.235876	−	0.244780i
$286$	−148.673			−0.519834
$287$			464.866i			1.61974i
$288$	50.8768	+	1.88579i	0.176655	+	0.00654790i
$289$	288.923			0.999732
$290$			5.41200i			0.0186621i
$291$	86.0583	−	82.9276i	0.295733	−	0.284975i
$292$	79.8481			0.273453
$293$			220.365i			0.752099i	0.926600	+	0.376050i	$0.122718\pi$
$293$			220.365i			0.752099i	−0.926600	+	0.376050i	$0.877282\pi$
$294$	334.543	+	347.173i	1.13790	+	1.18086i
$295$	−166.775			−0.565341
$296$		−	48.6376i		−	0.164316i
$297$	−209.692	+	187.591i	−0.706034	+	0.631619i
$298$	−238.443			−0.800145
$299$			48.3824i			0.161814i
$300$	21.6025	−	20.8166i	0.0720084	−	0.0693887i
$301$	−529.927			−1.76055
$302$		−	91.4174i		−	0.302707i
$303$	−216.893	−	225.082i	−0.715820	−	0.742844i
$304$	57.7687			0.190029
$305$		−	172.906i		−	0.566906i
$306$	−0.131148	+	3.53824i	−0.000428589	+	0.0115629i
$307$	559.586			1.82276			0.911378	−	0.411571i	$-0.135020\pi$
$307$	559.586			1.82276			0.911378	+	0.411571i	$0.135020\pi$
$308$			265.787i			0.862946i
$309$	56.2569	−	54.2104i	0.182061	−	0.175438i
$310$	−116.975			−0.377339
$311$		−	326.410i		−	1.04955i	−0.851241	−	0.524775i	$-0.824149\pi$
$311$		−	326.410i		−	1.04955i	0.851241	−	0.524775i	$-0.175851\pi$
$312$	59.3990	+	61.6415i	0.190381	+	0.197569i
$313$	−450.011			−1.43773			−0.718867	−	0.695148i	$-0.755339\pi$
$313$	−450.011			−1.43773			−0.718867	+	0.695148i	$0.755339\pi$
$314$			143.554i			0.457178i
$315$	−256.473	−	9.50641i	−0.814200	−	0.0301791i
$316$	−162.916			−0.515556
$317$			153.743i			0.484994i	0.970152	+	0.242497i	$0.0779665\pi$
$317$			153.743i			0.484994i	−0.970152	+	0.242497i	$0.922033\pi$
$318$	−63.3127	+	61.0095i	−0.199097	+	0.191854i
$319$	17.8340			0.0559061
$320$			17.8885i			0.0559017i
$321$	58.6338	+	60.8474i	0.182660	+	0.189556i
$322$	86.4950			0.268618
$323$			4.01754i			0.0124382i
$324$	161.555	+	11.9929i	0.498628	+	0.0370151i
$325$	50.4422			0.155207
$326$			196.011i			0.601260i
$327$	299.635	−	288.735i	0.916316	−	0.882982i
$328$	103.100			0.314331
$329$		−	936.543i		−	2.84663i
$330$	−68.5966	−	71.1863i	−0.207868	−	0.215716i
$331$	498.766			1.50685			0.753423	−	0.657536i	$-0.228401\pi$
$331$	498.766			1.50685			0.753423	+	0.657536i	$0.228401\pi$
$332$			74.3727i			0.224014i
$333$	5.73253	−	154.658i	0.0172148	−	0.464437i
$334$	−414.466			−1.24092
$335$		−	231.520i		−	0.691105i
$336$	110.199	−	106.190i	0.327972	−	0.316041i
$337$	−238.449			−0.707564			−0.353782	−	0.935328i	$-0.615104\pi$
$337$	−238.449			−0.707564			−0.353782	+	0.935328i	$0.615104\pi$
$338$		−	95.0683i		−	0.281267i
$339$	123.669	+	128.338i	0.364806	+	0.378579i
$340$	−1.24407			−0.00365902
$341$			385.466i			1.13040i
$342$	183.693	+	6.80874i	0.537113	+	0.0199086i
$343$	824.339			2.40332
$344$			117.530i			0.341657i
$345$	−23.1661	+	22.3233i	−0.0671481	+	0.0647053i
$346$	−197.855			−0.571836
$347$			225.681i			0.650377i	0.945649	+	0.325189i	$0.105428\pi$
$347$			225.681i			0.650377i	−0.945649	+	0.325189i	$0.894572\pi$
$348$	−7.12522	−	7.39421i	−0.0204748	−	0.0212477i
$349$	100.694			0.288521			0.144261	−	0.989540i	$-0.453920\pi$
$349$	100.694			0.288521			0.144261	+	0.989540i	$0.453920\pi$
$350$		−	90.1773i		−	0.257649i
$351$	181.612	+	203.008i	0.517412	+	0.578371i
$352$	58.9477			0.167465
$353$		−	443.896i		−	1.25749i	−0.777610	−	0.628747i	$-0.783568\pi$
$353$		−	443.896i		−	1.25749i	0.777610	−	0.628747i	$-0.216432\pi$
$354$	227.859	−	219.570i	0.643670	−	0.620253i
$355$	127.058			0.357910
$356$		−	258.859i		−	0.727132i
$357$	7.38500	+	7.66380i	0.0206863	+	0.0214672i
$358$	−110.165			−0.307723
$359$		−	39.2939i		−	0.109454i	−0.998501	−	0.0547269i	$-0.982571\pi$
$359$		−	39.2939i		−	0.109454i	0.998501	−	0.0547269i	$-0.0174288\pi$
$360$	−2.10838	+	56.8819i	−0.00585662	+	0.158005i
$361$	−152.424			−0.422226
$362$		−	55.5968i		−	0.153582i
$363$	26.8116	−	25.8363i	0.0738613	−	0.0711743i
$364$	257.316			0.706911
$365$			89.2729i			0.244583i
$366$	227.641	+	236.235i	0.621970	+	0.645451i
$367$	9.93672			0.0270755			0.0135378	−	0.999908i	$-0.495691\pi$
$367$	9.93672			0.0270755			0.0135378	+	0.999908i	$0.495691\pi$
$368$		−	19.1833i		−	0.0521286i
$369$	327.839	+	12.1516i	0.888452	+	0.0329313i
$370$	54.3784			0.146969
$371$			264.292i			0.712377i
$372$	159.819	−	154.005i	0.429620	−	0.413991i
$373$	680.417			1.82417			0.912087	−	0.409997i	$-0.134470\pi$
$373$	680.417			1.82417			0.912087	+	0.409997i	$0.134470\pi$
$374$			4.09954i			0.0109613i
$375$	23.2737	+	24.1523i	0.0620632	+	0.0644062i
$376$	−207.711			−0.552424
$377$		−	17.2656i		−	0.0457973i
$378$	362.925	−	324.673i	0.960119	−	0.858924i
$379$	−602.442			−1.58956			−0.794778	−	0.606900i	$-0.792413\pi$
$379$	−602.442			−1.58956			−0.794778	+	0.606900i	$0.792413\pi$
$380$			64.5874i			0.169967i
$381$	−275.560	+	265.535i	−0.723254	+	0.696942i
$382$	159.216			0.416797
