LMFDB - Embedded newform 690.3.g.a.461.12

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			461.12
Character	$\chi$	$=$	690.461
Dual form			690.3.g.a.461.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(-1.59356 + 2.54176i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-3.59459 - 2.25364i) q^{6} +10.3156 q^{7} -2.82843i q^{8} +(-3.92110 - 8.10092i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(-1.59356 + 2.54176i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-3.59459 - 2.25364i) q^{6} +10.3156 q^{7} -2.82843i q^{8} +(-3.92110 - 8.10092i) q^{9} -3.16228 q^{10} +14.4101i q^{11} +(3.18713 - 5.08352i) q^{12} +14.5857 q^{13} +14.5885i q^{14} +(-5.68355 - 3.56332i) q^{15} +4.00000 q^{16} -0.438401i q^{17} +(11.4564 - 5.54528i) q^{18} +30.5080 q^{19} -4.47214i q^{20} +(-16.4387 + 26.2199i) q^{21} -20.3790 q^{22} +4.79583i q^{23} +(7.18919 + 4.50728i) q^{24} -5.00000 q^{25} +20.6274i q^{26} +(26.8391 + 2.94284i) q^{27} -20.6313 q^{28} +23.6165i q^{29} +(5.03929 - 8.03776i) q^{30} +37.8103 q^{31} +5.65685i q^{32} +(-36.6271 - 22.9635i) q^{33} +0.619993 q^{34} +23.0665i q^{35} +(7.84220 + 16.2018i) q^{36} +3.95366 q^{37} +43.1448i q^{38} +(-23.2433 + 37.0735i) q^{39} +6.32456 q^{40} +0.897806i q^{41} +(-37.0806 - 23.2478i) q^{42} -47.5033 q^{43} -28.8203i q^{44} +(18.1142 - 8.76785i) q^{45} -6.78233 q^{46} +39.9836i q^{47} +(-6.37426 + 10.1670i) q^{48} +57.4126 q^{49} -7.07107i q^{50} +(1.11431 + 0.698620i) q^{51} -29.1715 q^{52} -67.0896i q^{53} +(-4.16180 + 37.9563i) q^{54} -32.2221 q^{55} -29.1771i q^{56} +(-48.6164 + 77.5440i) q^{57} -33.3988 q^{58} -43.7546i q^{59} +(11.3671 + 7.12664i) q^{60} -69.1629 q^{61} +53.4719i q^{62} +(-40.4487 - 83.5663i) q^{63} -8.00000 q^{64} +32.6147i q^{65} +(32.4753 - 51.7986i) q^{66} +15.9838 q^{67} +0.876802i q^{68} +(-12.1899 - 7.64247i) q^{69} -32.6209 q^{70} -32.7189i q^{71} +(-22.9129 + 11.0906i) q^{72} -136.933 q^{73} +5.59132i q^{74} +(7.96782 - 12.7088i) q^{75} -61.0159 q^{76} +148.650i q^{77} +(-52.4298 - 32.8710i) q^{78} -117.203 q^{79} +8.94427i q^{80} +(-50.2499 + 63.5291i) q^{81} -1.26969 q^{82} -72.3768i q^{83} +(32.8773 - 52.4398i) q^{84} +0.980294 q^{85} -67.1798i q^{86} +(-60.0276 - 37.6345i) q^{87} +40.7580 q^{88} +48.7209i q^{89} +(12.3996 + 25.6174i) q^{90} +150.461 q^{91} -9.59166i q^{92} +(-60.2532 + 96.1048i) q^{93} -56.5454 q^{94} +68.2179i q^{95} +(-14.3784 - 9.01456i) q^{96} +128.346 q^{97} +81.1936i q^{98} +(116.735 - 56.5036i) 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
$3$	−1.59356	+	2.54176i	−0.531188	+	0.847254i
$3$	−1.59356	+	2.54176i	−0.531188	+	0.847254i
$4$	−2.00000			−0.500000
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$	−3.59459	−	2.25364i	−0.599099	−	0.375607i
$7$	10.3156			1.47366			0.736832	−	0.676076i	$-0.236321\pi$
$7$	10.3156			1.47366			0.736832	+	0.676076i	$0.236321\pi$
$8$		−	2.82843i		−	0.353553i
$9$	−3.92110	−	8.10092i	−0.435678	−	0.900103i
$10$	−3.16228			−0.316228
$11$			14.4101i			1.31001i	0.755623	+	0.655006i	$0.227334\pi$
$11$			14.4101i			1.31001i	−0.755623	+	0.655006i	$0.772666\pi$
$12$	3.18713	−	5.08352i	0.265594	−	0.423627i
$13$	14.5857			1.12198			0.560990	−	0.827822i	$-0.310421\pi$
$13$	14.5857			1.12198			0.560990	+	0.827822i	$0.310421\pi$
$14$			14.5885i			1.04204i
$15$	−5.68355	−	3.56332i	−0.378903	−	0.237555i
$16$	4.00000			0.250000
$17$		−	0.438401i		−	0.0257883i	−0.999917	−	0.0128941i	$-0.995896\pi$
$17$		−	0.438401i		−	0.0257883i	0.999917	−	0.0128941i	$-0.00410445\pi$
$18$	11.4564	−	5.54528i	0.636469	−	0.308071i
$19$	30.5080			1.60568			0.802841	−	0.596193i	$-0.203321\pi$
$19$	30.5080			1.60568			0.802841	+	0.596193i	$0.203321\pi$
$20$		−	4.47214i		−	0.223607i
$21$	−16.4387	+	26.2199i	−0.782793	+	1.24857i
$22$	−20.3790			−0.926319
$23$			4.79583i			0.208514i
$23$			4.79583i			0.208514i
$24$	7.18919	+	4.50728i	0.299549	+	0.187803i
$25$	−5.00000			−0.200000
$26$			20.6274i			0.793360i
$27$	26.8391	+	2.94284i	0.994042	+	0.108994i
$28$	−20.6313			−0.736832
$29$			23.6165i			0.814363i	0.913347	+	0.407182i	$0.133488\pi$
$29$			23.6165i			0.814363i	−0.913347	+	0.407182i	$0.866512\pi$
$30$	5.03929	−	8.03776i	0.167976	−	0.267925i
$31$	37.8103			1.21969			0.609844	−	0.792522i	$-0.291232\pi$
$31$	37.8103			1.21969			0.609844	+	0.792522i	$0.291232\pi$
$32$			5.65685i			0.176777i
$33$	−36.6271	−	22.9635i	−1.10991	−	0.695863i
$34$	0.619993			0.0182351
$35$			23.0665i			0.659043i
$36$	7.84220	+	16.2018i	0.217839	+	0.450051i
$37$	3.95366			0.106856			0.0534278	−	0.998572i	$-0.482985\pi$
$37$	3.95366			0.106856			0.0534278	+	0.998572i	$0.482985\pi$
$38$			43.1448i			1.13539i
$39$	−23.2433	+	37.0735i	−0.595983	+	0.950602i
$40$	6.32456			0.158114
$41$			0.897806i			0.0218977i	0.999940	+	0.0109488i	$0.00348520\pi$
$41$			0.897806i			0.0218977i	−0.999940	+	0.0109488i	$0.996515\pi$
$42$	−37.0806	−	23.2478i	−0.882870	−	0.553518i
$43$	−47.5033			−1.10473			−0.552364	−	0.833603i	$-0.686274\pi$
$43$	−47.5033			−1.10473			−0.552364	+	0.833603i	$0.686274\pi$
$44$		−	28.8203i		−	0.655006i
$45$	18.1142	−	8.76785i	0.402538	−	0.194841i
$46$	−6.78233			−0.147442
$47$			39.9836i			0.850716i	0.905025	+	0.425358i	$0.139852\pi$
$47$			39.9836i			0.850716i	−0.905025	+	0.425358i	$0.860148\pi$
$48$	−6.37426	+	10.1670i	−0.132797	+	0.211813i
$49$	57.4126			1.17169
$50$		−	7.07107i		−	0.141421i
$51$	1.11431	+	0.698620i	0.0218492	+	0.0136984i
$52$	−29.1715			−0.560990
$53$		−	67.0896i		−	1.26584i	−0.774217	−	0.632920i	$-0.781856\pi$
$53$		−	67.0896i		−	1.26584i	0.774217	−	0.632920i	$-0.218144\pi$
$54$	−4.16180	+	37.9563i	−0.0770704	+	0.702894i
$55$	−32.2221			−0.585856
$56$		−	29.1771i		−	0.521019i
$57$	−48.6164	+	77.5440i	−0.852920	+	1.36042i
$58$	−33.3988			−0.575842
$59$		−	43.7546i		−	0.741604i	−0.928712	−	0.370802i	$-0.879083\pi$
$59$		−	43.7546i		−	0.741604i	0.928712	−	0.370802i	$-0.120917\pi$
$60$	11.3671	+	7.12664i	0.189452	+	0.118777i
$61$	−69.1629			−1.13382			−0.566909	−	0.823781i	$-0.691861\pi$
$61$	−69.1629			−1.13382			−0.566909	+	0.823781i	$0.691861\pi$
$62$			53.4719i			0.862449i
$63$	−40.4487	−	83.5663i	−0.642043	−	1.32645i
$64$	−8.00000			−0.125000
$65$			32.6147i			0.501765i
$66$	32.4753	−	51.7986i	0.492050	−	0.784827i
$67$	15.9838			0.238565			0.119282	−	0.992860i	$-0.461941\pi$
$67$	15.9838			0.238565			0.119282	+	0.992860i	$0.461941\pi$
$68$			0.876802i			0.0128941i
$69$	−12.1899	−	7.64247i	−0.176665	−	0.110760i
$70$	−32.6209			−0.466013
$71$		−	32.7189i		−	0.460830i	−0.973092	−	0.230415i	$-0.925992\pi$
$71$		−	32.7189i		−	0.460830i	0.973092	−	0.230415i	$-0.0740084\pi$
$72$	−22.9129	+	11.0906i	−0.318234	+	0.154035i
$73$	−136.933			−1.87580			−0.937900	−	0.346906i	$-0.887232\pi$
$73$	−136.933			−1.87580			−0.937900	+	0.346906i	$0.887232\pi$
$74$			5.59132i			0.0755584i
$75$	7.96782	−	12.7088i	0.106238	−	0.169451i
$76$	−61.0159			−0.802841
$77$			148.650i			1.93052i
$78$	−52.4298	−	32.8710i	−0.672177	−	0.421423i
$79$	−117.203			−1.48359			−0.741793	−	0.670629i	$-0.766024\pi$
$79$	−117.203			−1.48359			−0.741793	+	0.670629i	$0.766024\pi$
$80$			8.94427i			0.111803i
