LMFDB - Embedded newform 690.3.b.a.599.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(599,690)]

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, 1, 0]))

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

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

chi := DirichletCharacter("690.599");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.b (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:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			599.20
Character	$\chi$	$=$	690.599
Dual form			690.3.b.a.599.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(-0.996475 + 2.82967i) q^{3} +2.00000 q^{4} +(3.01455 - 3.98905i) q^{5} +(1.40923 - 4.00176i) q^{6} +10.6805i q^{7} -2.82843 q^{8} +(-7.01408 - 5.63939i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(-0.996475 + 2.82967i) q^{3} +2.00000 q^{4} +(3.01455 - 3.98905i) q^{5} +(1.40923 - 4.00176i) q^{6} +10.6805i q^{7} -2.82843 q^{8} +(-7.01408 - 5.63939i) q^{9} +(-4.26321 + 5.64137i) q^{10} -5.50721i q^{11} +(-1.99295 + 5.65934i) q^{12} -16.7611i q^{13} -15.1045i q^{14} +(8.28377 + 12.5052i) q^{15} +4.00000 q^{16} -9.80700 q^{17} +(9.91940 + 7.97530i) q^{18} +10.0985 q^{19} +(6.02910 - 7.97810i) q^{20} +(-30.2223 - 10.6429i) q^{21} +7.78837i q^{22} +4.79583 q^{23} +(2.81846 - 8.00352i) q^{24} +(-6.82500 - 24.0504i) q^{25} +23.7038i q^{26} +(22.9470 - 14.2280i) q^{27} +21.3610i q^{28} -28.0925i q^{29} +(-11.7150 - 17.6850i) q^{30} -47.2712 q^{31} -5.65685 q^{32} +(15.5836 + 5.48779i) q^{33} +13.8692 q^{34} +(42.6051 + 32.1969i) q^{35} +(-14.0282 - 11.2788i) q^{36} -63.2473i q^{37} -14.2814 q^{38} +(47.4284 + 16.7020i) q^{39} +(-8.52643 + 11.2827i) q^{40} +10.8343i q^{41} +(42.7408 + 15.0513i) q^{42} +68.8660i q^{43} -11.0144i q^{44} +(-43.6401 + 10.9793i) q^{45} -6.78233 q^{46} -48.4644 q^{47} +(-3.98590 + 11.3187i) q^{48} -65.0732 q^{49} +(9.65201 + 34.0123i) q^{50} +(9.77242 - 27.7506i) q^{51} -33.5222i q^{52} +0.337512 q^{53} +(-32.4519 + 20.1215i) q^{54} +(-21.9685 - 16.6017i) q^{55} -30.2090i q^{56} +(-10.0629 + 28.5754i) q^{57} +39.7288i q^{58} -81.8665i q^{59} +(16.5675 + 25.0103i) q^{60} +106.911 q^{61} +66.8515 q^{62} +(60.2316 - 74.9139i) q^{63} +8.00000 q^{64} +(-66.8608 - 50.5271i) q^{65} +(-22.0385 - 7.76091i) q^{66} +29.9541i q^{67} -19.6140 q^{68} +(-4.77892 + 13.5706i) q^{69} +(-60.2526 - 45.5333i) q^{70} -122.414i q^{71} +(19.8388 + 15.9506i) q^{72} -18.4676i q^{73} +89.4452i q^{74} +(74.8555 + 4.65305i) q^{75} +20.1970 q^{76} +58.8198 q^{77} +(-67.0738 - 23.6202i) q^{78} +59.0164 q^{79} +(12.0582 - 15.9562i) q^{80} +(17.3945 + 79.1102i) q^{81} -15.3220i q^{82} +94.7516 q^{83} +(-60.4446 - 21.2857i) q^{84} +(-29.5637 + 39.1206i) q^{85} -97.3913i q^{86} +(79.4926 + 27.9935i) q^{87} +15.5767i q^{88} -124.858i q^{89} +(61.7164 - 15.5270i) q^{90} +179.017 q^{91} +9.59166 q^{92} +(47.1045 - 133.762i) q^{93} +68.5391 q^{94} +(30.4424 - 40.2834i) q^{95} +(5.63691 - 16.0070i) q^{96} -148.042i q^{97} +92.0275 q^{98} +(-31.0573 + 38.6280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 176 q^{4} + 8 q^{9}+O(q^{10}) $ 88 * q + 176 * q^4 + 8 * q^9	$ 88 q + 176 q^{4} + 8 q^{9} + 32 q^{10} - 12 q^{15} + 352 q^{16} - 16 q^{19} - 176 q^{21} + 72 q^{25} - 72 q^{30} + 32 q^{31} + 160 q^{34} + 16 q^{36} + 144 q^{39} + 64 q^{40} + 92 q^{45} - 360 q^{49} + 48 q^{51} - 144 q^{54} + 16 q^{55} - 24 q^{60} + 208 q^{61} + 704 q^{64} + 512 q^{66} + 304 q^{70} + 536 q^{75} - 32 q^{76} + 448 q^{79} - 24 q^{81} - 352 q^{84} - 96 q^{85} + 32 q^{90} - 64 q^{91} + 160 q^{94} + 296 q^{99}+O(q^{100}) $ 88 * q + 176 * q^4 + 8 * q^9 + 32 * q^10 - 12 * q^15 + 352 * q^16 - 16 * q^19 - 176 * q^21 + 72 * q^25 - 72 * q^30 + 32 * q^31 + 160 * q^34 + 16 * q^36 + 144 * q^39 + 64 * q^40 + 92 * q^45 - 360 * q^49 + 48 * q^51 - 144 * q^54 + 16 * q^55 - 24 * q^60 + 208 * q^61 + 704 * q^64 + 512 * q^66 + 304 * q^70 + 536 * q^75 - 32 * q^76 + 448 * q^79 - 24 * q^81 - 352 * q^84 - 96 * q^85 + 32 * q^90 - 64 * q^91 + 160 * q^94 + 296 * 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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	−0.996475	+	2.82967i	−0.332158	+	0.943224i
$3$	−0.996475	+	2.82967i	−0.332158	+	0.943224i
$4$	2.00000			0.500000
$5$	3.01455	−	3.98905i	0.602910	−	0.797810i
$5$	3.01455	−	3.98905i	0.602910	−	0.797810i
$6$	1.40923	−	4.00176i	0.234871	−	0.666960i
$7$			10.6805i			1.52579i	0.646524	+	0.762893i	$0.276222\pi$
$7$			10.6805i			1.52579i	−0.646524	+	0.762893i	$0.723778\pi$
$8$	−2.82843			−0.353553
$9$	−7.01408	−	5.63939i	−0.779342	−	0.626599i
$10$	−4.26321	+	5.64137i	−0.426321	+	0.564137i
$11$		−	5.50721i		−	0.500655i	−0.968161	−	0.250328i	$-0.919462\pi$
$11$		−	5.50721i		−	0.500655i	0.968161	−	0.250328i	$-0.0805383\pi$
$12$	−1.99295	+	5.65934i	−0.166079	+	0.471612i
$13$		−	16.7611i		−	1.28931i	−0.764472	−	0.644657i	$-0.777000\pi$
$13$		−	16.7611i		−	1.28931i	0.764472	−	0.644657i	$-0.223000\pi$
$14$		−	15.1045i		−	1.07889i
$15$	8.28377	+	12.5052i	0.552252	+	0.833678i
$16$	4.00000			0.250000
$17$	−9.80700			−0.576882			−0.288441	−	0.957498i	$-0.593137\pi$
$17$	−9.80700			−0.576882			−0.288441	+	0.957498i	$0.593137\pi$
$18$	9.91940	+	7.97530i	0.551078	+	0.443072i
$19$	10.0985			0.531500			0.265750	−	0.964042i	$-0.414380\pi$
$19$	10.0985			0.531500			0.265750	+	0.964042i	$0.414380\pi$
$20$	6.02910	−	7.97810i	0.301455	−	0.398905i
$21$	−30.2223	−	10.6429i	−1.43916	−	0.506803i
$22$			7.78837i			0.354017i
$23$	4.79583			0.208514
$23$	4.79583			0.208514
$24$	2.81846	−	8.00352i	0.117436	−	0.333480i
$25$	−6.82500	−	24.0504i	−0.273000	−	0.962014i
$26$			23.7038i			0.911683i
$27$	22.9470	−	14.2280i	0.849888	−	0.526964i
$28$			21.3610i			0.762893i
$29$		−	28.0925i		−	0.968707i	−0.874872	−	0.484354i	$-0.839055\pi$
$29$		−	28.0925i		−	0.968707i	0.874872	−	0.484354i	$-0.160945\pi$
$30$	−11.7150	−	17.6850i	−0.390501	−	0.589499i
$31$	−47.2712			−1.52488			−0.762438	−	0.647061i	$-0.775998\pi$
$31$	−47.2712			−1.52488			−0.762438	+	0.647061i	$0.775998\pi$
$32$	−5.65685			−0.176777
$33$	15.5836	+	5.48779i	0.472230	+	0.166297i
$34$	13.8692			0.407917
$35$	42.6051	+	32.1969i	1.21729	+	0.919911i
$36$	−14.0282	−	11.2788i	−0.389671	−	0.313299i
$37$		−	63.2473i		−	1.70939i	−0.519133	−	0.854694i	$-0.673745\pi$
$37$		−	63.2473i		−	1.70939i	0.519133	−	0.854694i	$-0.326255\pi$
$38$	−14.2814			−0.375827
$39$	47.4284	+	16.7020i	1.21611	+	0.428256i
$40$	−8.52643	+	11.2827i	−0.213161	+	0.282068i
$41$			10.8343i			0.264252i	0.991233	+	0.132126i	$0.0421803\pi$
$41$			10.8343i			0.264252i	−0.991233	+	0.132126i	$0.957820\pi$
$42$	42.7408	+	15.0513i	1.01764	+	0.358364i
$43$			68.8660i			1.60154i	0.598975	+	0.800768i	$0.295575\pi$
$43$			68.8660i			1.60154i	−0.598975	+	0.800768i	$0.704425\pi$
$44$		−	11.0144i		−	0.250328i
$45$	−43.6401	+	10.9793i	−0.969779	+	0.243984i
$46$	−6.78233			−0.147442
$47$	−48.4644			−1.03116			−0.515579	−	0.856842i	$-0.672423\pi$
$47$	−48.4644			−1.03116			−0.515579	+	0.856842i	$0.672423\pi$
$48$	−3.98590	+	11.3187i	−0.0830395	+	0.235806i
$49$	−65.0732			−1.32803
$50$	9.65201	+	34.0123i	0.193040	+	0.680247i
$51$	9.77242	−	27.7506i	0.191616	−	0.544129i
$52$		−	33.5222i		−	0.644657i
$53$	0.337512			0.00636816			0.00318408	−	0.999995i	$-0.498986\pi$
$53$	0.337512			0.00636816			0.00318408	+	0.999995i	$0.498986\pi$
$54$	−32.4519	+	20.1215i	−0.600961	+	0.372620i
$55$	−21.9685	−	16.6017i	−0.399428	−	0.301850i
$56$		−	30.2090i		−	0.539447i
$57$	−10.0629	+	28.5754i	−0.176542	+	0.501323i
$58$			39.7288i			0.684980i
$59$		−	81.8665i		−	1.38757i	−0.720183	−	0.693784i	$-0.755942\pi$
$59$		−	81.8665i		−	1.38757i	0.720183	−	0.693784i	$-0.244058\pi$
$60$	16.5675	+	25.0103i	0.276126	+	0.416839i
$61$	106.911			1.75264			0.876318	−	0.481732i	$-0.159992\pi$