$383$		−	92.5380i		−	0.241613i	−0.992676	−	0.120807i	$-0.961452\pi$
$383$		−	92.5380i		−	0.241613i	0.992676	−	0.120807i	$-0.0385481\pi$
$384$	−23.5513	−	24.4404i	−0.0613316	−	0.0636470i
$385$	−297.159			−0.771842
$386$		−	460.490i		−	1.19298i
$387$	−13.8523	+	373.722i	−0.0357942	+	0.965689i
$388$	−79.6744			−0.205346
$389$		−	512.539i		−	1.31758i	−0.752326	−	0.658791i	$-0.771068\pi$
$389$		−	512.539i		−	1.31758i	0.752326	−	0.658791i	$-0.228932\pi$
$390$	−68.9173	+	66.4101i	−0.176711	+	0.170282i
$391$	1.33411			0.00341205
$392$		−	321.419i		−	0.819947i
$393$	51.6825	+	53.6337i	0.131508	+	0.136473i
$394$	−328.208			−0.833015
$395$		−	182.145i		−	0.461127i
$396$	187.442	+	6.94771i	0.473338	+	0.0175447i
$397$	734.655			1.85052			0.925258	−	0.379337i	$-0.123848\pi$
$397$	734.655			1.85052			0.925258	+	0.379337i	$0.123848\pi$
$398$			205.054i			0.515212i
$399$	397.877	−	383.402i	0.997185	−	0.960908i
$400$	−20.0000			−0.0500000
$401$		−	264.580i		−	0.659799i	−0.944016	−	0.329900i	$-0.892985\pi$
$401$		−	264.580i		−	0.659799i	0.944016	−	0.329900i	$-0.107015\pi$
$402$	304.810	+	316.318i	0.758234	+	0.786859i
$403$	373.179			0.926003
$404$			208.385i			0.515804i
$405$	−13.4085	+	180.625i	−0.0331073	+	0.445986i
$406$	−30.8663			−0.0760254
$407$		−	179.192i		−	0.440276i
$408$	1.69972	−	1.63788i	0.00416598	−	0.00401442i
$409$	−13.6447			−0.0333612			−0.0166806	−	0.999861i	$-0.505310\pi$
$409$	−13.6447			−0.0333612			−0.0166806	+	0.999861i	$0.505310\pi$
$410$			115.270i			0.281146i
$411$	−100.110	−	103.890i	−0.243578	−	0.252773i
$412$	−52.0837			−0.126417
$413$		−	951.173i		−	2.30308i
$414$	2.26099	−	60.9991i	0.00546132	−	0.147341i
$415$	−83.1513			−0.200364
$416$		−	57.0688i		−	0.137185i
$417$	−525.358	+	506.246i	−1.25985	+	1.21402i
$418$	212.833			0.509171
$419$			664.827i			1.58670i	0.608766	+	0.793350i	$0.291665\pi$
$419$			664.827i			1.58670i	−0.608766	+	0.793350i	$0.708335\pi$
$420$	118.724	+	123.206i	0.282675	+	0.293347i
$421$	−55.6544			−0.132196			−0.0660978	−	0.997813i	$-0.521055\pi$
$421$	−55.6544			−0.132196			−0.0660978	+	0.997813i	$0.521055\pi$
$422$			216.137i			0.512172i
$423$	−660.480	−	24.4813i	−1.56142	−	0.0578754i
$424$	58.6161			0.138246
$425$		−	1.39091i		−	0.00327272i
$426$	−173.595	+	167.279i	−0.407499	+	0.392675i
$427$	986.138			2.30946
$428$		−	56.3336i		−	0.131621i
$429$	218.840	+	227.102i	0.510116	+	0.529374i
$430$	−131.403			−0.305587
$431$			771.728i			1.79055i	0.445513	+	0.895276i	$0.353021\pi$
$431$			771.728i			1.79055i	−0.445513	+	0.895276i	$0.646979\pi$
$432$	−72.0078	−	80.4915i	−0.166685	−	0.186323i
$433$	853.202			1.97044			0.985222	−	0.171281i	$-0.0547905\pi$
$433$	853.202			1.97044			0.985222	+	0.171281i	$0.0547905\pi$
$434$		−	667.146i		−	1.53720i
$435$	8.26698	−	7.96623i	0.0190046	−	0.0183132i
$436$	−277.408			−0.636257
$437$		−	69.2622i		−	0.158495i
$438$	−117.533	−	121.970i	−0.268340	−	0.278471i
$439$	−593.263			−1.35140			−0.675698	−	0.737179i	$-0.736158\pi$
$439$	−593.263			−1.35140			−0.675698	+	0.737179i	$0.736158\pi$
$440$			65.9056i			0.149785i
$441$	37.8832	−	1022.05i	0.0859028	−	2.31757i
$442$	3.96887			0.00897935
$443$		−	467.644i		−	1.05563i	−0.849359	−	0.527815i	$-0.823011\pi$
$443$		−	467.644i		−	1.05563i	0.849359	−	0.527815i	$-0.176989\pi$
$444$	−74.2952	+	71.5924i	−0.167332	+	0.161244i
$445$	289.413			0.650367
$446$			389.877i			0.874164i
$447$	350.978	+	364.228i	0.785186	+	0.814829i
$448$	−102.024			−0.227732
$449$			863.590i			1.92336i	0.274168	+	0.961682i	$0.411597\pi$
$449$			863.590i			1.92336i	−0.274168	+	0.961682i	$0.588403\pi$
$450$	−63.5959	−	2.35724i	−0.141324	−	0.00523832i
$451$	379.846			0.842231
$452$		−	118.818i		−	0.262871i
$453$	−139.643	+	134.563i	−0.308262	+	0.297048i
$454$	−526.239			−1.15912
$455$			287.688i			0.632280i
$456$	−85.0330	−	88.2433i	−0.186476	−	0.193516i
$457$	−352.546			−0.771435			−0.385717	−	0.922617i	$-0.626046\pi$
$457$	−352.546			−0.771435			−0.385717	+	0.922617i	$0.626046\pi$
$458$		−	273.786i		−	0.597786i
$459$	5.59781	−	5.00781i	0.0121957	−	0.0109103i
$460$	21.4476			0.0466252
$461$		−	595.807i		−	1.29242i	−0.763158	−	0.646212i	$-0.776352\pi$
$461$		−	595.807i		−	1.29242i	0.763158	−	0.646212i	$-0.223648\pi$
$462$	405.998	−	391.228i	0.878783	−	0.846813i
$463$	671.390			1.45009			0.725043	−	0.688704i	$-0.241820\pi$
$463$	671.390			1.45009			0.725043	+	0.688704i	$0.241820\pi$
$464$			6.84570i			0.0147537i
$465$	172.182	+	178.683i	0.370285	+	0.384264i
$466$	−480.210			−1.03049
$467$			797.745i			1.70823i	0.520082	+	0.854116i	$0.325901\pi$
$467$			797.745i			1.70823i	−0.520082	+	0.854116i	$0.674099\pi$
$468$	6.72625	−	181.467i	0.0143723	−	0.387751i
$469$	1320.43			2.81542
$470$		−	232.228i		−	0.494103i
$471$	219.282	−	211.305i	0.465568	−	0.448631i
$472$	−210.956			−0.446941
$473$			433.008i			0.915450i