$81$	−50.2499	+	63.5291i	−0.620369	+	0.784310i
$82$	−1.26969			−0.0154840
$83$		−	72.3768i		−	0.872009i	−0.899944	−	0.436005i	$-0.856393\pi$
$83$		−	72.3768i		−	0.872009i	0.899944	−	0.436005i	$-0.143607\pi$
$84$	32.8773	−	52.4398i	0.391396	−	0.624284i
$85$	0.980294			0.0115329
$86$		−	67.1798i		−	0.781161i
$87$	−60.0276	−	37.6345i	−0.689973	−	0.432580i
$88$	40.7580			0.463159
$89$			48.7209i			0.547426i	0.961811	+	0.273713i	$0.0882519\pi$
$89$			48.7209i			0.547426i	−0.961811	+	0.273713i	$0.911748\pi$
$90$	12.3996	+	25.6174i	0.137773	+	0.284637i
$91$	150.461			1.65342
$92$		−	9.59166i		−	0.104257i
$93$	−60.2532	+	96.1048i	−0.647884	+	1.03339i
$94$	−56.5454			−0.601547
$95$			68.2179i			0.718083i
$96$	−14.3784	−	9.01456i	−0.149775	−	0.0939017i
$97$	128.346			1.32316			0.661579	−	0.749876i	$-0.269887\pi$
$97$	128.346			1.32316			0.661579	+	0.749876i	$0.269887\pi$
$98$			81.1936i			0.828507i
$99$	116.735	−	56.5036i	1.17915	−	0.570744i
$100$	10.0000			0.100000
$101$		−	97.9145i		−	0.969450i	−0.874666	−	0.484725i	$-0.838920\pi$
$101$		−	97.9145i		−	0.969450i	0.874666	−	0.484725i	$-0.161080\pi$
$102$	−0.987998	+	1.57587i	−0.00968626	+	0.0154497i
$103$	99.4761			0.965787			0.482894	−	0.875679i	$-0.339586\pi$
$103$	99.4761			0.965787			0.482894	+	0.875679i	$0.339586\pi$
$104$		−	41.2547i		−	0.396680i
$105$	−58.6295	−	36.7579i	−0.558376	−	0.350076i
$106$	94.8790			0.895085
$107$			155.354i			1.45191i	0.687742	+	0.725956i	$0.258602\pi$
$107$			155.354i			1.45191i	−0.687742	+	0.725956i	$0.741398\pi$
$108$	−53.6783	−	5.88568i	−0.497021	−	0.0544970i
$109$	44.8327			0.411309			0.205655	−	0.978625i	$-0.434068\pi$
$109$	44.8327			0.411309			0.205655	+	0.978625i	$0.434068\pi$
$110$		−	45.5689i		−	0.414262i
$111$	−6.30041	+	10.0493i	−0.0567605	+	0.0905339i
$112$	41.2626			0.368416
$113$			180.557i			1.59785i	0.601428	+	0.798927i	$0.294599\pi$
$113$			180.557i			1.59785i	−0.601428	+	0.798927i	$0.705401\pi$
$114$	−109.664	−	68.7540i	−0.961963	−	0.603105i
$115$	−10.7238			−0.0932505
$116$		−	47.2331i		−	0.407182i
$117$	−57.1922	−	118.158i	−0.488822	−	1.00990i
$118$	61.8784			0.524393
$119$		−	4.52239i		−	0.0380033i
$120$	−10.0786	+	16.0755i	−0.0839882	+	0.133963i
$121$	−86.6522			−0.716134
$122$		−	97.8111i		−	0.801730i
$123$	−2.28201	−	1.43071i	−0.0185529	−	0.0116318i
$124$	−75.6206			−0.609844
$125$		−	11.1803i		−	0.0894427i
$126$	118.181	−	57.2031i	0.937941	−	0.453993i
$127$	−180.797			−1.42360			−0.711800	−	0.702382i	$-0.752120\pi$
$127$	−180.797			−1.42360			−0.711800	+	0.702382i	$0.752120\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	75.6996	−	120.742i	0.586818	−	0.935985i
$130$	−46.1242			−0.354801
$131$		−	102.689i		−	0.783889i	−0.919989	−	0.391944i	$-0.871803\pi$
$131$		−	102.689i		−	0.783889i	0.919989	−	0.391944i	$-0.128197\pi$
$132$	73.2543	+	45.9270i	0.554957	+	0.347932i
$133$	314.709			2.36624
$134$			22.6045i			0.168691i
$135$	−6.58039	+	60.0142i	−0.0487436	+	0.444549i
$136$	−1.23999			−0.00911754
$137$		−	63.7156i		−	0.465077i	−0.972587	−	0.232539i	$-0.925297\pi$
$137$		−	63.7156i		−	0.465077i	0.972587	−	0.232539i	$-0.0747032\pi$
$138$	10.8081	−	17.2391i	0.0783194	−	0.124921i
$139$	198.895			1.43090			0.715451	−	0.698663i	$-0.246221\pi$
$139$	198.895			1.43090			0.715451	+	0.698663i	$0.246221\pi$
$140$		−	46.1330i		−	0.329521i
$141$	−101.629	−	63.7165i	−0.720772	−	0.451890i
$142$	46.2715			0.325856
$143$			210.183i			1.46981i
$144$	−15.6844	−	32.4037i	−0.108920	−	0.225026i
$145$	−52.8082			−0.364194
$146$		−	193.653i		−	1.32639i
$147$	−91.4907	+	145.929i	−0.622385	+	0.992715i
$148$	−7.90732			−0.0534278
$149$			77.1700i			0.517919i	0.965888	+	0.258960i	$0.0833797\pi$
$149$			77.1700i			0.517919i	−0.965888	+	0.258960i	$0.916620\pi$
$150$	17.9730	+	11.2682i	0.119820	+	0.0751214i
$151$	−122.875			−0.813741			−0.406871	−	0.913486i	$-0.633380\pi$
$151$	−122.875			−0.813741			−0.406871	+	0.913486i	$0.633380\pi$
$152$		−	86.2896i		−	0.567694i
$153$	−3.55145	+	1.71901i	−0.0232121	+	0.0112354i
$154$	−210.223			−1.36508
$155$			84.5464i			0.545461i
$156$	46.4867	−	74.1470i	0.297991	−	0.475301i
$157$	190.139			1.21108			0.605538	−	0.795817i	$-0.292958\pi$
$157$	190.139			1.21108			0.605538	+	0.795817i	$0.292958\pi$
$158$		−	165.750i		−	1.04905i
$159$	170.526	+	106.912i	1.07249	+	0.672400i
$160$	−12.6491			−0.0790569
$161$			49.4721i			0.307280i
$162$	−89.8437	−	71.0641i	−0.554591	−	0.438667i
$163$	41.0811			0.252031			0.126016	−	0.992028i	$-0.459781\pi$
$163$	41.0811			0.252031			0.126016	+	0.992028i	$0.459781\pi$
$164$		−	1.79561i		−	0.0109488i
$165$	51.3479	−	81.9008i	0.311200	−	0.496368i
$166$	102.356			0.616604
$167$			173.319i			1.03784i	0.854823	+	0.518920i	$0.173666\pi$
$167$			173.319i			1.03784i	−0.854823	+	0.518920i	$0.826334\pi$
$168$	74.1611	+	46.4955i	0.441435	+	0.276759i
$169$	43.7439			0.258840
$170$			1.38635i			0.00815497i
$171$	−119.625	−	247.143i	−0.699561	−	1.44528i
$172$	95.0066			0.552364
$173$			50.1795i			0.290055i	0.989428	+	0.145027i	$0.0463270\pi$
$173$			50.1795i			0.290055i	−0.989428	+	0.145027i	$0.953673\pi$
$174$	53.2232	−	84.8919i	0.305880	−	0.487884i
$175$	−51.5782			−0.294733
$176$			57.6406i			0.327503i
$177$	111.214	+	69.7258i	0.628327	+	0.393931i
$178$	−68.9018			−0.387089
$179$			192.115i			1.07327i	0.843816	+	0.536633i	$0.180304\pi$
$179$			192.115i			1.07327i	−0.843816	+	0.536633i	$0.819696\pi$
$180$	−36.2284	+	17.5357i	−0.201269	+	0.0974206i
$181$	89.0532			0.492007			0.246003	−	0.969269i	$-0.420883\pi$
$181$	89.0532			0.492007			0.246003	+	0.969269i	$0.420883\pi$
$182$			212.785i			1.16915i
$183$	110.216	−	175.796i	0.602271	−	0.960631i
$184$	13.5647			0.0737210
$185$			8.84065i			0.0477873i
$186$	−135.913	−	85.2109i	−0.730714	−	0.458123i
$187$	6.31742			0.0337830
$188$		−	79.9673i		−	0.425358i
$189$	276.863	+	30.3573i	1.46488	+	0.160621i
$190$	−96.4747			−0.507761
$191$		−	288.927i		−	1.51271i	−0.654163	−	0.756354i	$-0.726979\pi$
$191$		−	288.927i		−	1.51271i	0.654163	−	0.756354i	$-0.273021\pi$
$192$	12.7485	−	20.3341i	0.0663985	−	0.105907i
$193$	−315.184			−1.63308			−0.816539	−	0.577291i	$-0.804110\pi$
$193$	−315.184			−1.63308			−0.816539	+	0.577291i	$0.804110\pi$
$194$			181.509i			0.935613i
$195$	−82.8988	−	51.9737i	−0.425122	−	0.266532i
$196$	−114.825			−0.585843
$197$			177.931i			0.903202i	0.892220	+	0.451601i	$0.149147\pi$
$197$			177.931i			0.903202i	−0.892220	+	0.451601i	$0.850853\pi$
$198$	79.9082	+	165.089i	0.403577	+	0.833782i
$199$	−232.143			−1.16655			−0.583275	−	0.812275i	$-0.698229\pi$
$199$	−232.143			−1.16655			−0.583275	+	0.812275i	$0.698229\pi$
$200$			14.1421i			0.0707107i
$201$	−25.4713	+	40.6271i	−0.126723	+	0.202125i
$202$	138.472			0.685505
$203$			243.620i			1.20010i
$204$	−2.22862	−	1.39724i	−0.0109246	−	0.00684922i
$205$	−2.00755			−0.00979295
$206$			140.680i			0.682915i
$207$	38.8507	−	18.8049i	0.187684	−	0.0908452i
$208$	58.3430			0.280495
$209$			439.624i			2.10346i
$210$	51.9836	−	82.9146i	0.247541	−	0.394832i
$211$	240.137			1.13809			0.569045	−	0.822307i	$-0.307313\pi$
$211$	240.137			1.13809			0.569045	+	0.822307i	$0.307313\pi$
