LMFDB - Embedded newform 690.3.b.a.599.9

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			599.9
Character	$\chi$	$=$	690.599
Dual form			690.3.b.a.599.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(-2.16793 - 2.07367i) q^{3} +2.00000 q^{4} +(4.21296 - 2.69276i) q^{5} +(3.06591 + 2.93261i) q^{6} -3.87132i q^{7} -2.82843 q^{8} +(0.399825 + 8.99111i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(-2.16793 - 2.07367i) q^{3} +2.00000 q^{4} +(4.21296 - 2.69276i) q^{5} +(3.06591 + 2.93261i) q^{6} -3.87132i q^{7} -2.82843 q^{8} +(0.399825 + 8.99111i) q^{9} +(-5.95803 + 3.80814i) q^{10} +5.04237i q^{11} +(-4.33586 - 4.14733i) q^{12} -15.3444i q^{13} +5.47487i q^{14} +(-14.7173 - 2.89856i) q^{15} +4.00000 q^{16} -10.2474 q^{17} +(-0.565438 - 12.7154i) q^{18} -19.1628 q^{19} +(8.42592 - 5.38552i) q^{20} +(-8.02782 + 8.39274i) q^{21} -7.13098i q^{22} +4.79583 q^{23} +(6.13183 + 5.86521i) q^{24} +(10.4981 - 22.6890i) q^{25} +21.7003i q^{26} +(17.7778 - 20.3212i) q^{27} -7.74264i q^{28} -10.8847i q^{29} +(20.8134 + 4.09918i) q^{30} +0.921869 q^{31} -5.65685 q^{32} +(10.4562 - 10.9315i) q^{33} +14.4920 q^{34} +(-10.4245 - 16.3097i) q^{35} +(0.799650 + 17.9822i) q^{36} -31.4952i q^{37} +27.1003 q^{38} +(-31.8192 + 33.2656i) q^{39} +(-11.9161 + 7.61628i) q^{40} +28.3053i q^{41} +(11.3530 - 11.8691i) q^{42} -26.8720i q^{43} +10.0847i q^{44} +(25.8954 + 36.8026i) q^{45} -6.78233 q^{46} -53.0761 q^{47} +(-8.67171 - 8.29466i) q^{48} +34.0129 q^{49} +(-14.8465 + 32.0871i) q^{50} +(22.2155 + 21.2496i) q^{51} -30.6888i q^{52} -15.1211 q^{53} +(-25.1416 + 28.7385i) q^{54} +(13.5779 + 21.2433i) q^{55} +10.9497i q^{56} +(41.5436 + 39.7372i) q^{57} +15.3934i q^{58} +23.8577i q^{59} +(-29.4346 - 5.79711i) q^{60} -55.3744 q^{61} -1.30372 q^{62} +(34.8075 - 1.54785i) q^{63} +8.00000 q^{64} +(-41.3188 - 64.6454i) q^{65} +(-14.7873 + 15.4595i) q^{66} +43.6001i q^{67} -20.4947 q^{68} +(-10.3970 - 9.94495i) q^{69} +(14.7425 + 23.0654i) q^{70} -2.55319i q^{71} +(-1.13088 - 25.4307i) q^{72} -12.0538i q^{73} +44.5410i q^{74} +(-69.8084 + 27.4186i) q^{75} -38.3256 q^{76} +19.5206 q^{77} +(44.9991 - 47.0447i) q^{78} -101.853 q^{79} +(16.8518 - 10.7710i) q^{80} +(-80.6803 + 7.18975i) q^{81} -40.0298i q^{82} -146.715 q^{83} +(-16.0556 + 16.7855i) q^{84} +(-43.1717 + 27.5937i) q^{85} +38.0027i q^{86} +(-22.5713 + 23.5974i) q^{87} -14.2620i q^{88} -126.637i q^{89} +(-36.6216 - 52.0467i) q^{90} -59.4031 q^{91} +9.59166 q^{92} +(-1.99855 - 1.91165i) q^{93} +75.0609 q^{94} +(-80.7322 + 51.6009i) q^{95} +(12.2637 + 11.7304i) q^{96} +136.772i q^{97} -48.1015 q^{98} +(-45.3365 + 2.01606i) 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
$3$	−2.16793	−	2.07367i	−0.722643	−	0.691222i
$3$	−2.16793	−	2.07367i	−0.722643	−	0.691222i
$4$	2.00000			0.500000
$5$	4.21296	−	2.69276i	0.842592	−	0.538552i
$5$	4.21296	−	2.69276i	0.842592	−	0.538552i
$6$	3.06591	+	2.93261i	0.510986	+	0.488768i
$7$		−	3.87132i		−	0.553045i	−0.961007	−	0.276523i	$-0.910818\pi$
$7$		−	3.87132i		−	0.553045i	0.961007	−	0.276523i	$-0.0891821\pi$
$8$	−2.82843			−0.353553
$9$	0.399825	+	8.99111i	0.0444250	+	0.999013i
$10$	−5.95803	+	3.80814i	−0.595803	+	0.380814i
$11$			5.04237i			0.458397i	0.973380	+	0.229198i	$0.0736105\pi$
$11$			5.04237i			0.458397i	−0.973380	+	0.229198i	$0.926390\pi$
$12$	−4.33586	−	4.14733i	−0.361321	−	0.345611i
$13$		−	15.3444i		−	1.18034i	−0.807279	−	0.590170i	$-0.799061\pi$
$13$		−	15.3444i		−	1.18034i	0.807279	−	0.590170i	$-0.200939\pi$
$14$			5.47487i			0.391062i