$474$	239.805	+	248.858i	0.505917	+	0.525017i
$475$	−72.2109			−0.152023
$476$		−	7.09529i		−	0.0149061i
$477$	186.387	+	6.90862i	0.390749	+	0.0144835i
$478$	268.966			0.562690
$479$			706.387i			1.47471i	0.675505	+	0.737356i	$0.263926\pi$
$479$			706.387i			1.47471i	−0.675505	+	0.737356i	$0.736074\pi$
$480$	27.3252	−	26.3312i	0.0569276	−	0.0548566i
$481$	−173.481			−0.360666
$482$		−	6.30548i		−	0.0130819i
$483$	−127.317	−	132.124i	−0.263596	−	0.273548i
$484$	−24.8227			−0.0512866
$485$		−	89.0787i		−	0.183667i
$486$	−219.483	−	264.433i	−0.451612	−	0.544102i
$487$	747.631			1.53518			0.767589	−	0.640943i	$-0.221456\pi$
$487$	747.631			1.53518			0.767589	+	0.640943i	$0.221456\pi$
$488$		−	218.711i		−	0.448178i
$489$	299.412	−	288.520i	0.612294	−	0.590020i
$490$	359.358			0.733383
$491$		−	526.765i		−	1.07284i	−0.843951	−	0.536420i	$-0.819776\pi$
$491$		−	526.765i		−	1.07284i	0.843951	−	0.536420i	$-0.180224\pi$
$492$	−151.760	−	157.489i	−0.308454	−	0.320099i
$493$	−0.476087			−0.000965693
$494$		−	206.049i		−	0.417104i
$495$	−7.76777	+	209.566i	−0.0156925	+	0.423366i
$496$	−147.963			−0.298313
$497$			724.652i			1.45805i
$498$	113.606	−	109.474i	0.228125	−	0.219826i
$499$	836.489			1.67633			0.838165	−	0.545417i	$-0.183629\pi$
$499$	836.489			1.67633			0.838165	+	0.545417i	$0.183629\pi$
$500$		−	22.3607i		−	0.0447214i
$501$	610.076	+	633.108i	1.21772	+	1.26369i
$502$	45.5378			0.0907128
$503$			378.646i			0.752775i	0.926462	+	0.376387i	$0.122834\pi$
$503$			378.646i			0.752775i	−0.926462	+	0.376387i	$0.877166\pi$
$504$	−324.415	−	12.0248i	−0.643681	−	0.0238587i
$505$	−232.981			−0.461349
$506$		−	70.6759i		−	0.139676i
$507$	−145.219	+	139.937i	−0.286429	+	0.276009i
$508$	255.118			0.502201
$509$		−	449.590i		−	0.883280i	−0.897192	−	0.441640i	$-0.854397\pi$
$509$		−	449.590i		−	0.883280i	0.897192	−	0.441640i	$-0.145603\pi$
$510$	1.83121	+	1.90034i	0.00359061	+	0.00372616i
$511$	−509.151			−0.996382
$512$			22.6274i			0.0441942i
$513$	−259.987	−	290.618i	−0.506798	−	0.566507i
$514$	−642.824			−1.25063
$515$		−	58.2314i		−	0.113071i
$516$	179.530	−	172.999i	0.347927	−	0.335270i
$517$	−765.258			−1.48019
$518$			310.137i			0.598721i
$519$	291.234	+	302.229i	0.561145	+	0.582330i
$520$	63.8049			0.122702
$521$		−	644.286i		−	1.23663i	−0.785929	−	0.618317i	$-0.787815\pi$
$521$		−	644.286i		−	1.23663i	0.785929	−	0.618317i	$-0.212185\pi$
$522$	−0.806849	+	21.7679i	−0.00154569	+	0.0417010i
$523$	312.889			0.598257			0.299129	−	0.954213i	$-0.403304\pi$
$523$	312.889			0.598257			0.299129	+	0.954213i	$0.403304\pi$
$524$		−	49.6551i		−	0.0947616i
$525$	−137.748	+	132.737i	−0.262378	+	0.252833i
$526$	465.244			0.884494
$527$		−	10.2902i		−	0.0195259i
$528$	−86.7686	−	90.0443i	−0.164334	−	0.170538i
$529$	−23.0000			−0.0434783
$530$			65.5348i			0.123651i
$531$	−670.798	−	24.8637i	−1.26327	−	0.0468244i
$532$	−368.362			−0.692409
$533$		−	367.739i		−	0.689942i
$534$	−395.414	+	381.029i	−0.740476	+	0.713538i
$535$	62.9829			0.117725
$536$		−	292.853i		−	0.546367i
$537$	162.158	+	168.280i	0.301971	+	0.313371i
$538$	−50.2831			−0.0934629
$539$		−	1184.18i		−	2.19700i
$540$	89.9922	−	80.5072i	0.166652	−	0.149087i
$541$	−25.0281			−0.0462627			−0.0231314	−	0.999732i	$-0.507364\pi$
$541$	−25.0281			−0.0462627			−0.0231314	+	0.999732i	$0.507364\pi$
$542$		−	357.978i		−	0.660476i
$543$	−84.9256	+	81.8361i	−0.156401	+	0.150711i
$544$	−1.57363			−0.00289271
$545$		−	310.152i		−	0.569086i
$546$	−378.758	−	393.057i	−0.693695	−	0.719884i
$547$	−285.873			−0.522619			−0.261310	−	0.965255i	$-0.584154\pi$
$547$	−285.873			−0.522619			−0.261310	+	0.965255i	$0.584154\pi$
$548$			96.1832i			0.175517i
$549$	25.7777	−	695.456i	0.0469540	−	1.26677i
$550$	−73.6847			−0.133972
$551$			24.7167i			0.0448579i
$552$	−29.3031	+	28.2370i	−0.0530853	+	0.0511541i
$553$	1038.83			1.87854
$554$		−	466.898i		−	0.842776i
$555$	−80.0428	−	83.0646i	−0.144221	−	0.149666i
$556$	486.386			0.874795
$557$		−	768.565i		−	1.37983i	−0.723890	−	0.689915i	$-0.757648\pi$
$557$		−	768.565i		−	1.37983i	0.723890	−	0.689915i	$-0.242352\pi$
$558$	−470.493	−	17.4393i	−0.843177	−	0.0312531i
$559$	419.206			0.749922
$560$		−	114.066i		−	0.203690i
$561$	6.26216	−	6.03435i	0.0111625	−	0.0107564i
$562$	214.131			0.381016
$563$		−	472.921i		−	0.840002i	−0.907524	−	0.420001i	$-0.862030\pi$
$563$		−	472.921i		−	0.840002i	0.907524	−	0.420001i	$-0.137970\pi$
$564$	305.742	+	317.285i	0.542096	+	0.562562i
$565$	132.842			0.235119
$566$		−	303.552i		−	0.536311i
$567$	−1030.16	−	76.4726i	−1.81686	−	0.134872i
$568$	160.717			0.282953
$569$			44.6673i			0.0785013i	0.999229	+	0.0392507i	$0.0124971\pi$
$569$			44.6673i			0.0785013i	−0.999229	+	0.0392507i	$0.987503\pi$
$570$	98.6590	−	95.0698i	0.173086	−	0.166789i
$571$	−502.895			−0.880726			−0.440363	−	0.897820i	$-0.645150\pi$