$212$			134.179i			0.632920i
$213$	83.1637	+	52.1397i	0.390440	+	0.244787i
$214$	−219.704			−1.02666
$215$		−	106.221i		−	0.494049i
$216$	8.32361	−	75.9126i	0.0385352	−	0.351447i
$217$	390.038			1.79741
$218$			63.4030i			0.290840i
$219$	218.212	−	348.052i	0.996403	−	1.58928i
$220$	64.4441			0.292928
$221$		−	6.39440i		−	0.0289340i
$222$	−14.2118	−	8.91013i	−0.0640171	−	0.0401357i
$223$	−43.0954			−0.193253			−0.0966265	−	0.995321i	$-0.530805\pi$
$223$	−43.0954			−0.193253			−0.0966265	+	0.995321i	$0.530805\pi$
$224$			58.3541i			0.260509i
$225$	19.6055	+	40.5046i	0.0871356	+	0.180021i
$226$	−255.347			−1.12985
$227$		−	261.201i		−	1.15066i	−0.817920	−	0.575332i	$-0.804873\pi$
$227$		−	261.201i		−	1.15066i	0.817920	−	0.575332i	$-0.195127\pi$
$228$	97.2328	−	155.088i	0.426460	−	0.680210i
$229$	306.887			1.34012			0.670060	−	0.742307i	$-0.266268\pi$
$229$	306.887			1.34012			0.670060	+	0.742307i	$0.266268\pi$
$230$		−	15.1658i		−	0.0659380i
$231$	−377.833	−	236.883i	−1.63564	−	1.02547i
$232$	66.7977			0.287921
$233$			14.3031i			0.0613867i	0.999529	+	0.0306934i	$0.00977154\pi$
$233$			14.3031i			0.0613867i	−0.999529	+	0.0306934i	$0.990228\pi$
$234$	167.101	−	80.8820i	0.714105	−	0.345649i
$235$	−89.4061			−0.380452
$236$			87.5092i			0.370802i
$237$	186.771	−	297.903i	0.788063	−	1.25697i
$238$	6.39562			0.0268724
$239$		−	170.994i		−	0.715456i	−0.933826	−	0.357728i	$-0.883551\pi$
$239$		−	170.994i		−	0.715456i	0.933826	−	0.357728i	$-0.116449\pi$
$240$	−22.7342	−	14.2533i	−0.0947259	−	0.0593887i
$241$	206.779			0.858003			0.429002	−	0.903304i	$-0.358865\pi$
$241$	206.779			0.858003			0.429002	+	0.903304i	$0.358865\pi$
$242$		−	122.545i		−	0.506383i
$243$	−81.3993	−	228.961i	−0.334977	−	0.942226i
$244$	138.326			0.566909
$245$			128.378i			0.523994i
$246$	2.02333	−	3.22725i	0.00822492	−	0.0131189i
$247$	444.981			1.80154
$248$		−	106.944i		−	0.431225i
$249$	183.965	+	115.337i	0.738813	+	0.463201i
$250$	15.8114			0.0632456
$251$		−	288.871i		−	1.15088i	−0.817844	−	0.575439i	$-0.804831\pi$
$251$		−	288.871i		−	1.15088i	0.817844	−	0.575439i	$-0.195169\pi$
$252$	80.8974	+	167.133i	0.321021	+	0.663224i
$253$	−69.1086			−0.273157
$254$		−	255.686i		−	1.00664i
$255$	−1.56216	+	2.49167i	−0.00612613	+	0.00977127i
$256$	16.0000			0.0625000
$257$			383.396i			1.49181i	0.666050	+	0.745907i	$0.267984\pi$
$257$			383.396i			1.49181i	−0.666050	+	0.745907i	$0.732016\pi$
$258$	170.755	+	107.055i	0.661841	+	0.414943i
$259$	40.7846			0.157469
$260$		−	65.2294i		−	0.250882i
$261$	191.316	−	92.6029i	0.733011	−	0.354800i
$262$	145.225			0.554293
$263$		−	214.097i		−	0.814056i	−0.913416	−	0.407028i	$-0.866565\pi$
$263$		−	214.097i		−	0.814056i	0.913416	−	0.407028i	$-0.133435\pi$
$264$	−64.9506	+	103.597i	−0.246025	+	0.392414i
$265$	150.017			0.566101
$266$			445.066i			1.67318i
$267$	−123.837	−	77.6400i	−0.463809	−	0.290786i
$268$	−31.9677			−0.119282
$269$		−	251.023i		−	0.933173i	−0.884476	−	0.466586i	$-0.845484\pi$
$269$		−	251.023i		−	0.933173i	0.884476	−	0.466586i	$-0.154516\pi$
$270$	−84.8728	−	9.30607i	−0.314344	−	0.0344669i
$271$	228.635			0.843673			0.421837	−	0.906672i	$-0.361386\pi$
$271$	228.635			0.843673			0.421837	+	0.906672i	$0.361386\pi$
$272$		−	1.75360i		−	0.00644707i
$273$	−239.770	+	382.437i	−0.878278	+	1.40087i
$274$	90.1075			0.328859
$275$		−	72.0507i		−	0.262003i
$276$	24.3797	+	15.2849i	0.0883323	+	0.0553802i
$277$	−509.608			−1.83974			−0.919870	−	0.392223i	$-0.871706\pi$
$277$	−509.608			−1.83974			−0.919870	+	0.392223i	$0.871706\pi$
$278$			281.280i			1.01180i
$279$	−148.258	−	306.298i	−0.531391	−	1.09784i
$280$	65.2419			0.233007
$281$			16.5755i			0.0589876i	0.999565	+	0.0294938i	$0.00938953\pi$
$281$			16.5755i			0.0589876i	−0.999565	+	0.0294938i	$0.990610\pi$
$282$	90.1088	−	143.725i	0.319535	−	0.509663i
$283$	−125.782			−0.444461			−0.222230	−	0.974994i	$-0.571334\pi$
$283$	−125.782			−0.444461			−0.222230	+	0.974994i	$0.571334\pi$
$284$			65.4378i			0.230415i
$285$	−173.394	−	108.710i	−0.608399	−	0.381437i
$286$	−297.243			−1.03931
$287$			9.26145i			0.0322698i
$288$	45.8257	−	22.1811i	0.159117	−	0.0770177i
$289$	288.808			0.999335
$290$		−	74.6821i		−	0.257524i
$291$	−204.528	+	326.226i	−0.702845	+	1.12105i
$292$	273.867			0.937900
$293$		−	52.6345i		−	0.179640i	−0.995958	−	0.0898200i	$-0.971371\pi$
$293$		−	52.6345i		−	0.179640i	0.995958	−	0.0898200i	$-0.0286292\pi$
$294$	−206.375	−	129.387i	−0.701955	−	0.440093i
$295$	97.8383			0.331655
$296$		−	11.1826i		−	0.0377792i
$297$	−42.4067	+	386.756i	−0.142784	+	1.30221i
$298$	−109.135			−0.366224
$299$			69.9508i			0.233949i
$300$	−15.9356	+	25.4176i	−0.0531188	+	0.0847254i
$301$	−490.027			−1.62800
$302$		−	173.771i		−	0.575402i
$303$	248.875	+	156.033i	0.821371	+	0.514961i
$304$	122.032			0.401421
$305$		−	154.653i		−	0.507059i
$306$	−2.43105	−	5.02251i	−0.00794462	−	0.0164134i
$307$	−584.003			−1.90229			−0.951146	−	0.308742i	$-0.900092\pi$
$307$	−584.003			−1.90229			−0.951146	+	0.308742i	$0.900092\pi$
$308$		−	297.300i		−	0.965259i
$309$	−158.522	+	252.845i	−0.513015	+	0.818267i
$310$	−119.567			−0.385699
$311$		−	612.766i		−	1.97031i	−0.171668	−	0.985155i	$-0.554916\pi$
$311$		−	612.766i		−	1.97031i	0.171668	−	0.985155i	$-0.445084\pi$
$312$	104.860	+	65.7421i	0.336089	+	0.210712i
$313$	−448.197			−1.43194			−0.715970	−	0.698131i	$-0.754015\pi$
$313$	−448.197			−1.43194			−0.715970	+	0.698131i	$0.754015\pi$
$314$			268.897i			0.856360i
$315$	186.860	−	90.4461i	0.593206	−	0.287130i
$316$	234.407			0.741793
$317$		−	375.651i		−	1.18502i	−0.805563	−	0.592509i	$-0.798137\pi$
$317$		−	375.651i		−	1.18502i	0.805563	−	0.592509i	$-0.201863\pi$
$318$	−151.196	+	241.160i	−0.475458	+	0.758364i
$319$	−340.318			−1.06683
$320$		−	17.8885i		−	0.0559017i
$321$	−394.874	−	247.567i	−1.23014	−	0.771238i
$322$	−69.9641			−0.217280
$323$		−	13.3747i		−	0.0414078i
$324$	100.500	−	127.058i	0.310185	−	0.392155i
$325$	−72.9287			−0.224396
$326$			58.0974i			0.178213i
$327$	−71.4438	+	113.954i	−0.218483	+	0.348483i
$328$	2.53938			0.00774200
$329$			412.457i			1.25367i
$330$	115.825	+	72.6169i	0.350985	+	0.220051i
$331$	257.176			0.776967			0.388483	−	0.921456i	$-0.372999\pi$
$331$	257.176			0.776967			0.388483	+	0.921456i	$0.372999\pi$
$332$			144.754i			0.436005i
$333$	−15.5027	−	32.0283i	−0.0465547	−	0.0961811i
$334$	−245.110			−0.733864
$335$			35.7409i			0.106689i
$336$	−65.7546	+	104.880i	−0.195698	+	0.312142i
$337$	622.010			1.84573			0.922863	−	0.385128i	$-0.125843\pi$
$337$	622.010			1.84573			0.922863	+	0.385128i	$0.125843\pi$
$338$			61.8633i			0.183027i
$339$	−458.934	−	287.730i	−1.35379	−	0.848761i
$340$	−1.96059			−0.00576644
$341$			544.852i			1.59781i
$342$	349.513	−	169.175i	1.02197	−	0.494664i
$343$	86.7811			0.253006
$344$			134.360i			0.390580i
$345$	17.0891	−	27.2574i	0.0495336	−	0.0790068i
$346$	−70.9645			−0.205100
$347$			50.3108i			0.144988i	0.997369	+	0.0724939i	$0.0230958\pi$
$347$			50.3108i			0.144988i	−0.997369	+	0.0724939i	$0.976904\pi$
$348$	120.055	+	75.2690i	0.344986	+	0.216290i
$349$	479.971			1.37528			0.687638	−	0.726054i	$-0.258648\pi$