$61$	106.911			1.75264			0.876318	+	0.481732i	$0.159992\pi$
$62$	66.8515			1.07825
$63$	60.2316	−	74.9139i	0.956056	−	1.18911i
$64$	8.00000			0.125000
$65$	−66.8608	−	50.5271i	−1.02863	−	0.777340i
$66$	−22.0385	−	7.76091i	−0.333917	−	0.117590i
$67$			29.9541i			0.447077i	0.974695	+	0.223538i	$0.0717608\pi$
$67$			29.9541i			0.447077i	−0.974695	+	0.223538i	$0.928239\pi$
$68$	−19.6140			−0.288441
$69$	−4.77892	+	13.5706i	−0.0692598	+	0.196676i
$70$	−60.2526	−	45.5333i	−0.860752	−	0.650476i
$71$		−	122.414i		−	1.72415i	−0.506783	−	0.862073i	$-0.669166\pi$
$71$		−	122.414i		−	1.72415i	0.506783	−	0.862073i	$-0.330834\pi$
$72$	19.8388	+	15.9506i	0.275539	+	0.221536i
$73$		−	18.4676i		−	0.252980i	−0.991968	−	0.126490i	$-0.959629\pi$
$73$		−	18.4676i		−	0.252980i	0.991968	−	0.126490i	$-0.0403712\pi$
$74$			89.4452i			1.20872i
$75$	74.8555	+	4.65305i	0.998074	+	0.0620407i
$76$	20.1970			0.265750
$77$	58.8198			0.763893
$78$	−67.0738	−	23.6202i	−0.859921	−	0.302823i
$79$	59.0164			0.747043			0.373521	−	0.927622i	$-0.378150\pi$
$79$	59.0164			0.747043			0.373521	+	0.927622i	$0.378150\pi$
$80$	12.0582	−	15.9562i	0.150727	−	0.199452i
$81$	17.3945	+	79.1102i	0.214748	+	0.976670i
$82$		−	15.3220i		−	0.186854i
$83$	94.7516			1.14159			0.570793	−	0.821094i	$-0.306636\pi$
$83$	94.7516			1.14159			0.570793	+	0.821094i	$0.306636\pi$
$84$	−60.4446	−	21.2857i	−0.719579	−	0.253401i
$85$	−29.5637	+	39.1206i	−0.347808	+	0.460242i
$86$		−	97.3913i		−	1.13246i
$87$	79.4926	+	27.9935i	0.913708	+	0.321764i
$88$			15.5767i			0.177008i
$89$		−	124.858i		−	1.40290i	−0.712717	−	0.701452i	$-0.752536\pi$
$89$		−	124.858i		−	1.40290i	0.712717	−	0.701452i	$-0.247464\pi$
$90$	61.7164	−	15.5270i	0.685738	−	0.172523i
$91$	179.017			1.96722
$92$	9.59166			0.104257
$93$	47.1045	−	133.762i	0.506500	−	1.43830i
$94$	68.5391			0.729139
$95$	30.4424	−	40.2834i	0.320446	−	0.424036i
$96$	5.63691	−	16.0070i	0.0587178	−	0.166740i
$97$		−	148.042i		−	1.52621i	−0.646276	−	0.763103i	$-0.723675\pi$
$97$		−	148.042i		−	1.52621i	0.646276	−	0.763103i	$-0.276325\pi$
$98$	92.0275			0.939056
$99$	−31.0573	+	38.6280i	−0.313710	+	0.390182i
$100$	−13.6500	−	48.1007i	−0.136500	−	0.481007i
$101$			28.7770i			0.284921i	0.989800	+	0.142461i	$0.0455014\pi$
$101$			28.7770i			0.284921i	−0.989800	+	0.142461i	$0.954499\pi$
$102$	−13.8203	+	39.2452i	−0.135493	+	0.384757i
$103$			102.710i			0.997181i	0.866838	+	0.498590i	$0.166149\pi$
$103$			102.710i			0.997181i	−0.866838	+	0.498590i	$0.833851\pi$
$104$			47.4075i			0.455841i
$105$	−133.561	+	88.4749i	−1.27201	+	0.842618i
$106$	−0.477314			−0.00450297
$107$	142.426			1.33108			0.665540	−	0.746362i	$-0.268201\pi$
$107$	142.426			1.33108			0.665540	+	0.746362i	$0.268201\pi$
$108$	45.8939	−	28.4560i	0.424944	−	0.263482i
$109$	49.1052			0.450507			0.225253	−	0.974300i	$-0.427679\pi$
$109$	49.1052			0.450507			0.225253	+	0.974300i	$0.427679\pi$
$110$	31.0682	+	23.4784i	0.282438	+	0.213440i
$111$	178.969	+	63.0243i	1.61233	+	0.567787i
$112$			42.7220i			0.381447i
$113$	−59.1200			−0.523185			−0.261593	−	0.965178i	$-0.584248\pi$
$113$	−59.1200			−0.523185			−0.261593	+	0.965178i	$0.584248\pi$
$114$	14.2311	−	40.4117i	0.124834	−	0.354489i
$115$	14.4573	−	19.1308i	0.125715	−	0.166355i
$116$		−	56.1850i		−	0.484354i
$117$	−94.5223	+	117.564i	−0.807883	+	1.00482i
$118$			115.777i			0.981159i
$119$		−	104.744i		−	0.880199i
$120$	−23.4300	−	35.3699i	−0.195250	−	0.294750i
$121$	90.6707			0.749344
$122$	−151.195			−1.23930
$123$	−30.6576	−	10.7961i	−0.249249	−	0.0877734i
$124$	−94.5423			−0.762438
$125$	−116.512	−	45.2757i	−0.932098	−	0.362205i
$126$	−85.1803	+	105.944i	−0.676034	+	0.840827i
$127$		−	224.062i		−	1.76427i	−0.471001	−	0.882133i	$-0.656107\pi$
$127$		−	224.062i		−	1.76427i	0.471001	−	0.882133i	$-0.343893\pi$
$128$	−11.3137			−0.0883883
$129$	−194.868	−	68.6233i	−1.51061	−	0.531963i
$130$	94.5554	+	71.4561i	0.727349	+	0.549662i
$131$		−	24.6516i		−	0.188180i	−0.995564	−	0.0940900i	$-0.970006\pi$
$131$		−	24.6516i		−	0.188180i	0.995564	−	0.0940900i	$-0.0299942\pi$
$132$	31.1672	+	10.9756i	0.236115	+	0.0831484i
$133$			107.857i			0.810955i
$134$		−	42.3616i		−	0.316131i
$135$	12.4185	−	134.428i	0.0919888	−	0.995760i
$136$	27.7384			0.203959
$137$	38.9946			0.284632			0.142316	−	0.989821i	$-0.454545\pi$
$137$	38.9946			0.284632			0.142316	+	0.989821i	$0.454545\pi$
$138$	6.75842	−	19.1918i	0.0489741	−	0.139071i
$139$	−110.820			−0.797264			−0.398632	−	0.917111i	$-0.630515\pi$
$139$	−110.820			−0.797264			−0.398632	+	0.917111i	$0.630515\pi$
$140$	85.2101	+	64.3938i	0.608644	+	0.459956i
$141$	48.2936	−	137.138i	0.342508	−	0.972613i
$142$			173.120i			1.21916i
$143$	−92.3068			−0.645502
$144$	−28.0563	−	22.5576i	−0.194835	−	0.156650i
$145$	−112.062	−	84.6862i	−0.772844	−	0.584043i
$146$			26.1171i			0.178884i
$147$	64.8438	−	184.136i	0.441115	−	1.25263i
$148$		−	126.495i		−	0.854694i
$149$			86.8207i			0.582689i	0.956618	+	0.291345i	$0.0941026\pi$
$149$			86.8207i			0.582689i	−0.956618	+	0.291345i	$0.905897\pi$
$150$	−105.862	−	6.58041i	−0.705745	−	0.0438694i
$151$	−114.955			−0.761291			−0.380645	−	0.924721i	$-0.624298\pi$
$151$	−114.955			−0.761291			−0.380645	+	0.924721i	$0.624298\pi$
$152$	−28.5629			−0.187914
$153$	68.7870	+	55.3055i	0.449588	+	0.361474i
$154$	−83.1837			−0.540154
$155$	−142.501	+	188.567i	−0.919363	+	1.21656i
$156$	94.8567	+	33.4040i	0.608056	+	0.214128i
$157$			197.398i			1.25731i	0.777684	+	0.628655i	$0.216394\pi$
$157$			197.398i			1.25731i	−0.777684	+	0.628655i	$0.783606\pi$
$158$	−83.4618			−0.528239
$159$	−0.336322	+	0.955049i	−0.00211523	+	0.00600659i
$160$	−17.0529	+	22.5655i	−0.106580	+	0.141034i
$161$			51.2219i			0.318149i
$162$	−24.5996	−	111.879i	−0.151849	−	0.690610i
$163$		−	13.1307i		−	0.0805564i	−0.999189	−	0.0402782i	$-0.987176\pi$
$163$		−	13.1307i		−	0.0805564i	0.999189	−	0.0402782i	$-0.0128244\pi$
$164$			21.6686i			0.132126i
$165$	68.8685	−	45.6205i	0.417385	−	0.276488i
$166$	−133.999			−0.807223
$167$	−225.489			−1.35023			−0.675117	−	0.737711i	$-0.735907\pi$
$167$	−225.489			−1.35023			−0.675117	+	0.737711i	$0.735907\pi$
$168$	85.4816	+	30.1025i	0.508819	+	0.179182i
$169$	−111.934			−0.662331
$170$	41.8093	−	55.3248i	0.245937	−	0.325440i
$171$	−70.8316	−	56.9494i	−0.414220	−	0.333037i
$172$			137.732i			0.800768i
$173$	−107.311			−0.620295			−0.310147	−	0.950689i	$-0.600378\pi$
$173$	−107.311			−0.620295			−0.310147	+	0.950689i	$0.600378\pi$
$174$	−112.419	−	39.5887i	−0.646089	−	0.227522i
$175$	256.870	−	72.8945i	1.46783	−	0.416540i
$176$		−	22.0288i		−	0.125164i
$177$	231.655	+	81.5779i	1.30879	+	0.460892i
$178$			176.576i			0.992002i
$179$		−	352.761i		−	1.97073i	−0.170453	−	0.985366i	$-0.554523\pi$
$179$		−	352.761i		−	1.97073i	0.170453	−	0.985366i	$-0.445477\pi$
$180$	−87.2801	+	21.9585i	−0.484890	+	0.121992i
$181$	103.600			0.572378			0.286189	−	0.958173i	$-0.407611\pi$
$181$	103.600			0.572378			0.286189	+	0.958173i	$0.407611\pi$
$182$	−253.168			−1.39103
$183$	−106.534	+	302.523i	−0.582153	+	1.65313i
$184$	−13.5647			−0.0737210
$185$	−252.297	−	190.662i	−1.36377	−	1.03061i
$186$	−66.6158	+	189.168i	−0.358150	+	1.01703i
$187$			54.0092i			0.288819i
$188$	−96.9289			−0.515579
$189$	151.962	+	245.085i	0.804034	+	1.29675i
$190$	−43.0520	+	56.9693i	−0.226590	+	0.299838i
$191$			161.577i			0.845952i	0.906141	+	0.422976i	$0.139015\pi$
$191$			161.577i			0.845952i	−0.906141	+	0.422976i	$0.860985\pi$
$192$	−7.97180	+	22.6374i	−0.0415198	+	0.117903i
$193$			111.785i			0.579196i	0.957148	+	0.289598i	$0.0935215\pi$
$193$			111.785i			0.579196i	−0.957148	+	0.289598i	$0.906478\pi$
$194$			209.363i			1.07919i
$195$	209.600	−	138.845i	1.07487	−	0.712026i
$196$	−130.146			−0.664013
$197$	−259.757			−1.31856			−0.659282	−	0.751896i	$-0.729139\pi$