$571$	−502.895			−0.880726			−0.440363	+	0.897820i	$0.645150\pi$
$572$		−	210.255i		−	0.367578i
$573$	−234.360	−	243.207i	−0.409005	−	0.424446i
$574$	−657.420			−1.14533
$575$			23.9792i			0.0417029i
$576$	−2.66692	+	71.9506i	−0.00463006	+	0.124914i
$577$	−94.3235			−0.163472			−0.0817361	−	0.996654i	$-0.526046\pi$
$577$	−94.3235			−0.163472			−0.0817361	+	0.996654i	$0.526046\pi$
$578$			408.598i			0.706917i
$579$	−703.411	+	677.822i	−1.21487	+	1.17068i
$580$	−7.65372			−0.0131961
$581$		−	474.238i		−	0.816244i
$582$	117.277	+	121.705i	0.201507	+	0.209115i
$583$	215.955			0.370421
$584$			112.922i			0.193360i
$585$	202.887	+	7.52018i	0.346815	+	0.0128550i
$586$	−311.643			−0.531814
$587$			883.355i			1.50486i	0.658670	+	0.752432i	$0.271119\pi$
$587$			883.355i			1.50486i	−0.658670	+	0.752432i	$0.728881\pi$
$588$	−490.977	+	473.115i	−0.834994	+	0.804618i
$589$	−534.227			−0.907008
$590$		−	235.856i		−	0.399756i
$591$	483.108	+	501.347i	0.817442	+	0.848303i
$592$	68.7839			0.116189
$593$			951.840i			1.60513i	0.596567	+	0.802563i	$0.296531\pi$
$593$			951.840i			1.60513i	−0.596567	+	0.802563i	$0.703469\pi$
$594$	−265.294	−	296.549i	−0.446622	−	0.499241i
$595$	7.93278			0.0133324
$596$		−	337.209i		−	0.565788i
$597$	313.226	−	301.831i	0.524667	−	0.505580i
$598$	−68.4231			−0.114420
$599$			118.761i			0.198265i	0.995074	+	0.0991326i	$0.0316068\pi$
$599$			118.761i			0.198265i	−0.995074	+	0.0991326i	$0.968393\pi$
$600$	29.4392	+	30.5506i	0.0490653	+	0.0509176i
$601$	40.5976			0.0675500			0.0337750	−	0.999429i	$-0.489247\pi$
$601$	40.5976			0.0675500			0.0337750	+	0.999429i	$0.489247\pi$
$602$		−	749.430i		−	1.24490i
$603$	34.5162	−	931.212i	0.0572409	−	1.54430i
$604$	129.284			0.214046
$605$		−	27.7526i		−	0.0458721i
$606$	318.314	−	306.734i	0.525270	−	0.506161i
$607$	−1154.28			−1.90162			−0.950809	−	0.309777i	$-0.899746\pi$
$607$	−1154.28			−1.90162			−0.950809	+	0.309777i	$0.899746\pi$
$608$			81.6973i			0.134370i
$609$	45.4339	+	47.1492i	0.0746041	+	0.0774206i
$610$	244.526			0.400863
$611$			740.865i			1.21255i
$612$	−5.00383	−	0.185472i	−0.00817619	−	0.000303058i
$613$	−673.217			−1.09823			−0.549117	−	0.835746i	$-0.685036\pi$
$613$	−673.217			−1.09823			−0.549117	+	0.835746i	$0.685036\pi$
$614$			791.374i			1.28888i
$615$	176.078	−	169.672i	0.286306	−	0.275890i
$616$	−375.880			−0.610195
$617$		−	376.318i		−	0.609916i	−0.952366	−	0.304958i	$-0.901358\pi$
$617$		−	376.318i		−	0.609916i	0.952366	−	0.304958i	$-0.0986424\pi$
$618$	76.6650	+	79.5593i	0.124053	+	0.128737i
$619$	276.885			0.447310			0.223655	−	0.974668i	$-0.428201\pi$
$619$	276.885			0.447310			0.223655	+	0.974668i	$0.428201\pi$
$620$		−	165.428i		−	0.266819i
$621$	−96.5059	+	86.3343i	−0.155404	+	0.139025i
$622$	461.613			0.742144
$623$			1650.61i			2.64946i
$624$	−87.1742	+	84.0029i	−0.139702	+	0.134620i
$625$	25.0000			0.0400000
$626$		−	636.411i		−	1.01663i
$627$	−313.282	−	325.109i	−0.499652	−	0.518515i
$628$	−203.016			−0.323274
$629$			4.78360i			0.00760509i
$630$	13.4441	−	362.707i	0.0213398	−	0.575726i
$631$	−760.606			−1.20540			−0.602699	−	0.797969i	$-0.705908\pi$
$631$	−760.606			−1.20540			−0.602699	+	0.797969i	$0.705908\pi$
$632$		−	230.397i		−	0.364553i
$633$	330.155	−	318.144i	0.521572	−	0.502597i
$634$	−217.426			−0.342943
$635$			285.231i			0.449183i
$636$	−86.2804	−	89.5377i	−0.135661	−	0.140783i
$637$	−1146.44			−1.79975
$638$			25.2212i			0.0395316i
$639$	511.048	+	18.9425i	0.799762	+	0.0296439i
$640$	−25.2982			−0.0395285
$641$			292.499i			0.456316i	0.973624	+	0.228158i	$0.0732703\pi$
$641$			292.499i			0.456316i	−0.973624	+	0.228158i	$0.926730\pi$
$642$	−86.0512	+	82.9207i	−0.134036	+	0.129160i
$643$	487.514			0.758187			0.379094	−	0.925358i	$-0.376236\pi$
$643$	487.514			0.758187			0.379094	+	0.925358i	$0.376236\pi$
$644$			122.322i			0.189942i
$645$	193.419	+	200.721i	0.299874	+	0.311195i
$646$	−5.68166			−0.00879515
$647$		−	764.731i		−	1.18196i	−0.806685	−	0.590982i	$-0.798740\pi$
$647$		−	764.731i		−	1.18196i	0.806685	−	0.590982i	$-0.201260\pi$
$648$	−16.9605	+	228.474i	−0.0261736	+	0.352583i
$649$	−777.212			−1.19755
$650$			71.3360i			0.109748i
$651$	−1019.08	+	982.010i	−1.56541	+	1.50846i
$652$	−277.201			−0.425155
$653$			398.531i			0.610308i	0.952303	+	0.305154i	$0.0987079\pi$
$653$			398.531i			0.610308i	−0.952303	+	0.305154i	$0.901292\pi$
$654$	408.333	+	423.749i	0.624362	+	0.647934i
$655$	55.5161			0.0847573
$656$			145.806i			0.222265i
$657$	−13.3093	+	359.070i	−0.0202576	+	0.546530i
$658$	1324.47			2.01287
$659$		−	828.825i		−	1.25770i	−0.777526	−	0.628850i	$-0.783526\pi$
$659$		−	828.825i		−	1.25770i	0.777526	−	0.628850i	$-0.216474\pi$
$660$	100.673	−	97.0102i	0.152534	−	0.146985i
$661$	−1248.13			−1.88825			−0.944124	−	0.329591i	$-0.893089\pi$
$661$	−1248.13			−1.88825			−0.944124	+	0.329591i	$0.893089\pi$