$349$	479.971			1.37528			0.687638	+	0.726054i	$0.258648\pi$
$350$		−	72.9426i		−	0.208408i
$351$	391.469	+	42.9235i	1.11530	+	0.122289i
$352$	−81.5161			−0.231580
$353$			415.132i			1.17601i	0.808857	+	0.588005i	$0.200086\pi$
$353$			415.132i			1.17601i	−0.808857	+	0.588005i	$0.799914\pi$
$354$	−98.6072	+	157.280i	−0.278551	+	0.444294i
$355$	73.1617			0.206089
$356$		−	97.4419i		−	0.273713i
$357$	11.4948	+	7.20672i	0.0321984	+	0.0201869i
$358$	−271.691			−0.758913
$359$			3.52584i			0.00982129i	0.999988	+	0.00491064i	$0.00156311\pi$
$359$			3.52584i			0.00982129i	−0.999988	+	0.00491064i	$0.998437\pi$
$360$	−24.7992	−	51.2347i	−0.0688867	−	0.142319i
$361$	569.736			1.57822
$362$			125.940i			0.347901i
$363$	138.086	−	220.249i	0.380402	−	0.606747i
$364$	−300.923			−0.826711
$365$		−	306.192i		−	0.838883i
$366$	248.612	+	155.868i	0.679269	+	0.425870i
$367$	−64.7408			−0.176406			−0.0882028	−	0.996103i	$-0.528112\pi$
$367$	−64.7408			−0.176406			−0.0882028	+	0.996103i	$0.528112\pi$
$368$			19.1833i			0.0521286i
$369$	7.27305	−	3.52039i	0.0197102	−	0.00954035i
$370$	−12.5026			−0.0337907
$371$		−	692.072i		−	1.86542i
$372$	120.506	−	192.210i	0.323942	−	0.516693i
$373$	−209.857			−0.562618			−0.281309	−	0.959617i	$-0.590769\pi$
$373$	−209.857			−0.562618			−0.281309	+	0.959617i	$0.590769\pi$
$374$			8.93418i			0.0238882i
$375$	28.4178	+	17.8166i	0.0757807	+	0.0475109i
$376$	113.091			0.300773
$377$			344.465i			0.913700i
$378$	−42.9317	+	391.544i	−0.113576	+	1.03583i
$379$	27.5758			0.0727593			0.0363797	−	0.999338i	$-0.488417\pi$
$379$	27.5758			0.0727593			0.0363797	+	0.999338i	$0.488417\pi$
$380$		−	136.436i		−	0.359042i
$381$	288.112	−	459.544i	0.756200	−	1.20615i
$382$	408.605			1.06965
$383$		−	626.105i		−	1.63474i	−0.576113	−	0.817370i	$-0.695431\pi$
$383$		−	626.105i		−	1.63474i	0.576113	−	0.817370i	$-0.304569\pi$
$384$	28.7567	+	18.0291i	0.0748874	+	0.0469509i
$385$	−332.391			−0.863354
$386$		−	445.737i		−	1.15476i
$387$	186.265	+	384.821i	0.481306	+	0.994368i
$388$	−256.692			−0.661579
$389$		−	214.358i		−	0.551048i	−0.961294	−	0.275524i	$-0.911149\pi$
$389$		−	214.358i		−	0.551048i	0.961294	−	0.275524i	$-0.0888514\pi$
$390$	73.5019	−	117.237i	0.188466	−	0.300607i
$391$	2.10250			0.00537723
$392$		−	162.387i		−	0.414253i
$393$	261.012	+	163.642i	0.664153	+	0.416392i
$394$	−251.632			−0.638661
$395$		−	262.074i		−	0.663480i
$396$	−233.471	+	113.007i	−0.589573	+	0.285372i
$397$	−106.021			−0.267055			−0.133528	−	0.991045i	$-0.542631\pi$
$397$	−106.021			−0.267055			−0.133528	+	0.991045i	$0.542631\pi$
$398$		−	328.300i		−	0.824875i
$399$	−501.510	+	799.916i	−1.25692	+	2.00480i
$400$	−20.0000			−0.0500000
$401$			594.192i			1.48178i	0.671629	+	0.740888i	$0.265595\pi$
$401$			594.192i			1.48178i	−0.671629	+	0.740888i	$0.734405\pi$
$402$	−57.4554	−	36.0218i	−0.142924	−	0.0896065i
$403$	551.492			1.36847
$404$			195.829i			0.484725i
$405$	−142.055	−	112.362i	−0.350754	−	0.277438i
$406$	−344.531			−0.848597
$407$			56.9728i			0.139982i
$408$	1.97600	−	3.15175i	0.00484313	−	0.00772487i
$409$	152.159			0.372028			0.186014	−	0.982547i	$-0.440443\pi$
$409$	152.159			0.372028			0.186014	+	0.982547i	$0.440443\pi$
$410$		−	2.83911i		−	0.00692466i
$411$	161.950	+	101.535i	0.394039	+	0.247044i
$412$	−198.952			−0.482894
$413$		−	451.357i		−	1.09287i
$414$	26.5942	+	54.9431i	0.0642372	+	0.132713i
$415$	161.839			0.389974
$416$			82.5094i			0.198340i
$417$	−316.953	+	505.544i	−0.760078	+	1.21234i
$418$	−621.722			−1.48737
$419$			156.542i			0.373608i	0.982397	+	0.186804i	$0.0598130\pi$
$419$			156.542i			0.373608i	−0.982397	+	0.186804i	$0.940187\pi$
$420$	117.259	+	73.5159i	0.279188	+	0.175038i
$421$	−407.584			−0.968134			−0.484067	−	0.875031i	$-0.660841\pi$
$421$	−407.584			−0.968134			−0.484067	+	0.875031i	$0.660841\pi$
$422$			339.605i			0.804751i
$423$	323.904	−	156.780i	0.765731	−	0.370638i
$424$	−189.758			−0.447542
$425$			2.19200i			0.00515766i
$426$	−73.7367	+	117.611i	−0.173091	+	0.276083i
$427$	−713.460			−1.67087
$428$		−	310.709i		−	0.725956i
$429$	−534.234	−	334.940i	−1.24530	−	0.780745i
$430$	150.219			0.349346
$431$		−	439.199i		−	1.01902i	−0.860464	−	0.509511i	$-0.829826\pi$
$431$		−	439.199i		−	1.01902i	0.860464	−	0.509511i	$-0.170174\pi$
$432$	107.357	+	11.7714i	0.248511	+	0.0272485i
$433$	−27.2770			−0.0629954			−0.0314977	−	0.999504i	$-0.510028\pi$
$433$	−27.2770			−0.0629954			−0.0314977	+	0.999504i	$0.510028\pi$
$434$			551.597i			1.27096i
$435$	84.1533	−	134.226i	0.193456	−	0.308565i
$436$	−89.6654			−0.205655
$437$			146.311i			0.334808i
$438$	492.220	+	308.599i	1.12379	+	0.704563i
$439$	−230.229			−0.524441			−0.262220	−	0.965008i	$-0.584455\pi$
$439$	−230.229			−0.524441			−0.262220	+	0.965008i	$0.584455\pi$
$440$			91.1377i			0.207131i
$441$	−225.121	−	465.095i	−0.510478	−	1.05464i
$442$	9.04305			0.0204594
$443$		−	396.205i		−	0.894369i	−0.894442	−	0.447184i	$-0.852427\pi$
$443$		−	396.205i		−	0.894369i	0.894442	−	0.447184i	$-0.147573\pi$
$444$	12.6008	−	20.0985i	0.0283802	−	0.0452669i
$445$	−108.943			−0.244816
$446$		−	60.9461i		−	0.136650i
$447$	−196.148	−	122.975i	−0.438809	−	0.275113i
$448$	−82.5252			−0.184208
$449$			256.272i			0.570762i	0.958414	+	0.285381i	$0.0921202\pi$
$449$			256.272i			0.570762i	−0.958414	+	0.285381i	$0.907880\pi$
$450$	−57.2822	+	27.7264i	−0.127294	+	0.0616142i
$451$	−12.9375			−0.0286863
$452$		−	361.115i		−	0.798927i
$453$	195.809	−	312.319i	0.432250	−	0.689445i
$454$	369.394			0.813643
$455$			336.442i			0.739433i
$456$	219.327	+	137.508i	0.480981	+	0.301553i
$457$	0.112362			0.000245868			0.000122934	−	1.00000i	$-0.499961\pi$
$457$	0.112362			0.000245868			0.000122934		1.00000i	$0.499961\pi$
$458$			434.004i			0.947608i
$459$	1.29014	−	11.7663i	0.00281077	−	0.0256347i
$460$	21.4476			0.0466252
$461$		−	61.9220i		−	0.134321i	−0.997742	−	0.0671606i	$-0.978606\pi$
$461$		−	61.9220i		−	0.134321i	0.997742	−	0.0671606i	$-0.0213940\pi$
$462$	335.004	−	534.336i	0.725116	−	1.15657i
$463$	−327.777			−0.707941			−0.353971	−	0.935257i	$-0.615169\pi$
$463$	−327.777			−0.707941			−0.353971	+	0.935257i	$0.615169\pi$
$464$			94.4662i			0.203591i
$465$	−214.897	−	134.730i	−0.462144	−	0.289742i
$466$	−20.2276			−0.0434070
$467$		−	686.322i		−	1.46964i	−0.678262	−	0.734820i	$-0.737267\pi$
$467$		−	686.322i		−	1.46964i	0.678262	−	0.734820i	$-0.262733\pi$
$468$	114.384	+	236.316i	0.244411	+	0.504949i
$469$	164.884			0.351564
$470$		−	126.439i		−	0.269020i
$471$	−302.999	+	483.288i	−0.643309	+	1.02609i
$472$	−123.757			−0.262196
$473$		−	684.529i		−	1.44721i
$474$	421.298	+	264.134i	0.888815	+	0.557245i
$475$	−152.540			−0.321136
$476$			9.04478i			0.0190016i
$477$	−543.487	+	263.065i	−1.13939	+	0.551499i
$478$	241.822			0.505904
$479$			130.191i			0.271798i	0.990723	+	0.135899i	$0.0433922\pi$
$479$			130.191i			0.271798i	−0.990723	+	0.135899i	$0.956608\pi$
$480$	20.1572	−	32.1510i	0.0419941	−	0.0669813i
$481$	57.6671			0.119890
$482$			292.429i			0.606700i
$483$	−125.746	−	78.8370i	−0.260344	−	0.163224i
$484$	173.304			0.358067
$485$			286.991i			0.591734i