$197$	−259.757			−1.31856			−0.659282	+	0.751896i	$0.729139\pi$
$198$	43.9216	−	54.6282i	0.221827	−	0.275900i
$199$	−86.0655			−0.432490			−0.216245	−	0.976339i	$-0.569381\pi$
$199$	−86.0655			−0.432490			−0.216245	+	0.976339i	$0.569381\pi$
$200$	19.3040	+	68.0247i	0.0965201	+	0.340123i
$201$	−84.7604	−	29.8485i	−0.421693	−	0.148500i
$202$		−	40.6969i		−	0.201470i
$203$	300.042			1.47804
$204$	19.5448	−	55.5011i	0.0958081	−	0.272064i
$205$	43.2186	+	32.6606i	0.210823	+	0.159320i
$206$		−	145.253i		−	0.705113i
$207$	−33.6383	−	27.0456i	−0.162504	−	0.130655i
$208$		−	67.0443i		−	0.322329i
$209$		−	55.6145i		−	0.266098i
$210$	188.884	−	125.122i	0.899450	−	0.595821i
$211$	117.720			0.557914			0.278957	−	0.960304i	$-0.410011\pi$
$211$	117.720			0.557914			0.278957	+	0.960304i	$0.410011\pi$
$212$	0.675024			0.00318408
$213$	346.393	+	121.983i	1.62626	+	0.572690i
$214$	−201.420			−0.941216
$215$	274.710	+	207.600i	1.27772	+	0.965581i
$216$	−64.9038	+	40.2429i	−0.300481	+	0.186310i
$217$		−	504.880i		−	2.32664i
$218$	−69.4453			−0.318556
$219$	52.2571	+	18.4025i	0.238617	+	0.0840295i
$220$	−43.9370	−	33.2035i	−0.199714	−	0.150925i
$221$			164.376i			0.743782i
$222$	−253.101	−	89.1299i	−1.14009	−	0.401486i
$223$			316.140i			1.41767i	0.705375	+	0.708834i	$0.250779\pi$
$223$			316.140i			1.41767i	−0.705375	+	0.708834i	$0.749221\pi$
$224$		−	60.4181i		−	0.269724i
$225$	−87.7582	+	207.180i	−0.390037	+	0.920799i
$226$	83.6082			0.369948
$227$	−447.042			−1.96935			−0.984674	−	0.174404i	$-0.944200\pi$
$227$	−447.042			−1.96935			−0.984674	+	0.174404i	$0.944200\pi$
$228$	−20.1258	+	57.1508i	−0.0882710	+	0.250662i
$229$	46.2455			0.201945			0.100973	−	0.994889i	$-0.467805\pi$
$229$	46.2455			0.201945			0.100973	+	0.994889i	$0.467805\pi$
$230$	−20.4457	+	27.0550i	−0.0888942	+	0.117631i
$231$	−58.6124	+	166.441i	−0.253733	+	0.720522i
$232$			79.4576i			0.342490i
$233$	−4.37626			−0.0187823			−0.00939113	−	0.999956i	$-0.502989\pi$
$233$	−4.37626			−0.0187823			−0.00939113	+	0.999956i	$0.502989\pi$
$234$	133.675	−	166.260i	0.571260	−	0.710513i
$235$	−146.098	+	193.327i	−0.621695	+	0.822668i
$236$		−	163.733i		−	0.693784i
$237$	−58.8083	+	166.997i	−0.248136	+	0.704629i
$238$			148.130i			0.622395i
$239$			92.6709i			0.387744i	0.981027	+	0.193872i	$0.0621047\pi$
$239$			92.6709i			0.387744i	−0.981027	+	0.193872i	$0.937895\pi$
$240$	33.1351	+	50.0207i	0.138063	+	0.208419i
$241$	189.935			0.788111			0.394056	−	0.919087i	$-0.371072\pi$
$241$	189.935			0.788111			0.394056	+	0.919087i	$0.371072\pi$
$242$	−128.228			−0.529866
$243$	−241.189	−	29.6105i	−0.992548	−	0.121854i
$244$	213.822			0.876318
$245$	−196.166	+	259.580i	−0.800679	+	1.05951i
$246$	43.3564	+	15.2680i	0.176245	+	0.0620652i
$247$		−	169.262i		−	0.685270i
$248$	133.703			0.539125
$249$	−94.4176	+	268.116i	−0.379187	+	1.07677i
$250$	164.773	+	64.0295i	0.659093	+	0.256118i
$251$			139.189i			0.554536i	0.960793	+	0.277268i	$0.0894290\pi$
$251$			139.189i			0.554536i	−0.960793	+	0.277268i	$0.910571\pi$
$252$	120.463	−	149.828i	0.478028	−	0.594555i
$253$		−	26.4116i		−	0.104394i
$254$			316.871i			1.24752i
$255$	−81.2389	−	122.638i	−0.318584	−	0.480934i
$256$	16.0000			0.0625000
$257$	444.315			1.72885			0.864426	−	0.502761i	$-0.167682\pi$
$257$	444.315			1.72885			0.864426	+	0.502761i	$0.167682\pi$
$258$	275.585	+	97.0480i	1.06816	+	0.376155i
$259$	675.514			2.60816
$260$	−133.722	−	101.054i	−0.514314	−	0.388670i
$261$	−158.425	+	197.043i	−0.606991	+	0.754954i
$262$			34.8626i			0.133063i
$263$	−353.437			−1.34387			−0.671933	−	0.740612i	$-0.734536\pi$
$263$	−353.437			−1.34387			−0.671933	+	0.740612i	$0.734536\pi$
$264$	−44.0770	−	15.5218i	−0.166958	−	0.0587948i
$265$	1.01745	−	1.34635i	0.00383942	−	0.00508057i
$266$		−	152.533i		−	0.573432i
$267$	353.308	+	124.418i	1.32325	+	0.465986i
$268$			59.9083i			0.223538i
$269$			68.5693i			0.254904i	0.991845	+	0.127452i	$0.0406799\pi$
$269$			68.5693i			0.254904i	−0.991845	+	0.127452i	$0.959320\pi$
$270$	−17.5624	+	190.109i	−0.0650459	+	0.704109i
$271$	53.4646			0.197286			0.0986431	−	0.995123i	$-0.468550\pi$
$271$	53.4646			0.197286			0.0986431	+	0.995123i	$0.468550\pi$
$272$	−39.2280			−0.144221
$273$	−178.386	+	506.559i	−0.653428	+	1.85553i
$274$	−55.1467			−0.201265
$275$	−132.450	+	37.5867i	−0.481637	+	0.136679i
$276$	−9.55785	+	27.1413i	−0.0346299	+	0.0983379i
$277$		−	323.987i		−	1.16963i	−0.811167	−	0.584815i	$-0.801167\pi$
$277$		−	323.987i		−	1.16963i	0.811167	−	0.584815i	$-0.198833\pi$
$278$	156.723			0.563751
$279$	331.564	+	266.581i	1.18840	+	0.955486i
$280$	−120.505	−	91.0666i	−0.430376	−	0.325238i
$281$			151.475i			0.539057i	0.962992	+	0.269529i	$0.0868679\pi$
$281$			151.475i			0.539057i	−0.962992	+	0.269529i	$0.913132\pi$
$282$	−68.2974	+	193.943i	−0.242190	+	0.687741i
$283$		−	239.029i		−	0.844627i	−0.906450	−	0.422313i	$-0.861218\pi$
$283$		−	239.029i		−	0.844627i	0.906450	−	0.422313i	$-0.138782\pi$
$284$		−	244.829i		−	0.862073i
$285$	83.6536	+	126.283i	0.293522	+	0.443099i
$286$	130.541			0.456439
$287$	−115.716			−0.403192
$288$	39.6776	+	31.9012i	0.137769	+	0.110768i
$289$	−192.823			−0.667207
$290$	158.480	+	119.764i	0.546483	+	0.412981i
$291$	418.910	+	147.520i	1.43955	+	0.506942i
$292$		−	36.9351i		−	0.126490i
$293$	283.885			0.968891			0.484446	−	0.874821i	$-0.339021\pi$
$293$	283.885			0.968891			0.484446	+	0.874821i	$0.339021\pi$
$294$	−91.7030	+	260.407i	−0.311915	+	0.885740i
$295$	−326.569	−	246.791i	−1.10702	−	0.836578i
$296$			178.890i			0.604360i
$297$	−78.3567	−	126.374i	−0.263827	−	0.425501i
$298$		−	122.783i		−	0.412023i
$299$		−	80.3833i		−	0.268841i
$300$	149.711	+	9.30610i	0.499037	+	0.0310203i
$301$	−735.524			−2.44360
$302$	162.571			0.538314
$303$	−81.4295	−	28.6756i	−0.268744	−	0.0946389i
$304$	40.3940			0.132875
$305$	322.288	−	426.472i	1.05668	−	1.39827i
$306$	−97.2795	−	78.2138i	−0.317907	−	0.255601i
$307$		−	332.488i		−	1.08302i	−0.840693	−	0.541512i	$-0.817852\pi$
$307$		−	332.488i		−	1.08302i	0.840693	−	0.541512i	$-0.182148\pi$
$308$	117.640			0.381947
$309$	−290.634	−	102.348i	−0.940565	−	0.331222i
$310$	201.527	−	266.674i	0.650087	−	0.860238i
$311$		−	325.810i		−	1.04762i	−0.851835	−	0.523811i	$-0.824510\pi$
$311$		−	325.810i		−	1.04762i	0.851835	−	0.523811i	$-0.175490\pi$
$312$	−134.148	−	47.2404i	−0.429960	−	0.151411i
$313$			175.258i			0.559929i	0.960010	+	0.279965i	$0.0903227\pi$
$313$			175.258i			0.559929i	−0.960010	+	0.279965i	$0.909677\pi$
$314$		−	279.163i		−	0.889053i
$315$	−117.264	−	466.098i	−0.372267	−	1.47968i
$316$	118.033			0.373521
$317$	137.362			0.433319			0.216659	−	0.976247i	$-0.430484\pi$
$317$	137.362			0.433319			0.216659	+	0.976247i	$0.430484\pi$
$318$	0.475632	−	1.35064i	0.00149570	−	0.00424730i
$319$	−154.711			−0.484988
$320$	24.1164	−	31.9124i	0.0753637	−	0.0997262i
$321$	−141.924	+	403.018i	−0.442129	+	1.25551i
$322$		−	72.4387i		−	0.224965i
$323$	−99.0359			−0.306613
$324$	34.7891	+	158.220i	0.107374	+	0.488335i
$325$	−403.110	+	114.394i	−1.24034	+	0.351983i
$326$			18.5696i			0.0569620i
$327$	−48.9321	+	138.952i	−0.149639	+	0.424929i
$328$		−	30.6441i		−	0.0934271i
$329$		−	517.625i		−	1.57333i
$330$	−97.3948	+	64.5171i	−0.295136	+	0.195506i
$331$	−373.059			−1.12707			−0.563533	−	0.826093i	$-0.690558\pi$
$331$	−373.059			−1.12707			−0.563533	+	0.826093i	$0.690558\pi$
$332$	189.503			0.570793
$333$	−356.676	+	443.622i	−1.07110	+	1.33220i
$334$	318.890			0.954760
$335$	119.488	+	90.2982i	0.356682	+	0.269547i
$336$	−120.889	−	42.5714i	−0.359790	−	0.126701i
$337$			46.2129i			0.137130i	0.997647	+	0.0685652i	$0.0218421\pi$
$337$			46.2129i			0.137130i	−0.997647	+	0.0685652i	$0.978158\pi$
$338$	158.299			0.468339
$339$	58.9115	−	167.290i	0.173780	−	0.493481i