$662$			705.362i			1.06550i
$663$	−5.84201	−	6.06256i	−0.00881148	−	0.00914413i
$664$	−105.179			−0.158402
$665$		−	411.841i		−	0.619310i
$666$	218.719	+	8.10702i	0.328407	+	0.0121727i
$667$	8.20770			0.0123054
$668$		−	586.143i		−	0.877459i
$669$	595.548	−	573.883i	0.890206	−	0.857821i
$670$	327.419			0.488685
$671$		−	805.782i		−	1.20087i
$672$	150.175	+	155.844i	0.223475	+	0.231911i
$673$	−1228.15			−1.82489			−0.912447	−	0.409195i	$-0.865810\pi$
$673$	−1228.15			−1.82489			−0.912447	+	0.409195i	$0.865810\pi$
$674$		−	337.218i		−	0.500323i
$675$	90.0098	+	100.614i	0.133348	+	0.149058i
$676$	134.447			0.198886
$677$			197.067i			0.291089i	0.989352	+	0.145544i	$0.0464934\pi$
$677$			197.067i			0.291089i	−0.989352	+	0.145544i	$0.953507\pi$
$678$	−181.498	+	174.895i	−0.267696	+	0.257957i
$679$	508.044			0.748223
$680$		−	1.75937i		−	0.00258731i
$681$	774.601	+	803.844i	1.13745	+	1.18039i
$682$	−545.131			−0.799312
$683$		−	650.986i		−	0.953127i	−0.879140	−	0.476564i	$-0.841882\pi$
$683$		−	650.986i		−	0.953127i	0.879140	−	0.476564i	$-0.158118\pi$
$684$	−9.62901	+	259.781i	−0.0140775	+	0.379796i
$685$	−107.536			−0.156987
$686$			1165.79i			1.69940i
$687$	−418.216	+	403.001i	−0.608757	+	0.586610i
$688$	−166.213			−0.241588
$689$		−	209.072i		−	0.303443i
$690$	−31.5700	−	32.7618i	−0.0457536	−	0.0474809i
$691$	485.418			0.702486			0.351243	−	0.936284i	$-0.385759\pi$
$691$	485.418			0.702486			0.351243	+	0.936284i	$0.385759\pi$
$692$		−	279.809i		−	0.404349i
$693$	−1195.22	−	44.3020i	−1.72471	−	0.0639279i
$694$	−319.161			−0.459886
$695$			543.796i			0.782440i
$696$	10.4570	−	10.0766i	0.0150244	−	0.0144778i
$697$	−10.1401			−0.0145483
$698$			142.403i			0.204015i
$699$	706.848	+	733.534i	1.01123	+	1.04940i
$700$	127.530			0.182186
$701$			1073.24i			1.53101i	0.643431	+	0.765504i	$0.277510\pi$
$701$			1073.24i			1.53101i	−0.643431	+	0.765504i	$0.722490\pi$
$702$	−287.097	+	256.838i	−0.408970	+	0.365865i
$703$	248.347			0.353268
$704$			83.3647i			0.118416i
$705$	−354.735	+	341.830i	−0.503171	+	0.484866i
$706$	627.763			0.889183
$707$		−	1328.77i		−	1.87944i
$708$	310.518	+	322.241i	0.438585	+	0.455143i
$709$	−83.9792			−0.118447			−0.0592237	−	0.998245i	$-0.518863\pi$
$709$	−83.9792			−0.118447			−0.0592237	+	0.998245i	$0.518863\pi$
$710$			179.687i			0.253081i
$711$	27.1551	−	732.617i	0.0381929	−	1.03040i
$712$	366.082			0.514160
$713$			177.402i			0.248810i
$714$	−10.8383	+	10.4440i	−0.0151796	+	0.0146274i
$715$	235.072			0.328772
$716$		−	155.797i		−	0.217593i
$717$	−395.906	−	410.853i	−0.552170	−	0.573016i
$718$	55.5700			0.0773955
$719$		−	638.283i		−	0.887737i	−0.896092	−	0.443868i	$-0.853606\pi$
$719$		−	638.283i		−	0.887737i	0.896092	−	0.443868i	$-0.146394\pi$
$720$	−80.4432	−	2.98170i	−0.111727	−	0.00414125i
$721$	332.112			0.460626
$722$		−	215.560i		−	0.298559i
$723$	−9.63180	+	9.28140i	−0.0133220	+	0.0128374i
$724$	78.6257			0.108599
$725$		−	8.55712i		−	0.0118029i
$726$	36.5380	+	37.9174i	0.0503278	+	0.0522278i
$727$	344.419			0.473754			0.236877	−	0.971540i	$-0.423876\pi$
$727$	344.419			0.473754			0.236877	+	0.971540i	$0.423876\pi$
$728$			363.899i			0.499861i
$729$	−80.8594	+	724.502i	−0.110918	+	0.993830i
$730$	−126.251			−0.172947
$731$		−	11.5593i		−	0.0158130i
$732$	−334.087	+	321.933i	−0.456403	+	0.439799i
$733$	−511.714			−0.698109			−0.349054	−	0.937103i	$-0.613497\pi$
$733$	−511.714			−0.698109			−0.349054	+	0.937103i	$0.613497\pi$
$734$			14.0526i			0.0191453i
$735$	−528.959	−	548.929i	−0.719672	−	0.746842i
$736$	27.1293			0.0368605
$737$		−	1078.94i		−	1.46396i
$738$	−17.1850	+	463.634i	−0.0232859	+	0.628230i
$739$	256.144			0.346608			0.173304	−	0.984868i	$-0.444556\pi$
$739$	256.144			0.346608			0.173304	+	0.984868i	$0.444556\pi$
$740$			76.9027i			0.103923i
$741$	−314.746	+	303.296i	−0.424759	+	0.409306i
$742$	−373.765			−0.503727
$743$		−	74.9836i		−	0.100920i	−0.998726	−	0.0504600i	$-0.983931\pi$
$743$		−	74.9836i		−	0.100920i	0.998726	−	0.0504600i	$-0.0160687\pi$
$744$	217.796	+	226.018i	0.292736	+	0.303787i
$745$	377.012			0.506056
$746$			962.255i			1.28989i
$747$	−334.448	−	12.3966i	−0.447721	−	0.0165952i
$748$	−5.79763			−0.00775084
$749$			359.211i			0.479588i
$750$	−34.1566	+	32.9140i	−0.0455421	+	0.0438853i
$751$	−920.046			−1.22509			−0.612547	−	0.790434i	$-0.709855\pi$
$751$	−920.046			−1.22509			−0.612547	+	0.790434i	$0.709855\pi$
$752$		−	293.748i		−	0.390623i
$753$	−67.0298	−	69.5603i	−0.0890170	−	0.0923776i
$754$	24.4172			0.0323836
$755$			144.544i			0.191449i
$756$	459.158	+	513.254i	0.607351	+	0.678907i
$757$	1040.64			1.37469			0.687344	−	0.726332i	$-0.258777\pi$
$757$	1040.64			1.37469			0.687344	+	0.726332i	$0.258777\pi$
$758$		−	851.982i		−	1.12399i
$759$	−107.959	+	104.032i	−0.142239	+	0.137064i
$760$	−91.3403			−0.120185