$486$	323.800	−	115.116i	0.666255	−	0.236864i
$487$	138.291			0.283966			0.141983	−	0.989869i	$-0.454652\pi$
$487$	138.291			0.283966			0.141983	+	0.989869i	$0.454652\pi$
$488$			195.622i			0.400865i
$489$	−65.4654	+	104.418i	−0.133876	+	0.213534i
$490$	−181.554			−0.370519
$491$			642.931i			1.30943i	0.755875	+	0.654716i	$0.227212\pi$
$491$			642.931i			1.30943i	−0.755875	+	0.654716i	$0.772788\pi$
$492$	4.56402	+	2.86142i	0.00927645	+	0.00581590i
$493$	10.3535			0.0210010
$494$			629.299i			1.27388i
$495$	126.346	+	261.028i	0.255244	+	0.527330i
$496$	151.241			0.304922
$497$		−	337.517i		−	0.679108i
$498$	−163.111	+	260.165i	−0.327533	+	0.522420i
$499$	139.535			0.279630			0.139815	−	0.990178i	$-0.455349\pi$
$499$	139.535			0.279630			0.139815	+	0.990178i	$0.455349\pi$
$500$			22.3607i			0.0447214i
$501$	−440.536	−	276.195i	−0.879314	−	0.551288i
$502$	408.525			0.813794
$503$			887.770i			1.76495i	0.470358	+	0.882475i	$0.344125\pi$
$503$			887.770i			1.76495i	−0.470358	+	0.882475i	$0.655875\pi$
$504$	−236.361	+	114.406i	−0.468970	+	0.226996i
$505$	218.943			0.433551
$506$		−	97.7343i		−	0.193151i
$507$	−69.7088	+	111.187i	−0.137493	+	0.219303i
$508$	361.595			0.711800
$509$		−	436.679i		−	0.857916i	−0.903325	−	0.428958i	$-0.858881\pi$
$509$		−	436.679i		−	0.857916i	0.903325	−	0.428958i	$-0.141119\pi$
$510$	−3.52376	−	2.20923i	−0.00690933	−	0.00433183i
$511$	−1412.56			−2.76430
$512$			22.6274i			0.0441942i
$513$	818.808	+	89.7800i	1.59612	+	0.175010i
$514$	−542.204			−1.05487
$515$			222.435i			0.431913i
$516$	−151.399	+	241.484i	−0.293409	+	0.467992i
$517$	−576.170			−1.11445
$518$			57.6781i			0.111348i
$519$	−127.544	−	79.9643i	−0.245750	−	0.154074i
$520$	92.2483			0.177401
$521$			188.925i			0.362620i	0.983426	+	0.181310i	$0.0580338\pi$
$521$			188.925i			0.362620i	−0.983426	+	0.181310i	$0.941966\pi$
$522$	130.960	+	270.561i	0.250882	+	0.518317i
$523$	193.538			0.370053			0.185027	−	0.982733i	$-0.440763\pi$
$523$	193.538			0.370053			0.185027	+	0.982733i	$0.440763\pi$
$524$			205.379i			0.391944i
$525$	82.1933	−	131.100i	0.156559	−	0.249713i
$526$	302.778			0.575624
$527$		−	16.5761i		−	0.0314537i
$528$	−146.509	−	91.8540i	−0.277478	−	0.173966i
$529$	−23.0000			−0.0434783
$530$			212.156i			0.400294i
$531$	−354.453	+	171.566i	−0.667519	+	0.323100i
$532$	−629.419			−1.18312
$533$			13.0952i			0.0245688i
$534$	109.799	−	175.132i	0.205617	−	0.327962i
$535$	−347.383			−0.649314
$536$		−	45.2091i		−	0.0843453i
$537$	−488.309	−	306.147i	−0.909328	−	0.570106i
$538$	355.001			0.659853
$539$			827.323i			1.53492i
$540$	13.1608	−	120.028i	0.0243718	−	0.222275i
$541$	−224.735			−0.415407			−0.207704	−	0.978192i	$-0.566599\pi$
$541$	−224.735			−0.415407			−0.207704	+	0.978192i	$0.566599\pi$
$542$			323.339i			0.596567i
$543$	−141.912	+	226.352i	−0.261348	+	0.416855i
$544$	2.47997			0.00455877
$545$			100.249i			0.183943i
$546$	−540.848	−	339.086i	−0.990563	−	0.621037i
$547$	926.193			1.69322			0.846611	−	0.532212i	$-0.178639\pi$
$547$	926.193			1.69322			0.846611	+	0.532212i	$0.178639\pi$
$548$			127.431i			0.232539i
$549$	271.195	+	560.283i	0.493979	+	1.02055i
$550$	101.895			0.185264
$551$			720.493i			1.30761i
$552$	−21.6162	+	34.4781i	−0.0391597	+	0.0624604i
$553$	−1209.03			−2.18631
$554$		−	720.695i		−	1.30089i
$555$	−22.4708	−	14.0882i	−0.0404880	−	0.0253841i
$556$	−397.791			−0.715451
$557$			367.940i			0.660575i	0.943880	+	0.330288i	$0.107146\pi$
$557$			367.940i			0.660575i	−0.943880	+	0.330288i	$0.892854\pi$
$558$	433.171	−	209.669i	0.776293	−	0.375750i
$559$	−692.871			−1.23948
$560$			92.2660i			0.164761i
$561$	−10.0672	+	16.0574i	−0.0179451	+	0.0286228i
$562$	−23.4413			−0.0417105
$563$		−	480.071i		−	0.852701i	−0.904558	−	0.426351i	$-0.859799\pi$
$563$		−	480.071i		−	0.852701i	0.904558	−	0.426351i	$-0.140201\pi$
$564$	203.258	+	127.433i	0.360386	+	0.225945i
$565$	−403.739			−0.714582
$566$		−	177.883i		−	0.314281i
$567$	−518.360	+	655.344i	−0.914216	+	1.15581i
$568$	−92.5431			−0.162928
$569$		−	723.376i		−	1.27131i	−0.771973	−	0.635655i	$-0.780730\pi$
$569$		−	723.376i		−	1.27131i	0.771973	−	0.635655i	$-0.219270\pi$
$570$	153.739	−	245.216i	0.269717	−	0.430203i
$571$	−811.310			−1.42086			−0.710429	−	0.703769i	$-0.751499\pi$
$571$	−811.310			−1.42086			−0.710429	+	0.703769i	$0.751499\pi$
$572$		−	420.365i		−	0.734904i
$573$	734.384	+	460.424i	1.28165	+	0.803533i
$574$	−13.0977			−0.0228182
$575$		−	23.9792i		−	0.0417029i
$576$	31.3688	+	64.8074i	0.0544598	+	0.112513i
$577$	110.169			0.190934			0.0954672	−	0.995433i	$-0.469566\pi$
$577$	110.169			0.190934			0.0954672	+	0.995433i	$0.469566\pi$
$578$			408.436i			0.706637i
$579$	502.266	−	801.122i	0.867471	−	1.38363i
$580$	105.616			0.182097
$581$		−	746.613i		−	1.28505i
$582$	−461.353	−	289.246i	−0.792702	−	0.496987i
$583$	966.770			1.65827
$584$			387.306i			0.663195i
$585$	264.209	−	127.886i	0.451640	−	0.218608i
$586$	74.4365			0.127025
$587$			758.107i			1.29149i	0.763551	+	0.645747i	$0.223454\pi$
$587$			758.107i			1.29149i	−0.763551	+	0.645747i	$0.776546\pi$
$588$	182.981	−	291.858i	0.311193	−	0.496357i
$589$	1153.52			1.95843
$590$			138.364i			0.234516i
$591$	−452.258	−	283.544i	−0.765242	−	0.479771i
$592$	15.8146			0.0267139
$593$			634.205i			1.06949i	0.845015	+	0.534743i	$0.179591\pi$
$593$			634.205i			1.06949i	−0.845015	+	0.534743i	$0.820409\pi$
$594$	−546.955	−	59.9722i	−0.920800	−	0.100963i
$595$	10.1124			0.0169956
$596$		−	154.340i		−	0.258960i
$597$	369.935	−	590.053i	0.619657	−	0.988363i
$598$	−98.9253			−0.165427
$599$		−	346.330i		−	0.578180i	−0.957302	−	0.289090i	$-0.906647\pi$
$599$		−	346.330i		−	0.578180i	0.957302	−	0.289090i	$-0.0933527\pi$
$600$	−35.9459	−	22.5364i	−0.0599099	−	0.0375607i
$601$	−746.606			−1.24227			−0.621137	−	0.783702i	$-0.713329\pi$
$601$	−746.606			−1.24227			−0.621137	+	0.783702i	$0.713329\pi$
$602$		−	693.003i		−	1.15117i
$603$	−62.6742	−	129.484i	−0.103937	−	0.214733i
$604$	245.750			0.406871
$605$		−	193.760i		−	0.320265i
$606$	−220.664	+	351.963i	−0.364132	+	0.580797i
$607$	907.294			1.49472			0.747359	−	0.664420i	$-0.231321\pi$
$607$	907.294			1.49472			0.747359	+	0.664420i	$0.231321\pi$
$608$			172.579i			0.283847i
$609$	−619.224	−	388.224i	−1.01679	−	0.637478i
$610$	218.712			0.358545
$611$			583.191i			0.954486i
$612$	7.10290	−	3.43803i	0.0116061	−	0.00561770i
$613$	−361.864			−0.590316			−0.295158	−	0.955448i	$-0.595372\pi$
$613$	−361.864			−0.590316			−0.295158	+	0.955448i	$0.595372\pi$
$614$		−	825.906i		−	1.34512i
$615$	3.19917	−	5.10272i	0.00520190	−	0.00829711i
$616$	420.446			0.682541
$617$			3.49792i			0.00566925i	0.999996	+	0.00283462i	$0.000902290\pi$
$617$			3.49792i			0.00566925i	−0.999996	+	0.00283462i	$0.999098\pi$
$618$	−357.576	−	224.183i	−0.578602	−	0.362756i
$619$	48.8766			0.0789606			0.0394803	−	0.999220i	$-0.487430\pi$
$619$	48.8766			0.0789606			0.0394803	+	0.999220i	$0.487430\pi$
$620$		−	169.093i		−	0.272730i
$621$	−14.1134	+	128.716i	−0.0227268	+	0.207272i
$622$	866.582			1.39322
$623$			502.588i			0.806722i
$624$	−92.9733	+	148.294i	−0.148996	+	0.237651i