$340$	−59.1273	+	78.2411i	−0.173904	+	0.230121i
$341$			260.332i			0.763437i
$342$	100.171	+	80.5385i	0.292898	+	0.235493i
$343$		−	171.670i		−	0.500497i
$344$		−	194.783i		−	0.566228i
$345$	39.7276	+	59.9727i	0.115152	+	0.173834i
$346$	151.761			0.438614
$347$	−436.414			−1.25768			−0.628838	−	0.777536i	$-0.716469\pi$
$347$	−436.414			−1.25768			−0.628838	+	0.777536i	$0.716469\pi$
$348$	158.985	+	55.9869i	0.456854	+	0.160882i
$349$	−144.441			−0.413871			−0.206936	−	0.978355i	$-0.566349\pi$
$349$	−144.441			−0.413871			−0.206936	+	0.978355i	$0.566349\pi$
$350$	−363.269	+	103.088i	−1.03791	+	0.294538i
$351$	−238.477	−	384.616i	−0.679422	−	1.09577i
$352$			31.1535i			0.0885042i
$353$	−128.039			−0.362717			−0.181359	−	0.983417i	$-0.558049\pi$
$353$	−128.039			−0.362717			−0.181359	+	0.983417i	$0.558049\pi$
$354$	−327.610	−	115.369i	−0.925452	−	0.325900i
$355$	−488.317	−	369.024i	−1.37554	−	1.03950i
$356$		−	249.717i		−	0.701452i
$357$	296.390	+	104.374i	0.830225	+	0.292365i
$358$			498.879i			1.39352i
$359$			223.554i			0.622713i	0.950293	+	0.311357i	$0.100783\pi$
$359$			223.554i			0.622713i	−0.950293	+	0.311357i	$0.899217\pi$
$360$	123.433	−	31.0541i	0.342869	−	0.0862613i
$361$	−259.020			−0.717508
$362$	−146.513			−0.404733
$363$	−90.3510	+	256.568i	−0.248901	+	0.706799i
$364$	358.034			0.983609
$365$	−73.6680	−	55.6713i	−0.201830	−	0.152524i
$366$	150.662	−	427.831i	0.411644	−	1.16894i
$367$		−	239.940i		−	0.653788i	−0.945061	−	0.326894i	$-0.893998\pi$
$367$		−	239.940i		−	0.653788i	0.945061	−	0.326894i	$-0.106002\pi$
$368$	19.1833			0.0521286
$369$	61.0990	−	75.9928i	0.165580	−	0.205942i
$370$	356.801	+	269.637i	0.964328	+	0.728748i
$371$			3.60480i			0.00971645i
$372$	94.2090	−	267.524i	0.253250	−	0.719150i
$373$		−	233.984i		−	0.627302i	−0.949538	−	0.313651i	$-0.898448\pi$
$373$		−	233.984i		−	0.627302i	0.949538	−	0.313651i	$-0.101552\pi$
$374$		−	76.3805i		−	0.204226i
$375$	244.217	−	284.575i	0.651245	−	0.758868i
$376$	137.078			0.364570
$377$	−470.861			−1.24897
$378$	−214.907	−	346.603i	−0.568538	−	0.916939i
$379$	161.554			0.426263			0.213132	−	0.977024i	$-0.431634\pi$
$379$	161.554			0.426263			0.213132	+	0.977024i	$0.431634\pi$
$380$	60.8848	−	80.5667i	0.160223	−	0.212018i
$381$	634.021	+	223.272i	1.66410	+	0.586015i
$382$		−	228.504i		−	0.598179i
$383$	−444.654			−1.16098			−0.580488	−	0.814269i	$-0.697138\pi$
$383$	−444.654			−1.16098			−0.580488	+	0.814269i	$0.697138\pi$
$384$	11.2738	−	32.0141i	0.0293589	−	0.0833700i
$385$	177.315	−	234.635i	0.460559	−	0.609441i
$386$		−	158.087i		−	0.409553i
$387$	388.363	−	483.032i	1.00352	−	1.24814i
$388$		−	296.084i		−	0.763103i
$389$		−	469.314i		−	1.20646i	−0.797567	−	0.603231i	$-0.793880\pi$
$389$		−	469.314i		−	1.20646i	0.797567	−	0.603231i	$-0.206120\pi$
$390$	−296.419	+	196.357i	−0.760050	+	0.503478i
$391$	−47.0327			−0.120288
$392$	184.055			0.469528
$393$	69.7559	+	24.5647i	0.177496	+	0.0625055i
$394$	367.352			0.932365
$395$	177.908	−	235.419i	0.450399	−	0.595998i
$396$	−62.1146	+	77.2560i	−0.156855	+	0.195091i
$397$		−	48.3846i		−	0.121876i	−0.998142	−	0.0609378i	$-0.980591\pi$
$397$		−	48.3846i		−	0.121876i	0.998142	−	0.0609378i	$-0.0194091\pi$
$398$	121.715			0.305817
$399$	−305.200	−	107.477i	−0.764912	−	0.269365i
$400$	−27.3000	−	96.2014i	−0.0682500	−	0.240504i
$401$			430.001i			1.07232i	0.844116	+	0.536161i	$0.180126\pi$
$401$			430.001i			1.07232i	−0.844116	+	0.536161i	$0.819874\pi$
$402$	119.869	+	42.2122i	0.298182	+	0.105005i
$403$			792.316i			1.96604i
$404$			57.5541i			0.142461i
$405$	368.011	+	169.094i	0.908670	+	0.417516i
$406$	−424.324			−1.04513
$407$	−348.316			−0.855814
$408$	−27.6406	+	78.4905i	−0.0677465	+	0.192379i
$409$	206.431			0.504722			0.252361	−	0.967633i	$-0.418793\pi$
$409$	206.431			0.504722			0.252361	+	0.967633i	$0.418793\pi$
$410$	−61.1204	−	46.1890i	−0.149074	−	0.112656i
$411$	−38.8571	+	110.342i	−0.0945429	+	0.268472i
$412$			205.419i			0.498590i
$413$	874.376			2.11713
$414$	47.5718	+	38.2482i	0.114908	+	0.0923870i
$415$	285.633	−	377.969i	0.688273	−	0.910768i
$416$			94.8150i			0.227921i
$417$	110.429	−	313.583i	0.264818	−	0.751998i
$418$			78.6508i			0.188160i
$419$		−	78.5600i		−	0.187494i	−0.995596	−	0.0937471i	$-0.970115\pi$
$419$		−	78.5600i		−	0.187494i	0.995596	−	0.0937471i	$-0.0298845\pi$
$420$	−267.123	+	176.950i	−0.636007	+	0.421309i
$421$	−129.116			−0.306688			−0.153344	−	0.988173i	$-0.549004\pi$
$421$	−129.116			−0.306688			−0.153344	+	0.988173i	$0.549004\pi$
$422$	−166.481			−0.394505
$423$	339.933	+	273.310i	0.803625	+	0.646123i
$424$	−0.954629			−0.00225148
$425$	66.9328	+	235.862i	0.157489	+	0.554969i
$426$	−489.873	−	172.510i	−1.14994	−	0.404953i
$427$			1141.86i			2.67415i
$428$	284.851			0.665540
$429$	91.9814	−	261.198i	0.214409	−	0.608853i
$430$	−388.499	−	293.591i	−0.903485	−	0.682769i
$431$			221.506i			0.513935i	0.966420	+	0.256968i	$0.0827234\pi$
$431$			221.506i			0.513935i	−0.966420	+	0.256968i	$0.917277\pi$
$432$	91.7879	−	56.9121i	0.212472	−	0.131741i
$433$			374.938i			0.865907i	0.901416	+	0.432953i	$0.142529\pi$
$433$			374.938i			0.865907i	−0.901416	+	0.432953i	$0.857471\pi$
$434$			714.008i			1.64518i
$435$	351.301	−	232.712i	0.807590	−	0.534970i
$436$	98.2105			0.225253
$437$	48.4307			0.110825
$438$	−73.9027	−	26.0250i	−0.168728	−	0.0594178i
$439$	425.652			0.969595			0.484798	−	0.874626i	$-0.338893\pi$
$439$	425.652			0.969595			0.484798	+	0.874626i	$0.338893\pi$
$440$	62.1363	+	46.9568i	0.141219	+	0.106720i
$441$	456.429	+	366.973i	1.03499	+	0.832139i
$442$		−	232.463i		−	0.525933i
$443$	779.244			1.75902			0.879508	−	0.475884i	$-0.157872\pi$
$443$	779.244			1.75902			0.879508	+	0.475884i	$0.157872\pi$
$444$	357.938	+	126.049i	0.806167	+	0.283893i
$445$	−498.066	−	376.392i	−1.11925	−	0.845824i
$446$		−	447.090i		−	1.00244i
$447$	−245.674	−	86.5146i	−0.549606	−	0.193545i
$448$			85.4441i			0.190723i
$449$			521.041i			1.16045i	0.814457	+	0.580224i	$0.197035\pi$
$449$			521.041i			1.16045i	−0.814457	+	0.580224i	$0.802965\pi$
$450$	124.109	−	292.997i	0.275797	−	0.651103i
$451$	59.6669			0.132299
$452$	−118.240			−0.261593
$453$	114.550	−	325.285i	0.252869	−	0.718068i
$454$	632.213			1.39254
$455$	539.655	−	714.107i	1.18605	−	1.56947i
$456$	28.4622	−	80.8235i	0.0624170	−	0.177244i
$457$			108.265i			0.236904i	0.992960	+	0.118452i	$0.0377932\pi$
$457$			108.265i			0.236904i	−0.992960	+	0.118452i	$0.962207\pi$
$458$	−65.4010			−0.142797
$459$	−225.041	+	139.534i	−0.490285	+	0.303996i
$460$	28.9145	−	38.2616i	0.0628577	−	0.0831774i
$461$		−	528.878i		−	1.14724i	−0.819121	−	0.573620i	$-0.805538\pi$
$461$		−	528.878i		−	1.14724i	0.819121	−	0.573620i	$-0.194462\pi$
$462$	82.8905	−	235.383i	0.179417	−	0.509486i
$463$			270.858i			0.585007i	0.956264	+	0.292504i	$0.0944883\pi$
$463$			270.858i			0.585007i	−0.956264	+	0.292504i	$0.905512\pi$
$464$		−	112.370i		−	0.242177i
$465$	−391.584	−	591.134i	−0.842115	−	1.27126i
$466$	6.18897			0.0132811
$467$	−187.502			−0.401503			−0.200751	−	0.979642i	$-0.564338\pi$
$467$	−187.502			−0.401503			−0.200751	+	0.979642i	$0.564338\pi$
$468$	−189.045	+	235.127i	−0.403941	+	0.502408i
$469$	−319.925			−0.682144
$470$	206.614	−	273.406i	0.439605	−	0.581714i
$471$	−558.571	−	196.702i	−1.18593	−	0.417626i
$472$			231.553i			0.490579i
$473$	379.260			0.801817
$474$	83.1675	−	236.169i	0.175459	−	0.498248i
$475$	−68.9222	−	242.872i	−0.145099	−	0.511310i
$476$		−	209.487i		−	0.440100i
$477$	−2.36734	−	1.90336i	−0.00496297	−	0.00399028i
$478$		−	131.056i		−	0.274177i
$479$		−	17.1665i		−	0.0358382i	−0.999839	−	0.0179191i	$-0.994296\pi$
$479$		−	17.1665i		−	0.0358382i	0.999839	−	0.0179191i	$-0.00570414\pi$
$480$	−46.8601	−	70.7399i	−0.0976252	−	0.147375i
$481$	−1060.09			−2.20394