$761$		−	1047.60i		−	1.37662i	−0.725419	−	0.688308i	$-0.758354\pi$
$761$		−	1047.60i		−	1.37662i	0.725419	−	0.688308i	$-0.241646\pi$
$762$	−375.523	−	389.700i	−0.492813	−	0.511418i
$763$	1768.89			2.31834
$764$			225.166i			0.294720i
$765$	0.207364	−	5.59445i	0.000271063	−	0.00731301i
$766$	130.868			0.170847
$767$			752.439i			0.981015i
$768$	34.5640	−	33.3066i	0.0450052	−	0.0433680i
$769$	650.393			0.845764			0.422882	−	0.906185i	$-0.361018\pi$
$769$	650.393			0.845764			0.422882	+	0.906185i	$0.361018\pi$
$770$		−	420.247i		−	0.545775i
$771$	946.210	+	981.932i	1.22725	+	1.27358i
$772$	651.231			0.843564
$773$		−	1302.06i		−	1.68442i	−0.539149	−	0.842210i	$-0.681254\pi$
$773$		−	1302.06i		−	1.68442i	0.539149	−	0.842210i	$-0.318746\pi$
$774$	−528.522	−	19.5902i	−0.682845	−	0.0253103i
$775$	184.954			0.238650
$776$		−	112.677i		−	0.145202i
$777$	473.743	−	456.509i	0.609708	−	0.587528i
$778$	724.840			0.931671
$779$			526.439i			0.675788i
$780$	−93.9181	−	97.4637i	−0.120408	−	0.124953i
$781$	592.120			0.758156
$782$			1.88672i			0.00241268i
$783$	34.4388	−	30.8090i	0.0439831	−	0.0393474i
$784$	454.555			0.579790
$785$		−	226.979i		−	0.289145i
$786$	−75.8495	+	73.0902i	−0.0965006	+	0.0929900i
$787$	648.883			0.824501			0.412251	−	0.911070i	$-0.364743\pi$
$787$	648.883			0.824501			0.412251	+	0.911070i	$0.364743\pi$
$788$		−	464.156i		−	0.589031i
$789$	−684.819	−	710.673i	−0.867958	−	0.900726i
$790$	257.592			0.326066
$791$			757.642i			0.957828i
$792$	−9.82554	+	265.083i	−0.0124060	+	0.334701i
$793$	−780.098			−0.983731
$794$			1038.96i			1.30851i
$795$	100.106	−	96.4644i	0.125920	−	0.121339i
$796$	−289.991			−0.364310
$797$		−	1263.20i		−	1.58494i	−0.609910	−	0.792470i	$-0.708795\pi$
$797$		−	1263.20i		−	1.58494i	0.609910	−	0.792470i	$-0.291205\pi$
$798$	542.213	+	562.683i	0.679465	+	0.705116i
$799$	20.4288			0.0255680
$800$		−	28.2843i		−	0.0353553i
$801$	1164.07	+	43.1472i	1.45327	+	0.0538666i
$802$	374.172			0.466549
$803$			416.032i			0.518097i
$804$	−447.341	+	431.067i	−0.556394	+	0.536152i
$805$	−136.761			−0.169889
$806$			527.755i			0.654783i
$807$	74.0145	+	76.8088i	0.0917156	+	0.0951781i
$808$	−294.701			−0.364729
$809$			558.146i			0.689921i	0.938617	+	0.344960i	$0.112108\pi$
$809$			558.146i			0.689921i	−0.938617	+	0.344960i	$0.887892\pi$
$810$	−255.442	−	18.9624i	−0.315360	−	0.0234104i
$811$	−1420.30			−1.75130			−0.875649	−	0.482948i	$-0.839566\pi$
$811$	−1420.30			−1.75130			−0.875649	+	0.482948i	$0.839566\pi$
$812$		−	43.6516i		−	0.0537581i
$813$	−546.821	+	526.928i	−0.672597	+	0.648128i
$814$	253.416			0.311322
$815$		−	309.920i		−	0.380270i
$816$	2.31632	+	2.40377i	0.00283863	+	0.00294579i
$817$	−600.117			−0.734538
$818$		−	19.2965i		−	0.0235899i
$819$	−42.8899	+	1157.13i	−0.0523687	+	1.41285i
$820$	−163.016			−0.198800
$821$		−	141.444i		−	0.172283i	−0.996283	−	0.0861413i	$-0.972546\pi$
$821$		−	141.444i		−	0.172283i	0.996283	−	0.0861413i	$-0.0274536\pi$
$822$	146.922	−	141.578i	0.178738	−	0.172235i
$823$	−809.819			−0.983985			−0.491992	−	0.870600i	$-0.663731\pi$
$823$	−809.819			−0.983985			−0.491992	+	0.870600i	$0.663731\pi$
$824$		−	73.6575i		−	0.0893902i
$825$	108.461	+	112.555i	0.131468	+	0.136431i
$826$	1345.16			1.62852
$827$			670.772i			0.811091i	0.914075	+	0.405545i	$0.132918\pi$
$827$			670.772i			0.811091i	−0.914075	+	0.405545i	$0.867082\pi$
$828$	86.2657	+	3.19752i	0.104186	+	0.00386174i
$829$	−206.769			−0.249420			−0.124710	−	0.992193i	$-0.539800\pi$
$829$	−206.769			−0.249420			−0.124710	+	0.992193i	$0.539800\pi$
$830$		−	117.594i		−	0.141679i
$831$	−713.200	+	687.254i	−0.858243	+	0.827021i
$832$	80.7075			0.0970042
$833$			31.6122i			0.0379498i
$834$	−715.939	−	742.968i	−0.858440	−	0.890849i
$835$	655.328			0.784824
$836$			300.992i			0.360038i
$837$	665.907	+	744.361i	0.795587	+	0.889320i
$838$	−940.208			−1.12197
$839$		−	1069.52i		−	1.27475i	−0.770554	−	0.637375i	$-0.780020\pi$
$839$		−	1069.52i		−	1.27475i	0.770554	−	0.637375i	$-0.219980\pi$
$840$	−174.239	+	167.901i	−0.207428	+	0.199882i
$841$	838.071			0.996517
$842$		−	78.7072i		−	0.0934765i
$843$	−315.192	−	327.091i	−0.373893	−	0.388008i
$844$	−305.663			−0.362160
$845$			150.316i			0.177889i
$846$	34.6218	−	934.060i	0.0409241	−	1.10409i
$847$	158.282			0.186874
$848$			82.8957i			0.0977543i
$849$	−463.684	+	446.815i	−0.546153	+	0.526284i
$850$	1.96704			0.00231416
$851$		−	82.4690i		−	0.0969083i
$852$	−236.569	−	245.500i	−0.277663	−	0.288145i
$853$	−180.670			−0.211806			−0.105903	−	0.994376i	$-0.533773\pi$
$853$	−180.670			−0.211806			−0.105903	+	0.994376i	$0.533773\pi$
$854$			1394.61i			1.63303i
$855$	−290.444	−	10.7656i	−0.339700	−	0.0125913i
$856$	79.6678			0.0930698
$857$			380.526i			0.444021i	0.975044	+	0.222010i	$0.0712619\pi$
$857$			380.526i			0.444021i	−0.975044	+	0.222010i	$0.928738\pi$