$625$	25.0000			0.0400000
$626$		−	633.847i		−	1.01253i
$627$	−1117.42	−	700.570i	−1.78217	−	1.11734i
$628$	−380.278			−0.605538
$629$		−	1.73329i		−	0.00275562i
$630$	127.910	+	264.260i	0.203032	+	0.419460i
$631$	1130.12			1.79101			0.895503	−	0.445056i	$-0.146816\pi$
$631$	1130.12			1.79101			0.895503	+	0.445056i	$0.146816\pi$
$632$			331.501i			0.524527i
$633$	−382.674	+	610.370i	−0.604540	+	0.964250i
$634$	531.251			0.837935
$635$		−	404.275i		−	0.636654i
$636$	−341.051	−	213.823i	−0.536244	−	0.336200i
$637$	837.405			1.31461
$638$		−	481.282i		−	0.754360i
$639$	−265.053	+	128.294i	−0.414794	+	0.200773i
$640$	25.2982			0.0395285
$641$		−	1010.87i		−	1.57702i	−0.615023	−	0.788510i	$-0.710853\pi$
$641$		−	1010.87i		−	1.57702i	0.615023	−	0.788510i	$-0.289147\pi$
$642$	350.113	−	558.436i	0.545348	−	0.869838i
$643$	−979.174			−1.52282			−0.761410	−	0.648270i	$-0.775493\pi$
$643$	−979.174			−1.52282			−0.761410	+	0.648270i	$0.775493\pi$
$644$		−	98.9442i		−	0.153640i
$645$	269.987	+	169.269i	0.418585	+	0.262433i
$646$	18.9147			0.0292797
$647$		−	426.288i		−	0.658869i	−0.944178	−	0.329435i	$-0.893142\pi$
$647$		−	426.288i		−	0.658869i	0.944178	−	0.329435i	$-0.106858\pi$
$648$	179.687	+	142.128i	0.277295	+	0.219334i
$649$	630.510			0.971510
$650$		−	103.137i		−	0.158672i
$651$	−621.551	+	991.383i	−0.954763	+	1.52286i
$652$	−82.1622			−0.126016
$653$		−	903.600i		−	1.38377i	−0.722009	−	0.691884i	$-0.756781\pi$
$653$		−	903.600i		−	1.38377i	0.722009	−	0.691884i	$-0.243219\pi$
$654$	−161.155	−	101.037i	−0.246415	−	0.154491i
$655$	229.621			0.350566
$656$			3.59122i			0.00547442i
$657$	536.930	+	1109.29i	0.817245	+	1.68841i
$658$	−583.302			−0.886478
$659$		−	1085.47i		−	1.64715i	−0.567210	−	0.823573i	$-0.691977\pi$
$659$		−	1085.47i		−	1.64715i	0.567210	−	0.823573i	$-0.308023\pi$
$660$	−102.696	+	163.802i	−0.155600	+	0.248184i
$661$	−180.375			−0.272883			−0.136441	−	0.990648i	$-0.543567\pi$
$661$	−180.375			−0.272883			−0.136441	+	0.990648i	$0.543567\pi$
$662$			363.702i			0.549398i
$663$	16.2530	+	10.1899i	0.0245144	+	0.0153694i
$664$	−204.712			−0.308302
$665$			703.712i			1.05821i
$666$	45.2948	−	21.9241i	0.0680103	−	0.0329191i
$667$	−113.261			−0.169807
$668$		−	346.638i		−	0.518920i
$669$	68.6753	−	109.538i	0.102654	−	0.163734i
$670$	−50.5453			−0.0754408
$671$		−	996.647i		−	1.48532i
$672$	−148.322	−	92.9911i	−0.220718	−	0.138380i
$673$	1106.01			1.64341			0.821704	−	0.569914i	$-0.193024\pi$
$673$	1106.01			1.64341			0.821704	+	0.569914i	$0.193024\pi$
$674$			879.655i			1.30513i
$675$	−134.196	−	14.7142i	−0.198808	−	0.0217988i
$676$	−87.4879			−0.129420
$677$			1216.03i			1.79621i	0.439781	+	0.898105i	$0.355056\pi$
$677$			1216.03i			1.79621i	−0.439781	+	0.898105i	$0.644944\pi$
$678$	406.912	−	649.031i	0.600165	−	0.957273i
$679$	1323.97			1.94989
$680$		−	2.77269i		−	0.00407749i
$681$	663.910	+	416.240i	0.974905	+	0.611220i
$682$	−770.537			−1.12982
$683$		−	737.028i		−	1.07910i	−0.841952	−	0.539552i	$-0.818594\pi$
$683$		−	737.028i		−	1.07910i	0.841952	−	0.539552i	$-0.181406\pi$
$684$	239.250	+	494.285i	0.349780	+	0.722639i
$685$	142.472			0.207989
$686$			122.727i			0.178902i
$687$	−489.045	+	780.035i	−0.711856	+	1.13542i
$688$	−190.013			−0.276182
$689$		−	978.551i		−	1.42025i
$690$	38.5477	+	24.1676i	0.0558663	+	0.0350255i
$691$	507.773			0.734838			0.367419	−	0.930055i	$-0.380241\pi$
$691$	507.773			0.734838			0.367419	+	0.930055i	$0.380241\pi$
$692$		−	100.359i		−	0.145027i
$693$	1204.20	−	582.872i	1.73766	−	0.841085i
$694$	−71.1502			−0.102522
$695$			444.743i			0.639919i
$696$	−106.446	+	169.784i	−0.152940	+	0.243942i
$697$	0.393599			0.000564704
$698$			678.782i			0.972466i
$699$	−36.3551	−	22.7929i	−0.0520101	−	0.0326079i
$700$	103.156			0.147366
$701$		−	891.513i		−	1.27177i	−0.771783	−	0.635886i	$-0.780635\pi$
$701$		−	891.513i		−	1.27177i	0.771783	−	0.635886i	$-0.219365\pi$
$702$	−60.7030	+	553.621i	−0.0864715	+	0.788633i
$703$	120.618			0.171576
$704$		−	115.281i		−	0.163752i
$705$	142.474	−	227.249i	0.202091	−	0.322339i
$706$	−587.085			−0.831565
$707$		−	1010.05i		−	1.42864i
$708$	−222.428	−	139.452i	−0.314163	−	0.196966i
$709$	668.547			0.942944			0.471472	−	0.881881i	$-0.343723\pi$
$709$	668.547			0.942944			0.471472	+	0.881881i	$0.343723\pi$
$710$			103.466i			0.145727i
$711$	459.566	+	949.455i	0.646366	+	1.33538i
$712$	137.804			0.193544
$713$			181.332i			0.254322i
$714$	−10.1918	+	16.2562i	−0.0142743	+	0.0227677i
$715$	−469.983			−0.657318
$716$		−	384.229i		−	0.536633i
$717$	434.626	+	272.490i	0.606173	+	0.380042i
$718$	−4.98629			−0.00694470
$719$			501.263i			0.697167i	0.937278	+	0.348583i	$0.113337\pi$
$719$			501.263i			0.697167i	−0.937278	+	0.348583i	$0.886663\pi$
$720$	72.4569	−	35.0714i	0.100635	−	0.0487103i
$721$	1026.16			1.42325
$722$			805.728i			1.11597i
$723$	−329.515	+	525.582i	−0.455761	+	0.726946i
$724$	−178.106			−0.246003
$725$		−	118.083i		−	0.162873i
$726$	311.479	+	195.283i	0.429035	+	0.268985i
$727$	−462.615			−0.636334			−0.318167	−	0.948035i	$-0.603067\pi$
$727$	−462.615			−0.636334			−0.318167	+	0.948035i	$0.603067\pi$
$728$		−	425.569i		−	0.584573i
$729$	711.679	+	157.967i	0.976241	+	0.216689i
$730$	433.021			0.593180
$731$			20.8255i			0.0284890i
$732$	−220.431	+	351.591i	−0.301135	+	0.480316i
$733$	445.512			0.607792			0.303896	−	0.952705i	$-0.401712\pi$
$733$	445.512			0.607792			0.303896	+	0.952705i	$0.401712\pi$
$734$		−	91.5574i		−	0.124738i
$735$	−326.307	−	204.579i	−0.443956	−	0.278339i
$736$	−27.1293			−0.0368605
$737$			230.329i			0.312523i
$738$	4.97858	+	10.2857i	0.00674604	+	0.0139372i
$739$	−861.893			−1.16630			−0.583148	−	0.812366i	$-0.698179\pi$
$739$	−861.893			−1.16630			−0.583148	+	0.812366i	$0.698179\pi$
$740$		−	17.6813i		−	0.0238937i
$741$	−709.107	+	1131.04i	−0.956959	+	1.52637i
$742$	978.738			1.31905
$743$		−	1095.60i		−	1.47456i	−0.675587	−	0.737280i	$-0.736110\pi$
$743$		−	1095.60i		−	1.47456i	0.675587	−	0.737280i	$-0.263890\pi$
$744$	271.825	+	170.422i	0.365357	+	0.229062i
$745$	−172.557			−0.231621
$746$		−	296.782i		−	0.397831i
$747$	−586.319	+	283.797i	−0.784898	+	0.379915i
$748$	−12.6348			−0.0168915
$749$			1602.58i			2.13963i
$750$	−25.1965	+	40.1888i	−0.0335953	+	0.0535850i
$751$	1272.16			1.69396			0.846979	−	0.531626i	$-0.178419\pi$
$751$	1272.16			1.69396			0.846979	+	0.531626i	$0.178419\pi$
$752$			159.935i			0.212679i
$753$	734.240	+	460.334i	0.975086	+	0.611333i
$754$	−487.147			−0.646083
$755$		−	274.757i		−	0.363916i
$756$	−553.726	−	60.7146i	−0.732442	−	0.0803103i
$757$	−361.418			−0.477435			−0.238718	−	0.971089i	$-0.576727\pi$
$757$	−361.418			−0.477435			−0.238718	+	0.971089i	$0.576727\pi$
$758$			38.9980i			0.0514486i
$759$	110.129	−	175.658i	0.145098	−	0.231433i
$760$	192.949			0.253881
$761$		−	917.813i		−	1.20606i	−0.797718	−	0.603031i	$-0.793960\pi$
$761$		−	917.813i		−	1.20606i	0.797718	−	0.603031i	$-0.206040\pi$
$762$	649.893	+	407.452i	0.852878	+	0.534714i
$763$	462.478			0.606132
$764$			577.854i			0.756354i
$765$	−3.84383	−	7.94129i	−0.00502462	−	0.0103808i
$766$	885.447			1.15594