$482$	−268.608			−0.557279
$483$	−144.941	−	51.0413i	−0.300085	−	0.105676i
$484$	181.341			0.374672
$485$	−590.547	−	446.280i	−1.21762	−	0.920165i
$486$	341.093	+	41.8755i	0.701837	+	0.0861637i
$487$			128.206i			0.263257i	0.991299	+	0.131628i	$0.0420206\pi$
$487$			128.206i			0.263257i	−0.991299	+	0.131628i	$0.957979\pi$
$488$	−302.390			−0.619651
$489$	37.1556	+	13.0844i	0.0759827	+	0.0267575i
$490$	277.421	−	367.102i	0.566166	−	0.749188i
$491$			457.658i			0.932094i	0.884760	+	0.466047i	$0.154322\pi$
$491$			457.658i			0.932094i	−0.884760	+	0.466047i	$0.845678\pi$
$492$	−61.3151	−	21.5923i	−0.124624	−	0.0438867i
$493$			275.503i			0.558830i
$494$			239.372i			0.484559i
$495$	60.4651	+	240.335i	0.122152	+	0.485525i
$496$	−189.085			−0.381219
$497$	1307.45			2.63068
$498$	133.527	−	379.173i	0.268126	−	0.761392i
$499$	−522.868			−1.04783			−0.523916	−	0.851770i	$-0.675529\pi$
$499$	−522.868			−1.04783			−0.523916	+	0.851770i	$0.675529\pi$
$500$	−233.025	−	90.5513i	−0.466049	−	0.181103i
$501$	224.694	−	638.060i	0.448491	−	1.27357i
$502$		−	196.842i		−	0.392116i
$503$	−99.9634			−0.198734			−0.0993672	−	0.995051i	$-0.531682\pi$
$503$	−99.9634			−0.198734			−0.0993672	+	0.995051i	$0.531682\pi$
$504$	−170.361	+	211.889i	−0.338017	+	0.420414i
$505$	114.793	+	86.7497i	0.227313	+	0.171782i
$506$			37.3517i			0.0738176i
$507$	111.539	−	316.736i	0.219999	−	0.624727i
$508$		−	448.123i		−	0.882133i
$509$			120.324i			0.236392i	0.992990	+	0.118196i	$0.0377112\pi$
$509$			120.324i			0.236392i	−0.992990	+	0.118196i	$0.962289\pi$
$510$	114.889	+	173.436i	0.225273	+	0.340071i
$511$	197.243			0.385994
$512$	−22.6274			−0.0441942
$513$	231.730	−	143.682i	0.451715	−	0.280081i
$514$	−628.356			−1.22248
$515$	409.714	+	309.623i	0.795560	+	0.601210i
$516$	−389.737	−	137.247i	−0.755303	−	0.265982i
$517$			266.904i			0.516255i
$518$	−955.320			−1.84425
$519$	106.933	−	303.655i	0.206036	−	0.585077i
$520$	189.111	+	142.912i	0.363675	+	0.274831i
$521$			115.841i			0.222344i	0.993801	+	0.111172i	$0.0354604\pi$
$521$			115.841i			0.222344i	−0.993801	+	0.111172i	$0.964540\pi$
$522$	224.046	−	278.661i	0.429207	−	0.533833i
$523$		−	539.428i		−	1.03141i	−0.856766	−	0.515706i	$-0.827530\pi$
$523$		−	539.428i		−	1.03141i	0.856766	−	0.515706i	$-0.172470\pi$
$524$		−	49.3032i		−	0.0940900i
$525$	−49.6969	+	799.495i	−0.0946608	+	1.52285i
$526$	499.835			0.950256
$527$	463.588			0.879674
$528$	62.3343	+	21.9512i	0.118057	+	0.0415742i
$529$	23.0000			0.0434783
$530$	−1.43889	+	1.90403i	−0.00271488	+	0.00359251i
$531$	−461.677	+	574.218i	−0.869449	+	1.08139i
$532$			215.714i			0.405478i
$533$	181.595			0.340704
$534$	−499.653	−	175.954i	−0.935680	−	0.329502i
$535$	429.349	−	568.143i	0.802521	−	1.06195i
$536$		−	84.7231i		−	0.158065i
$537$	998.197	+	351.517i	1.85884	+	0.654595i
$538$		−	96.9716i		−	0.180245i
$539$			358.372i			0.664883i
$540$	24.8370	−	268.855i	0.0459944	−	0.497880i
$541$	96.6585			0.178666			0.0893332	−	0.996002i	$-0.471526\pi$
$541$	96.6585			0.178666			0.0893332	+	0.996002i	$0.471526\pi$
$542$	−75.6103			−0.139502
$543$	−103.235	+	293.155i	−0.190120	+	0.539881i
$544$	55.4767			0.101979
$545$	148.030	−	195.883i	0.271615	−	0.359419i
$546$	252.276	−	716.383i	0.462043	−	1.31206i
$547$		−	313.641i		−	0.573384i	−0.958023	−	0.286692i	$-0.907444\pi$
$547$		−	313.641i		−	0.573384i	0.958023	−	0.286692i	$-0.0925556\pi$
$548$	77.9892			0.142316
$549$	−749.881	−	602.912i	−1.36590	−	1.09820i
$550$	187.313	−	53.1556i	0.340569	−	0.0966466i
$551$		−	283.692i		−	0.514868i
$552$	13.5168	−	38.3835i	0.0244870	−	0.0695354i
$553$			630.325i			1.13983i
$554$			458.187i			0.827053i
$555$	790.918	−	523.926i	1.42508	−	0.944012i
$556$	−221.639			−0.398632
$557$	267.444			0.480150			0.240075	−	0.970754i	$-0.422828\pi$
$557$	267.444			0.480150			0.240075	+	0.970754i	$0.422828\pi$
$558$	−468.902	−	377.002i	−0.840326	−	0.675631i
$559$	1154.27			2.06488
$560$	170.420	+	128.788i	0.304322	+	0.229978i
$561$	−152.828	−	53.8188i	−0.272421	−	0.0959336i
$562$		−	214.218i		−	0.381171i
$563$	−543.496			−0.965358			−0.482679	−	0.875797i	$-0.660336\pi$
$563$	−543.496			−0.965358			−0.482679	+	0.875797i	$0.660336\pi$
$564$	96.5872	−	274.277i	0.171254	−	0.486307i
$565$	−178.220	+	235.832i	−0.315434	+	0.417402i
$566$			338.039i			0.597241i
$567$	−844.938	+	185.783i	−1.49019	+	0.327659i
$568$			346.240i			0.609578i
$569$		−	853.988i		−	1.50086i	−0.660951	−	0.750429i	$-0.729847\pi$
$569$		−	853.988i		−	1.50086i	0.660951	−	0.750429i	$-0.270153\pi$
$570$	−118.304	−	178.592i	−0.207551	−	0.313319i
$571$	−434.281			−0.760563			−0.380281	−	0.924871i	$-0.624173\pi$
$571$	−434.281			−0.760563			−0.380281	+	0.924871i	$0.624173\pi$
$572$	−184.614			−0.322751
$573$	−457.209	−	161.007i	−0.797922	−	0.280990i
$574$	163.647			0.285100
$575$	−32.7316	−	115.341i	−0.0569245	−	0.200594i
$576$	−56.1126	−	45.1151i	−0.0974177	−	0.0783249i
$577$			383.820i			0.665200i	0.943068	+	0.332600i	$0.107926\pi$
$577$			383.820i			0.665200i	−0.943068	+	0.332600i	$0.892074\pi$
$578$	272.693			0.471787
$579$	−316.314	−	111.391i	−0.546311	−	0.192385i
$580$	−224.125	−	169.372i	−0.386422	−	0.292021i
$581$			1012.00i			1.74182i
$582$	−592.429	−	208.625i	−1.01792	−	0.358462i
$583$		−	1.85875i		−	0.00318825i
$584$			52.2341i			0.0894420i
$585$	184.025	+	731.455i	0.314572	+	1.25035i
$586$	−401.474			−0.685110
$587$	1110.21			1.89133			0.945663	−	0.325149i	$-0.105415\pi$
$587$	1110.21			1.89133			0.945663	+	0.325149i	$0.105415\pi$
$588$	129.688	−	368.272i	0.220557	−	0.626313i
$589$	−477.368			−0.810471
$590$	461.839	+	349.015i	0.782778	+	0.591550i
$591$	258.841	−	735.027i	0.437972	−	1.24370i
$592$		−	252.989i		−	0.427347i
$593$	29.9752			0.0505484			0.0252742	−	0.999681i	$-0.491954\pi$
$593$	29.9752			0.0505484			0.0252742	+	0.999681i	$0.491954\pi$
$594$	110.813	+	178.719i	0.186554	+	0.300874i
$595$	−417.828	−	315.755i	−0.702231	−	0.530680i
$596$			173.641i			0.291345i
$597$	85.7621	−	243.537i	0.143655	−	0.407935i
$598$			113.679i			0.190099i
$599$			382.745i			0.638973i	0.947591	+	0.319487i	$0.103510\pi$
$599$			382.745i			0.638973i	−0.947591	+	0.319487i	$0.896490\pi$
$600$	−211.723	−	13.1608i	−0.352872	−	0.0219347i
$601$	961.642			1.60007			0.800035	−	0.599954i	$-0.204814\pi$
$601$	961.642			1.60007			0.800035	+	0.599954i	$0.204814\pi$
$602$	1040.19			1.72789
$603$	168.923	−	210.101i	0.280138	−	0.348426i
$604$	−229.910			−0.380645
$605$	273.331	−	361.690i	0.451787	−	0.597834i
$606$	115.159	+	40.5534i	0.190031	+	0.0669198i
$607$			229.123i			0.377468i	0.982028	+	0.188734i	$0.0604383\pi$
$607$			229.123i			0.377468i	−0.982028	+	0.188734i	$0.939562\pi$
$608$	−57.1257			−0.0939568
$609$	−298.985	+	849.021i	−0.490943	+	1.39412i
$610$	−455.784	+	603.123i	−0.747187	+	0.988727i
$611$			812.317i			1.32949i
$612$	137.574	+	110.611i	0.224794	+	0.180737i
$613$		−	1083.98i		−	1.76831i	−0.467191	−	0.884156i	$-0.654734\pi$
$613$		−	1083.98i		−	1.76831i	0.467191	−	0.884156i	$-0.345266\pi$
$614$			470.210i			0.765814i
$615$	−135.485	+	89.7491i	−0.220301	+	0.145933i
$616$	−166.367			−0.270077
$617$	−1155.91			−1.87344			−0.936721	−	0.350076i	$-0.886156\pi$
$617$	−1155.91			−1.87344			−0.936721	+	0.350076i	$0.886156\pi$
$618$	411.019	+	144.741i	0.665080	+	0.234209i
$619$	−85.6341			−0.138343			−0.0691713	−	0.997605i	$-0.522036\pi$
$619$	−85.6341			−0.138343			−0.0691713	+	0.997605i	$0.522036\pi$
$620$	−285.002	+	377.134i	−0.459681	+	0.608280i
$621$	110.050	−	68.2352i	0.177214	−	0.109880i
$622$			460.765i			0.740780i
$623$	1333.55			2.14053
$624$	189.713	+	66.8080i	0.304028	+	0.107064i
$625$	−531.839	+	328.287i	−0.850942	+	0.525260i
$626$		−	247.852i		−	0.395930i
$627$	157.371	+	55.4184i	0.250990	+	0.0883867i
$628$			394.796i			0.628655i