$858$	−321.170	+	309.486i	−0.374324	+	0.360707i
$859$	610.050			0.710186			0.355093	−	0.934831i	$-0.384449\pi$
$859$	610.050			0.710186			0.355093	+	0.934831i	$0.384449\pi$
$860$		−	185.831i		−	0.216083i
$861$	967.694	+	1004.23i	1.12392	+	1.16635i
$862$	−1091.39			−1.26611
$863$			419.269i			0.485827i	0.970048	+	0.242914i	$0.0781031\pi$
$863$			419.269i			0.485827i	−0.970048	+	0.242914i	$0.921897\pi$
$864$	113.832	−	101.834i	0.131750	−	0.117864i
$865$	312.837			0.361661
$866$			1206.61i			1.39331i
$867$	624.145	−	601.439i	0.719891	−	0.693702i
$868$	943.487			1.08697
$869$		−	848.838i		−	0.976798i
$870$	11.2660	+	11.6913i	0.0129494	+	0.0134382i
$871$	−1044.55			−1.19925
$872$		−	392.314i		−	0.449902i
$873$	13.2803	−	358.289i	0.0152123	−	0.410411i
$874$	97.9516			0.112073
$875$			142.583i			0.162952i
$876$	172.492	−	166.217i	0.196909	−	0.189745i
$877$	−90.4273			−0.103110			−0.0515549	−	0.998670i	$-0.516418\pi$
$877$	−90.4273			−0.103110			−0.0515549	+	0.998670i	$0.516418\pi$
$878$		−	839.000i		−	0.955581i
$879$	458.726	+	476.044i	0.521872	+	0.541574i
$880$	−93.2046			−0.105914
$881$			703.988i			0.799078i	0.916716	+	0.399539i	$0.130830\pi$
$881$			703.988i			0.799078i	−0.916716	+	0.399539i	$0.869170\pi$
$882$	1445.39	+	53.5749i	1.63877	+	0.0607425i
$883$	1434.69			1.62479			0.812397	−	0.583105i	$-0.198162\pi$
$883$	1434.69			1.62479			0.812397	+	0.583105i	$0.198162\pi$
$884$			5.61283i			0.00634936i
$885$	−360.277	+	347.170i	−0.407092	+	0.392283i
$886$	661.349			0.746443
$887$			126.538i			0.142658i	0.997453	+	0.0713292i	$0.0227241\pi$
$887$			126.538i			0.142658i	−0.997453	+	0.0713292i	$0.977276\pi$
$888$	−101.247	−	105.069i	−0.114017	−	0.118321i
$889$	−1626.76			−1.82988
$890$			409.292i			0.459879i
$891$	−62.4865	+	841.751i	−0.0701307	+	0.944727i
$892$	−551.370			−0.618127
$893$		−	1060.59i		−	1.18767i
$894$	−515.097	+	496.358i	−0.576171	+	0.555210i
$895$	174.186			0.194621
$896$		−	144.284i		−	0.161031i
$897$	100.716	+	104.518i	0.112281	+	0.116520i
$898$	−1221.30			−1.36002
$899$		−	63.3070i		−	0.0704193i
$900$	3.33364	−	89.9382i	0.00370405	−	0.0999314i
$901$	−5.76501			−0.00639846
$902$			537.184i			0.595547i
$903$	−1144.77	+	1103.13i	−1.26775	+	1.22163i
$904$	168.034			0.185878
$905$			87.9062i			0.0971339i
$906$	−190.300	−	197.485i	−0.210044	−	0.217974i
$907$	320.451			0.353309			0.176654	−	0.984273i	$-0.443473\pi$
$907$	320.451			0.353309			0.176654	+	0.984273i	$0.443473\pi$
$908$		−	744.214i		−	0.819619i
$909$	−937.089	−	34.7341i	−1.03090	−	0.0382113i
$910$	−406.852			−0.447090
$911$		−	491.726i		−	0.539765i	−0.962893	−	0.269883i	$-0.913015\pi$
$911$		−	491.726i		−	0.539765i	0.962893	−	0.269883i	$-0.0869849\pi$
$912$	124.795	−	120.255i	0.136836	−	0.131858i
$913$	−387.504			−0.424429
$914$		−	498.575i		−	0.545487i
$915$	−359.932	−	373.521i	−0.393369	−	0.408219i
$916$	387.192			0.422699
$917$			316.625i			0.345284i
$918$	7.08211	+	7.91650i	0.00771472	+	0.00862363i
$919$	−290.874			−0.316512			−0.158256	−	0.987398i	$-0.550587\pi$
$919$	−290.874			−0.316512			−0.158256	+	0.987398i	$0.550587\pi$
$920$			30.3315i			0.0329690i
$921$	1208.85	−	1164.87i	1.31254	−	1.26479i
$922$	842.598			0.913881
$923$		−	573.246i		−	0.621068i
$924$	553.280	+	574.167i	0.598787	+	0.621393i
$925$	−85.9799			−0.0929512
$926$			949.488i			1.02537i
$927$	8.68143	−	234.216i	0.00936508	−	0.252660i
$928$	−9.68128			−0.0104324
$929$		−	615.743i		−	0.662802i	−0.943490	−	0.331401i	$-0.892479\pi$
$929$		−	615.743i		−	0.662802i	0.943490	−	0.331401i	$-0.107521\pi$
$930$	−252.696	+	243.503i	−0.271716	+	0.261831i
$931$	1641.19			1.76283
$932$		−	679.119i		−	0.728669i
$933$	−679.475	−	705.127i	−0.728270	−	0.755764i
$934$	−1128.18			−1.20790
$935$		−	6.48194i		−	0.00693256i
$936$	256.633	+	9.51236i	0.274181	+	0.0101628i
$937$	−1364.00			−1.45571			−0.727853	−	0.685733i	$-0.759482\pi$
$937$	−1364.00			−1.45571			−0.727853	+	0.685733i	$0.759482\pi$
$938$			1867.37i			1.99080i
$939$	−972.136	+	936.770i	−1.03529	+	0.997625i
$940$	328.421			0.349384
$941$		−	438.209i		−	0.465684i	−0.972515	−	0.232842i	$-0.925197\pi$
$941$		−	438.209i		−	0.465684i	0.972515	−	0.232842i	$-0.0748025\pi$
$942$	298.831	+	310.112i	0.317230	+	0.329206i
$943$	174.815			0.185382
$944$		−	298.337i		−	0.316035i
$945$	−573.835	+	513.354i	−0.607233	+	0.543232i
$946$	−612.366			−0.647321
$947$			1451.44i			1.53268i	0.642438	+	0.766338i	$0.277923\pi$
$947$			1451.44i			1.53268i	−0.642438	+	0.766338i	$0.722077\pi$
$948$	−351.938	+	339.135i	−0.371243	+	0.357738i
$949$	402.771			0.424417
$950$		−	102.122i		−	0.107496i
$951$	320.042	+	332.124i	0.336532	+	0.349237i
$952$	10.0343			0.0105402
$953$			1227.03i			1.28754i	0.765217	+	0.643772i	$0.222632\pi$
$953$			1227.03i			1.28754i	−0.765217	+	0.643772i	$0.777368\pi$
$954$	−9.77026	+	263.591i	−0.0102414	+	0.276301i