$767$		−	638.194i		−	0.832065i
$768$	−25.4970	+	40.6682i	−0.0331993	+	0.0529534i
$769$	692.243			0.900186			0.450093	−	0.892982i	$-0.351391\pi$
$769$	692.243			0.900186			0.450093	+	0.892982i	$0.351391\pi$
$770$		−	470.072i		−	0.610484i
$771$	−974.502	−	610.967i	−1.26395	−	0.792434i
$772$	630.368			0.816539
$773$			996.702i			1.28939i	0.764438	+	0.644697i	$0.223017\pi$
$773$			996.702i			1.28939i	−0.764438	+	0.644697i	$0.776983\pi$
$774$	−544.218	+	263.419i	−0.703125	+	0.340334i
$775$	−189.052			−0.243938
$776$		−	363.018i		−	0.467807i
$777$	−64.9928	+	103.665i	−0.0836459	+	0.133416i
$778$	303.148			0.389650
$779$			27.3902i			0.0351607i
$780$	165.798	+	103.947i	0.212561	+	0.133266i
$781$	471.484			0.603693
$782$			2.97338i			0.00380228i
$783$	−69.4997	+	633.848i	−0.0887608	+	0.809512i
$784$	229.650			0.292921
$785$			425.163i			0.541610i
$786$	−231.425	+	369.127i	−0.294434	+	0.469627i
$787$	−557.004			−0.707756			−0.353878	−	0.935292i	$-0.615137\pi$
$787$	−557.004			−0.707756			−0.353878	+	0.935292i	$0.615137\pi$
$788$		−	355.862i		−	0.451601i
$789$	544.183	+	341.177i	0.689712	+	0.432417i
$790$	370.629			0.469151
$791$			1862.57i			2.35470i
$792$	−159.816	−	330.178i	−0.201788	−	0.416891i
$793$	−1008.79			−1.27212
$794$		−	149.936i		−	0.188837i
$795$	−239.062	+	381.307i	−0.300706	+	0.479631i
$796$	464.287			0.583275
$797$		−	592.997i		−	0.744037i	−0.928225	−	0.372018i	$-0.878666\pi$
$797$		−	592.997i		−	0.744037i	0.928225	−	0.372018i	$-0.121334\pi$
$798$	−1131.25	−	709.242i	−1.41761	−	0.888774i
$799$	17.5289			0.0219385
$800$		−	28.2843i		−	0.0353553i
$801$	394.685	−	191.040i	0.492740	−	0.238502i
$802$	−840.314			−1.04777
$803$		−	1973.23i		−	2.45732i
$804$	50.9425	−	81.2542i	0.0633614	−	0.101062i
$805$	−110.623			−0.137420
$806$			779.927i			0.967651i
$807$	638.042	+	400.022i	0.790634	+	0.495690i
$808$	−276.944			−0.342752
$809$		−	1262.86i		−	1.56101i	−0.625149	−	0.780505i	$-0.714962\pi$
$809$		−	1262.86i		−	1.56101i	0.625149	−	0.780505i	$-0.285038\pi$
$810$	158.904	−	200.897i	0.196178	−	0.248021i
$811$	44.5761			0.0549643			0.0274822	−	0.999622i	$-0.491251\pi$
$811$	44.5761			0.0549643			0.0274822	+	0.999622i	$0.491251\pi$
$812$		−	487.240i		−	0.600049i
$813$	−364.345	+	581.137i	−0.448149	+	0.714806i
$814$	−80.5717			−0.0989824
$815$			91.8601i			0.112712i
$816$	4.45724	+	2.79448i	0.00546231	+	0.00342461i
$817$	−1449.23			−1.77384
$818$			215.186i			0.263063i
$819$	−589.975	−	1218.88i	−0.720360	−	1.48825i
$820$	4.01511			0.00489647
$821$			1506.42i			1.83486i	0.397900	+	0.917429i	$0.369739\pi$
$821$			1506.42i			1.83486i	−0.397900	+	0.917429i	$0.630261\pi$
$822$	−143.592	+	229.032i	−0.174686	+	0.278627i
$823$	387.143			0.470404			0.235202	−	0.971946i	$-0.424425\pi$
$823$	387.143			0.470404			0.235202	+	0.971946i	$0.424425\pi$
$824$		−	281.361i		−	0.341457i
$825$	183.136	+	114.817i	0.221983	+	0.139173i
$826$	638.315			0.772779
$827$		−	968.662i		−	1.17130i	−0.810565	−	0.585648i	$-0.800840\pi$
$827$		−	968.662i		−	1.17130i	0.810565	−	0.585648i	$-0.199160\pi$
$828$	−77.7013	+	37.6099i	−0.0938422	+	0.0454226i
$829$	308.190			0.371761			0.185880	−	0.982572i	$-0.440486\pi$
$829$	308.190			0.371761			0.185880	+	0.982572i	$0.440486\pi$
$830$			228.875i			0.275754i
$831$	812.094	−	1295.30i	0.977249	−	1.55873i
$832$	−116.686			−0.140248
$833$		−	25.1697i		−	0.0302158i
$834$	−714.948	−	448.239i	−0.857252	−	0.537456i
$835$	−387.554			−0.464136
$836$		−	879.248i		−	1.05173i
$837$	1014.80	+	111.270i	1.21242	+	0.132939i
$838$	−221.384			−0.264181
$839$			244.724i			0.291686i	0.989308	+	0.145843i	$0.0465894\pi$
$839$			244.724i			0.291686i	−0.989308	+	0.145843i	$0.953411\pi$
$840$	−103.967	+	165.829i	−0.123770	+	0.197416i
$841$	283.259			0.336812
$842$		−	576.411i		−	0.684574i
$843$	−42.1310	−	26.4141i	−0.0499774	−	0.0313335i
$844$	−480.274			−0.569045
$845$			97.8144i			0.115757i
$846$	221.720	+	458.070i	0.262081	+	0.541454i
$847$	−893.873			−1.05534
$848$		−	268.358i		−	0.316460i
$849$	200.442	−	319.709i	0.236092	−	0.376571i
$850$	−3.09996			−0.00364701
$851$			18.9611i			0.0222809i
$852$	−166.327	−	104.279i	−0.195220	−	0.122394i
$853$	−326.235			−0.382455			−0.191228	−	0.981546i	$-0.561247\pi$
$853$	−326.235			−0.382455			−0.191228	+	0.981546i	$0.561247\pi$
$854$		−	1008.98i		−	1.18148i
$855$	552.628	−	267.489i	0.646348	−	0.312853i
$856$	439.409			0.513328
$857$			112.667i			0.131467i	0.997837	+	0.0657333i	$0.0209387\pi$
$857$			112.667i			0.131467i	−0.997837	+	0.0657333i	$0.979061\pi$
$858$	473.676	−	755.521i	0.552070	−	0.880561i
$859$	1044.12			1.21551			0.607753	−	0.794126i	$-0.292071\pi$
$859$	1044.12			1.21551			0.607753	+	0.794126i	$0.292071\pi$
$860$			212.441i			0.247025i
$861$	−23.5404	−	14.7587i	−0.0273407	−	0.0171414i
$862$	621.121			0.720558
$863$		−	209.566i		−	0.242834i	−0.992602	−	0.121417i	$-0.961256\pi$
$863$		−	209.566i		−	0.242834i	0.992602	−	0.121417i	$-0.0387438\pi$
$864$	−16.6472	+	151.825i	−0.0192676	+	0.175724i
$865$	−112.205			−0.129716
$866$		−	38.5755i		−	0.0445445i
$867$	−460.234	+	734.081i	−0.530835	+	0.846690i
$868$	−780.076			−0.898705
$869$		−	1688.92i		−	1.94352i
$870$	189.824	+	119.011i	0.218188	+	0.136794i
$871$	233.136			0.267665
$872$		−	126.806i		−	0.145420i
$873$	−503.259	−	1039.72i	−0.576470	−	1.19098i
$874$	−206.915			−0.236745
$875$		−	115.332i		−	0.131809i
$876$	−436.424	+	696.104i	−0.498201	+	0.794639i
$877$	136.662			0.155829			0.0779146	−	0.996960i	$-0.475174\pi$
$877$	136.662			0.155829			0.0779146	+	0.996960i	$0.475174\pi$
$878$		−	325.594i		−	0.370836i
$879$	133.784	+	83.8765i	0.152201	+	0.0954227i
$880$	−128.888			−0.146464
$881$		−	778.020i		−	0.883110i	−0.897234	−	0.441555i	$-0.854427\pi$
$881$		−	778.020i		−	0.883110i	0.897234	−	0.441555i	$-0.145573\pi$
$882$	657.743	−	318.369i	0.745741	−	0.360962i
$883$	1228.01			1.39073			0.695365	−	0.718657i	$-0.255243\pi$
$883$	1228.01			1.39073			0.695365	+	0.718657i	$0.255243\pi$
$884$			12.7888i			0.0144670i
$885$	−155.912	+	248.682i	−0.176171	+	0.280996i
$886$	560.319			0.632414
$887$		−	113.117i		−	0.127527i	−0.997965	−	0.0637637i	$-0.979690\pi$
$887$		−	113.117i		−	0.127527i	0.997965	−	0.0637637i	$-0.0203104\pi$
$888$	28.4236	+	17.8203i	0.0320086	+	0.0200679i
$889$	−1865.04			−2.09791
$890$		−	154.069i		−	0.173111i
$891$	−915.463	−	724.108i	−1.02746	−	0.812692i
$892$	86.1908			0.0966265
$893$			1219.82i			1.36598i
$894$	173.913	−	277.395i	0.194534	−	0.310285i
$895$	−429.581			−0.479979
$896$		−	116.708i		−	0.130255i
$897$	−177.798	−	111.471i	−0.198214	−	0.124271i
$898$	−362.424			−0.403590
$899$			892.949i			0.993269i
$900$	−39.2110	−	81.0092i	−0.0435678	−	0.0900103i
$901$	−29.4121			−0.0326439
$902$		−	18.2964i		−	0.0202843i
$903$	780.890	−	1245.53i	0.864773	−	1.37933i
$904$	510.694			0.564927
$905$			199.129i			0.220032i
$906$	441.685	+	276.916i	0.487511	+	0.305647i
$907$	837.639			0.923527			0.461763	−	0.887003i	$-0.347217\pi$
$907$	837.639			0.923527			0.461763	+	0.887003i	$0.347217\pi$
$908$			522.402i			0.575332i
$909$	−793.198	+	383.933i	−0.872605	+	0.422368i
$910$	−475.801			−0.522858