$629$			620.266i			0.986115i
$630$	165.837	+	659.162i	0.263233	+	1.04629i
$631$	630.139			0.998636			0.499318	−	0.866419i	$-0.333584\pi$
$631$	630.139			0.998636			0.499318	+	0.866419i	$0.333584\pi$
$632$	−166.924			−0.264120
$633$	−117.305	+	333.108i	−0.185316	+	0.526238i
$634$	−194.259			−0.306403
$635$	−893.793	−	675.445i	−1.40755	−	1.06369i
$636$	−0.672645	+	1.91010i	−0.00105762	+	0.00300330i
$637$			1090.70i			1.71224i
$638$	218.795			0.342939
$639$	−690.343	+	858.624i	−1.08035	+	1.34370i
$640$	−34.1057	+	45.1309i	−0.0532902	+	0.0705171i
$641$			283.428i			0.442165i	0.975255	+	0.221083i	$0.0709591\pi$
$641$			283.428i			0.442165i	−0.975255	+	0.221083i	$0.929041\pi$
$642$	200.710	−	569.953i	0.312633	−	0.887778i
$643$		−	1037.58i		−	1.61366i	−0.590785	−	0.806829i	$-0.701182\pi$
$643$		−	1037.58i		−	1.61366i	0.590785	−	0.806829i	$-0.298818\pi$
$644$			102.444i			0.159074i
$645$	−861.181	+	570.471i	−1.33516	+	0.884451i
$646$	140.058			0.216808
$647$	−1085.51			−1.67776			−0.838878	−	0.544320i	$-0.816788\pi$
$647$	−1085.51			−1.67776			−0.838878	+	0.544320i	$0.816788\pi$
$648$	−49.1992	−	223.758i	−0.0759247	−	0.345305i
$649$	−450.856			−0.694693
$650$	570.084	−	161.778i	0.877052	−	0.248889i
$651$	1428.64	+	503.100i	2.19454	+	0.772811i
$652$		−	26.2614i		−	0.0402782i
$653$	1104.68			1.69170			0.845851	−	0.533420i	$-0.179093\pi$
$653$	1104.68			1.69170			0.845851	+	0.533420i	$0.179093\pi$
$654$	69.2005	−	196.507i	0.105811	−	0.300470i
$655$	−98.3364	−	74.3134i	−0.150132	−	0.113456i
$656$			43.3373i			0.0660629i
$657$	−104.146	+	129.533i	−0.158517	+	0.197158i
$658$			732.032i			1.11251i
$659$			1185.91i			1.79955i	0.436351	+	0.899777i	$0.356271\pi$
$659$			1185.91i			1.79955i	−0.436351	+	0.899777i	$0.643729\pi$
$660$	137.737	−	91.2409i	0.208693	−	0.138244i
$661$	3.97567			0.00601463			0.00300732	−	0.999995i	$-0.499043\pi$
$661$	3.97567			0.00601463			0.00300732	+	0.999995i	$0.499043\pi$
$662$	527.585			0.796957
$663$	−465.130	−	163.796i	−0.701553	−	0.247053i
$664$	−267.998			−0.403612
$665$	430.247	+	325.140i	0.646988	+	0.488933i
$666$	504.417	−	627.376i	0.757382	−	0.942006i
$667$		−	134.727i		−	0.201989i
$668$	−450.978			−0.675117
$669$	−894.572	−	315.026i	−1.33718	−	0.470890i
$670$	−168.982	−	127.701i	−0.252212	−	0.190598i
$671$		−	588.780i		−	0.877467i
$672$	170.963	+	60.2051i	0.254410	+	0.0895909i
$673$			549.345i			0.816263i	0.912923	+	0.408131i	$0.133819\pi$
$673$			549.345i			0.816263i	−0.912923	+	0.408131i	$0.866181\pi$
$674$		−	65.3549i		−	0.0969658i
$675$	−498.802	−	454.776i	−0.738966	−	0.673743i
$676$	−223.868			−0.331166
$677$	−262.064			−0.387096			−0.193548	−	0.981091i	$-0.562000\pi$
$677$	−262.064			−0.387096			−0.193548	+	0.981091i	$0.562000\pi$
$678$	−83.3135	+	236.584i	−0.122881	+	0.348944i
$679$	1581.16			2.32867
$680$	83.6186	−	110.650i	0.122969	−	0.162720i
$681$	445.466	−	1264.98i	0.654135	−	1.85754i
$682$		−	368.165i		−	0.539832i
$683$	420.062			0.615024			0.307512	−	0.951544i	$-0.400504\pi$
$683$	420.062			0.615024			0.307512	+	0.951544i	$0.400504\pi$
$684$	−141.663	−	113.899i	−0.207110	−	0.166519i
$685$	117.551	−	155.551i	0.171607	−	0.227082i
$686$			242.779i			0.353905i
$687$	−46.0825	+	130.860i	−0.0670778	+	0.190480i
$688$			275.464i			0.400384i
$689$		−	5.65707i		−	0.00821055i
$690$	−56.1833	−	84.8141i	−0.0814250	−	0.122919i
$691$	495.971			0.717758			0.358879	−	0.933384i	$-0.383159\pi$
$691$	495.971			0.717758			0.358879	+	0.933384i	$0.383159\pi$
$692$	−214.622			−0.310147
$693$	−412.566	−	331.708i	−0.595334	−	0.478655i
$694$	617.182			0.889311
$695$	−334.071	+	442.065i	−0.480678	+	0.636065i
$696$	−224.839	−	79.1775i	−0.323044	−	0.113761i
$697$		−	106.252i		−	0.152442i
$698$	204.270			0.292651
$699$	4.36084	−	12.3834i	0.00623868	−	0.0177159i
$700$	513.740	−	145.789i	0.733914	−	0.208270i
$701$			29.5797i			0.0421964i	0.999777	+	0.0210982i	$0.00671627\pi$
$701$			29.5797i			0.0421964i	−0.999777	+	0.0210982i	$0.993284\pi$
$702$	337.258	+	543.929i	0.480424	+	0.774828i
$703$		−	638.703i		−	0.908539i
$704$		−	44.0577i		−	0.0625819i
$705$	−401.468	−	606.056i	−0.569459	−	0.859654i
$706$	181.075			0.256480
$707$	−307.353			−0.434729
$708$	463.311	+	163.156i	0.654394	+	0.230446i
$709$	−912.295			−1.28673			−0.643367	−	0.765558i	$-0.722463\pi$
$709$	−912.295			−1.28673			−0.643367	+	0.765558i	$0.722463\pi$
$710$	690.585	+	521.879i	0.972654	+	0.735041i
$711$	−413.946	−	332.816i	−0.582202	−	0.468096i
$712$			353.153i			0.496001i
$713$	−226.705			−0.317959
$714$	−419.159	−	147.608i	−0.587057	−	0.206734i
$715$	−278.263	+	368.216i	−0.389179	+	0.514988i
$716$		−	705.522i		−	0.985366i
$717$	−262.228	−	92.3442i	−0.365730	−	0.128792i
$718$		−	316.153i		−	0.440325i
$719$			55.2032i			0.0767777i	0.999263	+	0.0383889i	$0.0122226\pi$
$719$			55.2032i			0.0767777i	−0.999263	+	0.0383889i	$0.987777\pi$
$720$	−174.560	+	43.9171i	−0.242445	+	0.0609960i
$721$	−1096.99			−1.52149
$722$	366.310			0.507355
$723$	−189.265	+	537.453i	−0.261778	+	0.743365i
$724$	207.201			0.286189
$725$	−675.635	+	191.731i	−0.931910	+	0.264457i
$726$	127.776	−	362.842i	0.175999	−	0.499783i
$727$		−	262.617i		−	0.361234i	−0.983554	−	0.180617i	$-0.942191\pi$
$727$		−	262.617i		−	0.361234i	0.983554	−	0.180617i	$-0.0578094\pi$
$728$	−506.336			−0.695517
$729$	324.127	−	652.980i	0.444618	−	0.895720i
$730$	104.182	+	78.7312i	0.142715	+	0.107851i
$731$		−	675.369i		−	0.923897i
$732$	−213.068	+	605.045i	−0.291076	+	0.826564i
$733$			889.774i			1.21388i	0.794748	+	0.606940i	$0.207603\pi$
$733$			889.774i			1.21388i	−0.794748	+	0.606940i	$0.792397\pi$
$734$			339.326i			0.462298i
$735$	−539.052	−	813.752i	−0.733404	−	1.10714i
$736$	−27.1293			−0.0368605
$737$	164.964			0.223831
$738$	−86.4070	+	107.470i	−0.117083	+	0.145623i
$739$	−1099.71			−1.48811			−0.744053	−	0.668121i	$-0.767099\pi$
$739$	−1099.71			−1.48811			−0.744053	+	0.668121i	$0.767099\pi$
$740$	−504.593	−	381.324i	−0.681883	−	0.515303i
$741$	478.955	+	168.665i	0.646363	+	0.227618i
$742$		−	5.09796i		−	0.00687057i
$743$	589.255			0.793076			0.396538	−	0.918018i	$-0.370212\pi$
$743$	589.255			0.793076			0.396538	+	0.918018i	$0.370212\pi$
$744$	−133.232	+	378.336i	−0.179075	+	0.508516i
$745$	346.332	+	261.725i	0.464875	+	0.351309i
$746$			330.903i			0.443570i
$747$	−664.595	−	534.342i	−0.889686	−	0.715317i
$748$			108.018i			0.144410i
$749$			1521.18i			2.03095i
$750$	−345.375	+	402.450i	−0.460500	+	0.536601i
$751$	1379.99			1.83753			0.918766	−	0.394802i	$-0.129187\pi$
$751$	1379.99			1.83753			0.918766	+	0.394802i	$0.129187\pi$
$752$	−193.858			−0.257790
$753$	−393.858	−	138.698i	−0.523052	−	0.184194i
$754$	665.898			0.883154
$755$	−346.537	+	458.561i	−0.458990	+	0.607365i
$756$	303.925	+	490.171i	0.402017	+	0.648374i
$757$		−	878.486i		−	1.16048i	−0.814444	−	0.580242i	$-0.802958\pi$
$757$		−	878.486i		−	1.16048i	0.814444	−	0.580242i	$-0.197042\pi$
$758$	−228.471			−0.301413
$759$	74.7363	+	26.3185i	0.0984667	+	0.0346753i
$760$	−86.1041	+	113.939i	−0.113295	+	0.149919i
$761$		−	722.402i		−	0.949280i	−0.880180	−	0.474640i	$-0.842578\pi$
$761$		−	722.402i		−	0.949280i	0.880180	−	0.474640i	$-0.157422\pi$
$762$	−896.641	−	315.754i	−1.17669	−	0.414375i
$763$			524.469i			0.687377i
$764$			323.154i			0.422976i
$765$	427.978	−	107.674i	0.559448	−	0.140750i
$766$	628.836			0.820934
$767$	−1372.17			−1.78901
$768$	−15.9436	+	45.2747i	−0.0207599	+	0.0589515i
$769$	800.009			1.04032			0.520162	−	0.854068i	$-0.325872\pi$
$769$	800.009			1.04032			0.520162	+	0.854068i	$0.325872\pi$
$770$	−250.761	+	331.824i	−0.325664	+	0.430940i
$771$	−442.748	+	1257.26i	−0.574252	+	1.63069i
$772$			223.569i			0.289598i
$773$	−615.477			−0.796219			−0.398109	−	0.917338i	$-0.630334\pi$
$773$	−615.477			−0.796219			−0.398109	+	0.917338i	$0.630334\pi$