$955$	−251.743			−0.263605
$956$			380.375i			0.397882i
$957$	38.5260	−	37.1245i	0.0402571	−	0.0387925i
$958$	−998.982			−1.04278
$959$		−	613.312i		−	0.639532i
$960$	37.2379	+	38.6437i	0.0387895	+	0.0402539i
$961$	407.319			0.423849
$962$		−	245.338i		−	0.255030i
$963$	253.327	+	9.38981i	0.263061	+	0.00975059i
$964$	8.91730			0.00925031
$965$			728.099i			0.754507i
$966$	186.851	−	180.053i	0.193427	−	0.186391i
$967$	−1518.58			−1.57040			−0.785201	−	0.619241i	$-0.787440\pi$
$967$	−1518.58			−1.57040			−0.785201	+	0.619241i	$0.787440\pi$
$968$		−	35.1046i		−	0.0362651i
$969$	8.36317	+	8.67890i	0.00863072	+	0.00895655i
$970$	125.976			0.129872
$971$		−	931.400i		−	0.959218i	−0.877482	−	0.479609i	$-0.840779\pi$
$971$		−	931.400i		−	0.959218i	0.877482	−	0.479609i	$-0.159221\pi$
$972$	373.965	−	310.396i	0.384738	−	0.319338i
$973$	−3101.44			−3.18750
$974$			1057.31i			1.08553i
$975$	108.968	−	105.004i	0.111762	−	0.107696i
$976$	309.304			0.316910
$977$			193.460i			0.198014i	0.995087	+	0.0990069i	$0.0315666\pi$
$977$			193.460i			0.198014i	−0.995087	+	0.0990069i	$0.968433\pi$
$978$	408.028	+	423.433i	0.417207	+	0.432958i
$979$	1348.73			1.37766
$980$			508.208i			0.518580i
$981$	46.2390	−	1247.48i	0.0471345	−	1.27164i
$982$	744.958			0.758613
$983$		−	931.941i		−	0.948057i	−0.880509	−	0.474029i	$-0.842799\pi$
$983$		−	931.941i		−	0.948057i	0.880509	−	0.474029i	$-0.157201\pi$
$984$	222.723	−	214.620i	0.226344	−	0.218110i
$985$	518.942			0.526845
$986$		−	0.673288i		−	0.000682848i
$987$	−1949.57	−	2023.17i	−1.97524	−	2.04981i
$988$	291.398			0.294937
$989$			199.282i			0.201498i
$990$	−296.372	−	10.9853i	−0.299365	−	0.0110963i
$991$	−905.380			−0.913602			−0.456801	−	0.889569i	$-0.651005\pi$
$991$	−905.380			−0.913602			−0.456801	+	0.889569i	$0.651005\pi$
$992$		−	209.252i		−	0.210939i
$993$	1077.46	−	1038.26i	1.08506	−	1.04558i
$994$	−1024.81			−1.03100
$995$		−	324.219i		−	0.325849i
$996$	154.819	+	160.664i	0.155441	+	0.161309i
$997$	−1704.19			−1.70931			−0.854657	−	0.519193i	$-0.826233\pi$
$997$	−1704.19			−1.70931			−0.854657	+	0.519193i	$0.826233\pi$
$998$			1182.97i			1.18534i
$999$	−309.561	−	346.032i	−0.309871	−	0.346379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.g.a.461.10	yes	56
3.2	odd	2	inner	690.3.g.a.461.9	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.g.a.461.9	✓	56	3.2	odd	2	inner
690.3.g.a.461.10	yes	56	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(2.16025 - 2.08166i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(2.94392 + 3.05506i) q^{6} +12.7530 q^{7} -2.82843i q^{8} +(0.333364 - 8.99382i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(2.16025 - 2.08166i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(2.94392 + 3.05506i) q^{6} +12.7530 q^{7} -2.82843i q^{8} +(0.333364 - 8.99382i) q^{9} +3.16228 q^{10} -10.4206i q^{11} +(-4.32050 + 4.16332i) q^{12} -10.0884 q^{13} +18.0355i q^{14} +(-4.65474 - 4.83047i) q^{15} +4.00000 q^{16} +0.278181i q^{17} +(12.7192 + 0.471449i) q^{18} +14.4422 q^{19} +4.47214i q^{20} +(27.5497 - 26.5474i) q^{21} +14.7369 q^{22} -4.79583i q^{23} +(-5.88783 - 6.11011i) q^{24} -5.00000 q^{25} -14.2672i q^{26} +(-18.0020 - 20.1229i) q^{27} -25.5060 q^{28} +1.71142i q^{29} +(6.83131 - 6.58279i) q^{30} -36.9908 q^{31} +5.65685i q^{32} +(-21.6921 - 22.5111i) q^{33} -0.393408 q^{34} -28.5166i q^{35} +(-0.666729 + 17.9876i) q^{36} +17.1960 q^{37} +20.4243i q^{38} +(-21.7936 + 21.0007i) q^{39} -6.32456 q^{40} +36.4515i q^{41} +(37.5437 + 38.9611i) q^{42} -41.5531 q^{43} +20.8412i q^{44} +(-20.1108 - 0.745426i) q^{45} +6.78233 q^{46} -73.4371i q^{47} +(8.64100 - 8.32665i) q^{48} +113.639 q^{49} -7.07107i q^{50} +(0.579080 + 0.600942i) q^{51} +20.1769 q^{52} +20.7239i q^{53} +(28.4580 - 25.4586i) q^{54} -23.3011 q^{55} -36.0709i q^{56} +(31.1987 - 30.0637i) q^{57} -2.42032 q^{58} -74.5843i q^{59} +(9.30948 + 9.66093i) q^{60} +77.3260 q^{61} -52.3129i q^{62} +(4.25139 - 114.698i) q^{63} -8.00000 q^{64} +22.5584i q^{65} +(31.8355 - 30.6773i) q^{66} +103.539 q^{67} -0.556363i q^{68} +(-9.98330 - 10.3602i) q^{69} +40.3285 q^{70} +56.8221i q^{71} +(-25.4384 - 0.942897i) q^{72} -39.9241 q^{73} +24.3188i q^{74} +(-10.8013 + 10.4083i) q^{75} -28.8843 q^{76} -132.894i q^{77} +(-29.6995 - 30.8207i) q^{78} +81.4578 q^{79} -8.94427i q^{80} +(-80.7777 - 5.99644i) q^{81} -51.5502 q^{82} -37.1864i q^{83} +(-55.0993 + 53.0949i) q^{84} +0.622033 q^{85} -58.7650i q^{86} +(3.56261 + 3.69711i) q^{87} -29.4739 q^{88} +129.429i q^{89} +(1.05419 - 28.4410i) q^{90} -128.658 q^{91} +9.59166i q^{92} +(-79.9094 + 77.0024i) q^{93} +103.856 q^{94} -32.2937i q^{95} +(11.7757 + 12.2202i) q^{96} +39.8372 q^{97} +160.710i q^{98} +(-93.7209 - 3.47385i) 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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