$911$			897.889i			0.985608i	0.870140	+	0.492804i	$0.164028\pi$
$911$			897.889i			0.985608i	−0.870140	+	0.492804i	$0.835972\pi$
$912$	−194.466	+	310.176i	−0.213230	+	0.340105i
$913$	1042.96			1.14234
$914$			0.158904i			0.000173855i
$915$	393.091	+	246.449i	0.429607	+	0.269344i
$916$	−613.775			−0.670060
$917$		−	1059.31i		−	1.15519i
$918$	16.6401	+	1.82454i	0.0181264	+	0.00198751i
$919$	343.208			0.373458			0.186729	−	0.982411i	$-0.440211\pi$
$919$	343.208			0.373458			0.186729	+	0.982411i	$0.440211\pi$
$920$			30.3315i			0.0329690i
$921$	930.647	−	1484.40i	1.01047	−	1.61172i
$922$	87.5710			0.0949794
$923$		−	477.230i		−	0.517042i
$924$	755.665	+	473.767i	0.817820	+	0.512734i
$925$	−19.7683			−0.0213711
$926$		−	463.546i		−	0.500590i
$927$	−390.056	−	805.848i	−0.420772	−	0.869308i
$928$	−133.595			−0.143960
$929$			164.950i			0.177557i	0.996051	+	0.0887784i	$0.0282963\pi$
$929$			164.950i			0.177557i	−0.996051	+	0.0887784i	$0.971704\pi$
$930$	190.537	−	303.910i	0.204879	−	0.326785i
$931$	1751.54			1.88135
$932$		−	28.6062i		−	0.0306934i
$933$	1557.51	+	976.483i	1.66935	+	1.04661i
$934$	970.606			1.03919
$935$			14.1262i			0.0151082i
$936$	−334.201	+	161.764i	−0.357053	+	0.172825i
$937$	378.255			0.403687			0.201844	−	0.979418i	$-0.435307\pi$
$937$	378.255			0.403687			0.201844	+	0.979418i	$0.435307\pi$
$938$			233.181i			0.248593i
$939$	714.231	−	1139.21i	0.760630	−	1.21322i
$940$	178.812			0.190226
$941$			770.511i			0.818822i	0.912350	+	0.409411i	$0.134266\pi$
$941$			770.511i			0.818822i	−0.912350	+	0.409411i	$0.865734\pi$
$942$	−683.472	−	428.505i	−0.725554	−	0.454888i
$943$	−4.30572			−0.00456599
$944$		−	175.018i		−	0.185401i
$945$	−67.8810	+	619.085i	−0.0718317	+	0.655116i
$946$	968.070			1.02333
$947$			112.319i			0.118605i	0.998240	+	0.0593027i	$0.0188877\pi$
$947$			112.319i			0.118605i	−0.998240	+	0.0593027i	$0.981112\pi$
$948$	−373.542	+	595.806i	−0.394032	+	0.628487i
$949$	−1997.28			−2.10461
$950$		−	215.724i		−	0.227078i
$951$	954.815	+	598.624i	1.00401	+	0.629468i
$952$	−12.7912			−0.0134362
$953$		−	1753.44i		−	1.83992i	−0.392013	−	0.919960i	$-0.628221\pi$
$953$		−	1753.44i		−	1.83992i	0.392013	−	0.919960i	$-0.371779\pi$
$954$	−372.030	−	768.607i	−0.389969	−	0.805668i
$955$	646.061			0.676503
$956$			341.988i			0.357728i
$957$	542.318	−	865.006i	0.566686	−	0.903873i
$958$	−184.118			−0.192190
$959$		−	657.268i		−	0.685368i
$960$	45.4684	+	28.5066i	0.0473629	+	0.0296943i
$961$	468.620			0.487638
$962$			81.5536i			0.0847750i
$963$	1258.51	−	609.161i	1.30687	−	0.632566i
$964$	−413.557			−0.429002
$965$		−	704.773i		−	0.730334i
$966$	111.492	−	177.832i	0.115417	−	0.184091i
$967$	−1301.12			−1.34553			−0.672763	−	0.739858i	$-0.734893\pi$
$967$	−1301.12			−1.34553			−0.672763	+	0.739858i	$0.734893\pi$
$968$			245.089i			0.253192i
$969$	33.9953	+	21.3135i	0.0350829	+	0.0219953i
$970$	−405.866			−0.418419
$971$			1222.65i			1.25916i	0.776934	+	0.629582i	$0.216774\pi$
$971$			1222.65i			1.25916i	−0.776934	+	0.629582i	$0.783226\pi$
$972$	162.799	+	457.922i	0.167488	+	0.471113i
$973$	2051.73			2.10867
$974$			195.574i			0.200794i
$975$	116.217	−	185.367i	0.119197	−	0.190120i
$976$	−276.651			−0.283454
$977$			1237.91i			1.26706i	0.773720	+	0.633528i	$0.218394\pi$
$977$			1237.91i			1.26706i	−0.773720	+	0.633528i	$0.781606\pi$
$978$	−147.670	−	92.5820i	−0.150992	−	0.0946646i
$979$	−702.076			−0.717135
$980$		−	256.757i		−	0.261997i
$981$	−175.794	−	363.186i	−0.179198	−	0.370221i
$982$	−909.242			−0.925908
$983$			644.812i			0.655964i	0.944684	+	0.327982i	$0.106368\pi$
$983$			644.812i			0.655964i	−0.944684	+	0.327982i	$0.893632\pi$
$984$	−4.04666	+	6.45449i	−0.00411246	+	0.00655944i
$985$	−397.866			−0.403924
$986$			14.6421i			0.0148500i
$987$	−1048.37	−	657.277i	−1.06218	−	0.665934i
$988$	−889.963			−0.900772
$989$		−	227.818i		−	0.230352i
$990$	−369.150	+	178.680i	−0.372879	+	0.180485i
$991$	1386.21			1.39880			0.699401	−	0.714729i	$-0.253450\pi$
$991$	1386.21			1.39880			0.699401	+	0.714729i	$0.253450\pi$
$992$			213.887i			0.215612i
$993$	−409.826	+	653.680i	−0.412716	+	0.658288i
$994$	477.321			0.480202
$995$		−	519.088i		−	0.521697i
$996$	−367.929	−	230.674i	−0.369407	−	0.231601i
$997$	832.496			0.835001			0.417500	−	0.908677i	$-0.362906\pi$
$997$	832.496			0.835001			0.417500	+	0.908677i	$0.362906\pi$
$998$			197.332i			0.197728i
$999$	106.113	+	11.6350i	0.106219	+	0.0116466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.g.a.461.12	yes	56
3.2	odd	2	inner	690.3.g.a.461.11	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.g.a.461.11	✓	56	3.2	odd	2	inner
690.3.g.a.461.12	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)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(-1.59356 + 2.54176i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-3.59459 - 2.25364i) q^{6} +10.3156 q^{7} -2.82843i q^{8} +(-3.92110 - 8.10092i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(-1.59356 + 2.54176i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-3.59459 - 2.25364i) q^{6} +10.3156 q^{7} -2.82843i q^{8} +(-3.92110 - 8.10092i) q^{9} -3.16228 q^{10} +14.4101i q^{11} +(3.18713 - 5.08352i) q^{12} +14.5857 q^{13} +14.5885i q^{14} +(-5.68355 - 3.56332i) q^{15} +4.00000 q^{16} -0.438401i q^{17} +(11.4564 - 5.54528i) q^{18} +30.5080 q^{19} -4.47214i q^{20} +(-16.4387 + 26.2199i) q^{21} -20.3790 q^{22} +4.79583i q^{23} +(7.18919 + 4.50728i) q^{24} -5.00000 q^{25} +20.6274i q^{26} +(26.8391 + 2.94284i) q^{27} -20.6313 q^{28} +23.6165i q^{29} +(5.03929 - 8.03776i) q^{30} +37.8103 q^{31} +5.65685i q^{32} +(-36.6271 - 22.9635i) q^{33} +0.619993 q^{34} +23.0665i q^{35} +(7.84220 + 16.2018i) q^{36} +3.95366 q^{37} +43.1448i q^{38} +(-23.2433 + 37.0735i) q^{39} +6.32456 q^{40} +0.897806i q^{41} +(-37.0806 - 23.2478i) q^{42} -47.5033 q^{43} -28.8203i q^{44} +(18.1142 - 8.76785i) q^{45} -6.78233 q^{46} +39.9836i q^{47} +(-6.37426 + 10.1670i) q^{48} +57.4126 q^{49} -7.07107i q^{50} +(1.11431 + 0.698620i) q^{51} -29.1715 q^{52} -67.0896i q^{53} +(-4.16180 + 37.9563i) q^{54} -32.2221 q^{55} -29.1771i q^{56} +(-48.6164 + 77.5440i) q^{57} -33.3988 q^{58} -43.7546i q^{59} +(11.3671 + 7.12664i) q^{60} -69.1629 q^{61} +53.4719i q^{62} +(-40.4487 - 83.5663i) q^{63} -8.00000 q^{64} +32.6147i q^{65} +(32.4753 - 51.7986i) q^{66} +15.9838 q^{67} +0.876802i q^{68} +(-12.1899 - 7.64247i) q^{69} -32.6209 q^{70} -32.7189i q^{71} +(-22.9129 + 11.0906i) q^{72} -136.933 q^{73} +5.59132i q^{74} +(7.96782 - 12.7088i) q^{75} -61.0159 q^{76} +148.650i q^{77} +(-52.4298 - 32.8710i) q^{78} -117.203 q^{79} +8.94427i q^{80} +(-50.2499 + 63.5291i) q^{81} -1.26969 q^{82} -72.3768i q^{83} +(32.8773 - 52.4398i) q^{84} +0.980294 q^{85} -67.1798i q^{86} +(-60.0276 - 37.6345i) q^{87} +40.7580 q^{88} +48.7209i q^{89} +(12.3996 + 25.6174i) q^{90} +150.461 q^{91} -9.59166i q^{92} +(-60.2532 + 96.1048i) q^{93} -56.5454 q^{94} +68.2179i q^{95} +(-14.3784 - 9.01456i) q^{96} +128.346 q^{97} +81.1936i q^{98} +(116.735 - 56.5036i) 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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