$774$	−549.228	+	683.110i	−0.709596	+	0.882571i
$775$	322.626	+	1136.89i	0.416291	+	1.46695i
$776$			418.726i			0.539596i
$777$	−673.132	+	1911.48i	−0.866322	+	2.46008i
$778$			663.710i			0.853097i
$779$			109.410i			0.140450i
$780$	419.200	−	277.690i	0.537436	−	0.356013i
$781$	−674.162			−0.863203
$782$	66.5143			0.0850566
$783$	−399.701	−	644.638i	−0.510474	−	0.823292i
$784$	−260.293			−0.332006
$785$	787.429	+	595.065i	1.00309	+	0.758045i
$786$	−98.6497	−	34.7397i	−0.125509	−	0.0441981i
$787$		−	804.892i		−	1.02273i	−0.859362	−	0.511367i	$-0.829139\pi$
$787$		−	804.892i		−	1.02273i	0.859362	−	0.511367i	$-0.170861\pi$
$788$	−519.514			−0.659282
$789$	352.191	−	1000.11i	0.446376	−	1.26757i
$790$	−251.600	+	332.933i	−0.318480	+	0.421434i
$791$		−	631.431i		−	0.798270i
$792$	87.8433	−	109.256i	0.110913	−	0.137950i
$793$		−	1791.94i		−	2.25970i
$794$			68.4262i			0.0861791i
$795$	2.79587	+	4.22065i	0.00351682	+	0.00530899i
$796$	−172.131			−0.216245
$797$	−1327.88			−1.66610			−0.833051	−	0.553196i	$-0.813408\pi$
$797$	−1327.88			−1.66610			−0.833051	+	0.553196i	$0.813408\pi$
$798$	431.618	+	151.995i	0.540875	+	0.190470i
$799$	475.291			0.594857
$800$	38.6080	+	136.049i	0.0482601	+	0.170062i
$801$	−704.125	+	875.766i	−0.879058	+	1.09334i
$802$		−	608.113i		−	0.758246i
$803$	−101.705			−0.126656
$804$	−169.521	−	59.6971i	−0.210847	−	0.0742501i
$805$	204.327	+	154.411i	0.253822	+	0.191815i
$806$		−	1120.50i		−	1.39020i
$807$	−194.029	−	68.3275i	−0.240432	−	0.0846686i
$808$		−	81.3937i		−	0.100735i
$809$		−	808.503i		−	0.999385i	−0.866203	−	0.499693i	$-0.833446\pi$
$809$		−	808.503i		−	0.999385i	0.866203	−	0.499693i	$-0.166554\pi$
$810$	−520.446	−	239.135i	−0.642526	−	0.295228i
$811$	320.234			0.394863			0.197431	−	0.980317i	$-0.436740\pi$
$811$	320.234			0.394863			0.197431	+	0.980317i	$0.436740\pi$
$812$	600.085			0.739020
$813$	−53.2761	+	151.287i	−0.0655302	+	0.186085i
$814$	492.593			0.605152
$815$	−52.3790	−	39.5831i	−0.0642687	−	0.0485682i
$816$	39.0897	−	111.002i	0.0479040	−	0.136032i
$817$			695.443i			0.851216i
$818$	−291.938			−0.356892
$819$	−1255.64	−	1009.55i	−1.53314	−	1.23266i
$820$	86.4373	+	65.3212i	0.105411	+	0.0796600i
$821$			920.659i			1.12139i	0.828024	+	0.560693i	$0.189465\pi$
$821$			920.659i			1.12139i	−0.828024	+	0.560693i	$0.810535\pi$
$822$	54.9523	−	156.047i	0.0668519	−	0.189838i
$823$		−	707.429i		−	0.859573i	−0.902930	−	0.429787i	$-0.858589\pi$
$823$		−	707.429i		−	0.859573i	0.902930	−	0.429787i	$-0.141411\pi$
$824$		−	290.507i		−	0.352557i
$825$	25.6253	−	412.245i	0.0310610	−	0.499691i
$826$	−1236.55			−1.49704
$827$	1125.84			1.36136			0.680680	−	0.732581i	$-0.261685\pi$
$827$	1125.84			1.36136			0.680680	+	0.732581i	$0.261685\pi$
$828$	−67.2767	−	54.0911i	−0.0812520	−	0.0653275i
$829$	1349.79			1.62822			0.814109	−	0.580711i	$-0.197226\pi$
$829$	1349.79			1.62822			0.814109	+	0.580711i	$0.197226\pi$
$830$	−403.947	+	534.529i	−0.486683	+	0.644010i
$831$	916.778	+	322.845i	1.10322	+	0.388502i
$832$		−	134.089i		−	0.161164i
$833$	638.173			0.766114
$834$	−156.170	+	443.474i	−0.187254	+	0.531743i
$835$	−679.748	+	899.487i	−0.814069	+	1.07723i
$836$		−	111.229i		−	0.133049i
$837$	−1084.73	+	672.575i	−1.29597	+	0.803555i
$838$			111.101i			0.132578i
$839$		−	1130.65i		−	1.34761i	−0.738909	−	0.673805i	$-0.764659\pi$
$839$		−	1130.65i		−	1.34761i	0.738909	−	0.673805i	$-0.235341\pi$
$840$	377.769	−	250.245i	0.449725	−	0.297910i
$841$	51.8108			0.0616061
$842$	182.597			0.216861
$843$	−428.625	−	150.941i	−0.508452	−	0.179052i
$844$	235.440			0.278957
$845$	−337.430	+	446.510i	−0.399326	+	0.528414i
$846$	−480.738	−	386.519i	−0.568249	−	0.456878i
$847$			968.409i			1.14334i
$848$	1.35005			0.00159204
$849$	676.374	+	238.187i	0.796672	+	0.280550i
$850$	−94.6572	−	333.559i	−0.111361	−	0.392422i
$851$		−	303.324i		−	0.356432i
$852$	692.785	+	243.966i	0.813128	+	0.286345i
$853$		−	1110.13i		−	1.30144i	−0.759319	−	0.650718i	$-0.774468\pi$
$853$		−	1110.13i		−	1.30144i	0.759319	−	0.650718i	$-0.225532\pi$
$854$		−	1614.84i		−	1.89091i
$855$	−440.699	+	110.874i	−0.515437	+	0.129677i
$856$	−402.841			−0.470608
$857$	−1486.49			−1.73453			−0.867265	−	0.497847i	$-0.834124\pi$
$857$	−1486.49			−1.73453			−0.867265	+	0.497847i	$0.834124\pi$
$858$	−130.081	+	369.390i	−0.151610	+	0.430524i
$859$	1194.01			1.39000			0.695001	−	0.719009i	$-0.255404\pi$
$859$	1194.01			1.39000			0.695001	+	0.719009i	$0.255404\pi$
$860$	549.420	+	415.200i	0.638860	+	0.482791i
$861$	115.308	−	327.438i	0.133923	−	0.380300i
$862$		−	313.257i		−	0.363407i
$863$	−205.277			−0.237864			−0.118932	−	0.992902i	$-0.537947\pi$
$863$	−205.277			−0.237864			−0.118932	+	0.992902i	$0.537947\pi$
$864$	−129.808	+	80.4858i	−0.150240	+	0.0931549i
$865$	−323.494	+	428.069i	−0.373982	+	0.494877i
$866$		−	530.242i		−	0.612289i
$867$	192.143	−	545.625i	0.221618	−	0.629326i
$868$		−	1009.76i		−	1.16332i
$869$		−	325.016i		−	0.374011i
$870$	−496.815	+	329.104i	−0.571052	+	0.378281i
$871$	502.064			0.576422
$872$	−138.891			−0.159278
$873$	−834.867	+	1038.38i	−0.956320	+	1.18944i
$874$	−68.4913			−0.0783654
$875$	483.567	−	1244.41i	0.552648	−	1.42218i
$876$	104.514	+	36.8049i	0.119308	+	0.0420147i
$877$		−	800.543i		−	0.912820i	−0.889770	−	0.456410i	$-0.849135\pi$
$877$		−	800.543i		−	0.912820i	0.889770	−	0.456410i	$-0.150865\pi$
$878$	−601.963			−0.685607
$879$	−282.884	+	803.302i	−0.321825	+	0.913881i
$880$	−87.8741	−	66.4070i	−0.0998569	−	0.0754625i
$881$			282.213i			0.320332i	0.987090	+	0.160166i	$0.0512030\pi$
$881$			282.213i			0.320332i	−0.987090	+	0.160166i	$0.948797\pi$
$882$	−645.488	−	518.979i	−0.731845	−	0.588411i
$883$			788.760i			0.893273i	0.894716	+	0.446636i	$0.147378\pi$
$883$			788.760i			0.893273i	−0.894716	+	0.446636i	$0.852622\pi$
$884$			328.752i			0.371891i
$885$	1023.75	−	678.164i	1.15678	−	0.766287i
$886$	−1102.02			−1.24381
$887$	−81.0394			−0.0913635			−0.0456817	−	0.998956i	$-0.514546\pi$
$887$	−81.0394			−0.0913635			−0.0456817	+	0.998956i	$0.514546\pi$
$888$	−506.201	−	178.260i	−0.570046	−	0.200743i
$889$	2393.09			2.69189
$890$	704.372	+	532.298i	0.791429	+	0.598088i
$891$	435.677	−	95.7954i	0.488975	−	0.107514i
$892$			632.280i			0.708834i
$893$	−489.418			−0.548060
$894$	347.435	+	122.350i	0.388630	+	0.136857i
$895$	−1407.18	−	1063.41i	−1.57227	−	1.18817i
$896$		−	120.836i		−	0.134862i
$897$	227.458	+	80.1000i	0.253577	+	0.0892976i
$898$		−	736.863i		−	0.820560i
$899$			1327.97i			1.47716i
$900$	−175.516	+	414.360i	−0.195018	+	0.460400i
$901$	−3.30998			−0.00367367
$902$	−84.3817			−0.0935495
$903$	732.931	−	2081.29i	0.811663	−	2.30486i
$904$	167.216			0.184974
$905$	312.309	−	413.267i	0.345092	−	0.456649i
$906$	−161.998	+	460.022i	−0.178805	+	0.507751i
$907$			1229.22i			1.35526i	0.735405	+	0.677628i	$0.236992\pi$
$907$			1229.22i			1.35526i	−0.735405	+	0.677628i	$0.763008\pi$
$908$	−894.084			−0.984674
$909$	162.285	−	201.844i	0.178531	−	0.222051i
$910$	−763.187	+	1009.90i	−0.838668	+	1.10978i
$911$			613.166i			0.673069i	0.941671	+	0.336534i	$0.109255\pi$
$911$			613.166i			0.673069i	−0.941671	+	0.336534i	$0.890745\pi$
$912$	−40.2516	+	114.302i	−0.0441355	+	0.125331i
$913$		−	521.817i		−	0.571541i
$914$		−	153.110i		−	0.167516i
$915$	885.625	+	1336.94i	0.967896	+	1.46113i
$916$	92.4910			0.100973
$917$	263.291			0.287123
$918$	318.256	−	197.331i	0.346684	−	0.214958i
$919$	1349.58			1.46853			0.734263	−	0.678865i	$-0.237528\pi$
$919$	1349.58			1.46853			0.734263	+	0.678865i	$0.237528\pi$
$920$	−40.8913	+	54.1101i	−0.0444471	+	0.0588153i
$921$	940.833	+	331.316i	1.02153	+	0.359735i
$922$			747.946i			0.811222i
$923$	−2051.80			−2.22297
$924$	−117.225	+	332.881i	−0.126867	+	0.360261i
$925$	−1521.12	+	431.663i	−1.64445	+	0.466663i
$926$		−	383.052i		−	0.413663i
$927$	579.220	−	720.413i	0.624833	−	0.777145i
$928$			158.915i			0.171245i
$929$			707.214i			0.761264i	0.924727	+	0.380632i	$0.124294\pi$
$929$			707.214i			0.761264i	−0.924727	+	0.380632i	$0.875706\pi$
$930$	553.783	+	835.989i	0.595465	+	0.898913i
$931$	−657.142			−0.705845
$932$	−8.75253			−0.00939113
$933$	921.936	+	324.662i	0.988141	+	0.347976i
$934$	265.168			0.283905
$935$	215.445	+	162.813i	0.230423	+	0.174132i
$936$	267.349	−	332.520i	0.285630	−	0.355256i
$937$			910.608i			0.971833i	0.874005	+	0.485917i	$0.161514\pi$
$937$			910.608i			0.971833i	−0.874005	+	0.485917i	$0.838486\pi$
$938$	452.443			0.482349
$939$	−495.922	−	174.640i	−0.528138	−	0.185985i
$940$	−292.197	+	386.654i	−0.310848	+	0.411334i
$941$			755.654i			0.803033i	0.915852	+	0.401517i	$0.131517\pi$
$941$			755.654i			0.803033i	−0.915852	+	0.401517i	$0.868483\pi$
$942$	789.938	+	278.178i	0.838576	+	0.295306i
$943$			51.9596i			0.0551003i
$944$		−	327.466i		−	0.346892i
$945$	1435.76	+	132.636i	1.51932	+	0.140355i
$946$	−536.354			−0.566971
$947$	1431.51			1.51162			0.755812	−	0.654789i	$-0.227242\pi$
$947$	1431.51			1.51162			0.755812	+	0.654789i	$0.227242\pi$
$948$	−117.617	+	333.994i	−0.124068	+	0.352314i
$949$	−309.536			−0.326171
$950$	97.4708	+	343.473i	0.102601	+	0.361551i
$951$	−136.878	+	388.689i	−0.143930	+	0.408716i
$952$			296.260i			0.311197i
$953$	397.022			0.416602			0.208301	−	0.978065i	$-0.433207\pi$
$953$	397.022			0.416602			0.208301	+	0.978065i	$0.433207\pi$
$954$	3.34792	+	2.69176i	0.00350935	+	0.00282155i
$955$	644.538	+	487.081i	0.674909	+	0.510033i
$956$			185.342i			0.193872i
$957$	154.166	−	437.782i	0.161093	−	0.457453i
$958$			24.2771i			0.0253415i
$959$			416.482i			0.434288i
$960$	66.2702	+	100.041i	0.0690314	+	0.104210i
$961$	1273.56			1.32525
$962$	1499.20			1.55842
$963$	−998.985	−	803.194i	−1.03737	−	0.834054i
$964$	379.870			0.394056
$965$	445.915	+	336.980i	0.462088	+	0.349203i
$966$	204.978	+	72.1833i	0.212192	+	0.0747240i
$967$		−	1611.96i		−	1.66697i	−0.552541	−	0.833486i	$-0.686342\pi$
$967$		−	1611.96i		−	1.66697i	0.552541	−	0.833486i	$-0.313658\pi$
$968$	−256.455			−0.264933
$969$	98.6867	−	280.239i	0.101844	−	0.289204i
$970$	835.159	+	631.135i	0.860989	+	0.650655i
$971$			1159.75i			1.19438i	0.802098	+	0.597192i	$0.203717\pi$
$971$			1159.75i			1.19438i	−0.802098	+	0.597192i	$0.796283\pi$
$972$	−482.378	−	59.2210i	−0.496274	−	0.0609269i
$973$		−	1183.61i		−	1.21645i
$974$		−	181.311i		−	0.186151i
$975$	77.9902	−	1254.66i	0.0799899	−	1.28683i
$976$	427.643			0.438159
$977$	1542.30			1.57861			0.789305	−	0.614001i	$-0.210441\pi$
$977$	1542.30			1.57861			0.789305	+	0.614001i	$0.210441\pi$
$978$	−52.5459	−	18.5041i	−0.0537279	−	0.0189204i
$979$	−687.621			−0.702371
$980$	−392.333	+	519.161i	−0.400340	+	0.529756i
$981$	−344.428	−	276.924i	−0.351099	−	0.282287i
$982$		−	647.226i		−	0.659090i
$983$	365.454			0.371774			0.185887	−	0.982571i	$-0.440484\pi$
$983$	365.454			0.371774			0.185887	+	0.982571i	$0.440484\pi$
$984$	86.7127	+	30.5361i	0.0881227	+	0.0310326i
$985$	−783.050	+	1036.18i	−0.794974	+	1.05196i
$986$		−	389.620i		−	0.395152i
$987$	1464.71	+	515.800i	1.48400	+	0.522594i
$988$		−	338.523i		−	0.342635i
$989$			330.270i			0.333943i
$990$	−85.5106	−	339.885i	−0.0863744	−	0.343318i
$991$	185.858			0.187546			0.0937730	−	0.995594i	$-0.470107\pi$
$991$	185.858			0.187546			0.0937730	+	0.995594i	$0.470107\pi$
$992$	267.406			0.269563
$993$	371.744	−	1055.63i	0.374365	−	1.06308i
$994$	−1849.01			−1.86017
$995$	−259.449	+	343.320i	−0.260752	+	0.345045i
$996$	−188.835	+	536.232i	−0.189594	+	0.538386i
$997$			679.636i			0.681681i	0.940121	+	0.340840i	$0.110712\pi$
$997$			679.636i			0.681681i	−0.940121	+	0.340840i	$0.889288\pi$
$998$	739.447			0.740929
$999$	−899.884	−	1451.33i	−0.900785	−	1.45279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.b.a.599.20	yes	88
3.2	odd	2	inner	690.3.b.a.599.70	yes	88
5.4	even	2	inner	690.3.b.a.599.69	yes	88
15.14	odd	2	inner	690.3.b.a.599.19	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.b.a.599.19	✓	88	15.14	odd	2	inner
690.3.b.a.599.20	yes	88	1.1	even	1	trivial
690.3.b.a.599.69	yes	88	5.4	even	2	inner
690.3.b.a.599.70	yes	88	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(-0.996475 + 2.82967i) q^{3} +2.00000 q^{4} +(3.01455 - 3.98905i) q^{5} +(1.40923 - 4.00176i) q^{6} +10.6805i q^{7} -2.82843 q^{8} +(-7.01408 - 5.63939i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(-0.996475 + 2.82967i) q^{3} +2.00000 q^{4} +(3.01455 - 3.98905i) q^{5} +(1.40923 - 4.00176i) q^{6} +10.6805i q^{7} -2.82843 q^{8} +(-7.01408 - 5.63939i) q^{9} +(-4.26321 + 5.64137i) q^{10} -5.50721i q^{11} +(-1.99295 + 5.65934i) q^{12} -16.7611i q^{13} -15.1045i q^{14} +(8.28377 + 12.5052i) q^{15} +4.00000 q^{16} -9.80700 q^{17} +(9.91940 + 7.97530i) q^{18} +10.0985 q^{19} +(6.02910 - 7.97810i) q^{20} +(-30.2223 - 10.6429i) q^{21} +7.78837i q^{22} +4.79583 q^{23} +(2.81846 - 8.00352i) q^{24} +(-6.82500 - 24.0504i) q^{25} +23.7038i q^{26} +(22.9470 - 14.2280i) q^{27} +21.3610i q^{28} -28.0925i q^{29} +(-11.7150 - 17.6850i) q^{30} -47.2712 q^{31} -5.65685 q^{32} +(15.5836 + 5.48779i) q^{33} +13.8692 q^{34} +(42.6051 + 32.1969i) q^{35} +(-14.0282 - 11.2788i) q^{36} -63.2473i q^{37} -14.2814 q^{38} +(47.4284 + 16.7020i) q^{39} +(-8.52643 + 11.2827i) q^{40} +10.8343i q^{41} +(42.7408 + 15.0513i) q^{42} +68.8660i q^{43} -11.0144i q^{44} +(-43.6401 + 10.9793i) q^{45} -6.78233 q^{46} -48.4644 q^{47} +(-3.98590 + 11.3187i) q^{48} -65.0732 q^{49} +(9.65201 + 34.0123i) q^{50} +(9.77242 - 27.7506i) q^{51} -33.5222i q^{52} +0.337512 q^{53} +(-32.4519 + 20.1215i) q^{54} +(-21.9685 - 16.6017i) q^{55} -30.2090i q^{56} +(-10.0629 + 28.5754i) q^{57} +39.7288i q^{58} -81.8665i q^{59} +(16.5675 + 25.0103i) q^{60} +106.911 q^{61} +66.8515 q^{62} +(60.2316 - 74.9139i) q^{63} +8.00000 q^{64} +(-66.8608 - 50.5271i) q^{65} +(-22.0385 - 7.76091i) q^{66} +29.9541i q^{67} -19.6140 q^{68} +(-4.77892 + 13.5706i) q^{69} +(-60.2526 - 45.5333i) q^{70} -122.414i q^{71} +(19.8388 + 15.9506i) q^{72} -18.4676i q^{73} +89.4452i q^{74} +(74.8555 + 4.65305i) q^{75} +20.1970 q^{76} +58.8198 q^{77} +(-67.0738 - 23.6202i) q^{78} +59.0164 q^{79} +(12.0582 - 15.9562i) q^{80} +(17.3945 + 79.1102i) q^{81} -15.3220i q^{82} +94.7516 q^{83} +(-60.4446 - 21.2857i) q^{84} +(-29.5637 + 39.1206i) q^{85} -97.3913i q^{86} +(79.4926 + 27.9935i) q^{87} +15.5767i q^{88} -124.858i q^{89} +(61.7164 - 15.5270i) q^{90} +179.017 q^{91} +9.59166 q^{92} +(47.1045 - 133.762i) q^{93} +68.5391 q^{94} +(30.4424 - 40.2834i) q^{95} +(5.63691 - 16.0070i) q^{96} -148.042i q^{97} +92.0275 q^{98} +(-31.0573 + 38.6280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 176 q^{4} + 8 q^{9}+O(q^{10}) \) 88 * q + 176 * q^4 + 8 * q^9	\( 88 q + 176 q^{4} + 8 q^{9} + 32 q^{10} - 12 q^{15} + 352 q^{16} - 16 q^{19} - 176 q^{21} + 72 q^{25} - 72 q^{30} + 32 q^{31} + 160 q^{34} + 16 q^{36} + 144 q^{39} + 64 q^{40} + 92 q^{45} - 360 q^{49} + 48 q^{51} - 144 q^{54} + 16 q^{55} - 24 q^{60} + 208 q^{61} + 704 q^{64} + 512 q^{66} + 304 q^{70} + 536 q^{75} - 32 q^{76} + 448 q^{79} - 24 q^{81} - 352 q^{84} - 96 q^{85} + 32 q^{90} - 64 q^{91} + 160 q^{94} + 296 q^{99}+O(q^{100}) \) 88 * q + 176 * q^4 + 8 * q^9 + 32 * q^10 - 12 * q^15 + 352 * q^16 - 16 * q^19 - 176 * q^21 + 72 * q^25 - 72 * q^30 + 32 * q^31 + 160 * q^34 + 16 * q^36 + 144 * q^39 + 64 * q^40 + 92 * q^45 - 360 * q^49 + 48 * q^51 - 144 * q^54 + 16 * q^55 - 24 * q^60 + 208 * q^61 + 704 * q^64 + 512 * q^66 + 304 * q^70 + 536 * q^75 - 32 * q^76 + 448 * q^79 - 24 * q^81 - 352 * q^84 - 96 * q^85 + 32 * q^90 - 64 * q^91 + 160 * q^94 + 296 * q^99

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