$15$	−14.7173	−	2.89856i	−0.981152	−	0.193237i
$16$	4.00000			0.250000
$17$	−10.2474			−0.602786			−0.301393	−	0.953500i	$-0.597452\pi$
$17$	−10.2474			−0.602786			−0.301393	+	0.953500i	$0.597452\pi$
$18$	−0.565438	−	12.7154i	−0.0314132	−	0.706409i
$19$	−19.1628			−1.00857			−0.504284	−	0.863538i	$-0.668244\pi$
$19$	−19.1628			−1.00857			−0.504284	+	0.863538i	$0.668244\pi$
$20$	8.42592	−	5.38552i	0.421296	−	0.269276i
$21$	−8.02782	+	8.39274i	−0.382277	+	0.399654i
$22$		−	7.13098i		−	0.324136i
$23$	4.79583			0.208514
$23$	4.79583			0.208514
$24$	6.13183	+	5.86521i	0.255493	+	0.244384i
$25$	10.4981	−	22.6890i	0.419923	−	0.907560i
$26$			21.7003i			0.834626i
$27$	17.7778	−	20.3212i	0.658436	−	0.752637i
$28$		−	7.74264i		−	0.276523i
$29$		−	10.8847i		−	0.375336i	−0.982233	−	0.187668i	$-0.939907\pi$
$29$		−	10.8847i		−	0.375336i	0.982233	−	0.187668i	$-0.0600929\pi$
$30$	20.8134	+	4.09918i	0.693779	+	0.136639i
$31$	0.921869			0.0297377			0.0148689	−	0.999889i	$-0.495267\pi$
$31$	0.921869			0.0297377			0.0148689	+	0.999889i	$0.495267\pi$
$32$	−5.65685			−0.176777
$33$	10.4562	−	10.9315i	0.316854	−	0.331257i
$34$	14.4920			0.426234
$35$	−10.4245	−	16.3097i	−0.297844	−	0.465992i
$36$	0.799650	+	17.9822i	0.0222125	+	0.499506i
$37$		−	31.4952i		−	0.851222i	−0.904906	−	0.425611i	$-0.860059\pi$
$37$		−	31.4952i		−	0.851222i	0.904906	−	0.425611i	$-0.139941\pi$
$38$	27.1003			0.713166
$39$	−31.8192	+	33.2656i	−0.815876	+	0.852964i
$40$	−11.9161	+	7.61628i	−0.297901	+	0.190407i
$41$			28.3053i			0.690374i	0.938534	+	0.345187i	$0.112184\pi$
$41$			28.3053i			0.690374i	−0.938534	+	0.345187i	$0.887816\pi$
$42$	11.3530	−	11.8691i	0.270311	−	0.282598i
$43$		−	26.8720i		−	0.624930i	−0.949929	−	0.312465i	$-0.898845\pi$
$43$		−	26.8720i		−	0.624930i	0.949929	−	0.312465i	$-0.101155\pi$
$44$			10.0847i			0.229198i
$45$	25.8954	+	36.8026i	0.575453	+	0.817835i
$46$	−6.78233			−0.147442
$47$	−53.0761			−1.12928			−0.564639	−	0.825338i	$-0.690985\pi$
$47$	−53.0761			−1.12928			−0.564639	+	0.825338i	$0.690985\pi$
$48$	−8.67171	−	8.29466i	−0.180661	−	0.172805i
$49$	34.0129			0.694141
$50$	−14.8465	+	32.0871i	−0.296930	+	0.641742i
$51$	22.2155	+	21.2496i	0.435599	+	0.416659i
$52$		−	30.6888i		−	0.590170i
$53$	−15.1211			−0.285304			−0.142652	−	0.989773i	$-0.545563\pi$
$53$	−15.1211			−0.285304			−0.142652	+	0.989773i	$0.545563\pi$
$54$	−25.1416	+	28.7385i	−0.465584	+	0.532195i
$55$	13.5779	+	21.2433i	0.246871	+	0.386242i
$56$			10.9497i			0.195531i
$57$	41.5436	+	39.7372i	0.728835	+	0.697145i
$58$			15.3934i			0.265403i
$59$			23.8577i			0.404368i	0.979348	+	0.202184i	$0.0648040\pi$
$59$			23.8577i			0.404368i	−0.979348	+	0.202184i	$0.935196\pi$
$60$	−29.4346	−	5.79711i	−0.490576	−	0.0966186i
$61$	−55.3744			−0.907777			−0.453889	−	0.891058i	$-0.649964\pi$
$61$	−55.3744			−0.907777			−0.453889	+	0.891058i	$0.649964\pi$
$62$	−1.30372			−0.0210277
$63$	34.8075	−	1.54785i	0.552499	−	0.0245691i
$64$	8.00000			0.125000
$65$	−41.3188	−	64.6454i	−0.635675	−	0.994545i
$66$	−14.7873	+	15.4595i	−0.224050	+	0.234234i
$67$			43.6001i			0.650748i	0.945585	+	0.325374i	$0.105490\pi$
$67$			43.6001i			0.650748i	−0.945585	+	0.325374i	$0.894510\pi$
$68$	−20.4947			−0.301393
$69$	−10.3970	−	9.94495i	−0.150681	−	0.144130i
$70$	14.7425	+	23.0654i	0.210607	+	0.329506i
$71$		−	2.55319i		−	0.0359605i	−0.999838	−	0.0179802i	$-0.994276\pi$
$71$		−	2.55319i		−	0.0359605i	0.999838	−	0.0179802i	$-0.00572359\pi$
$72$	−1.13088	−	25.4307i	−0.0157066	−	0.353204i
$73$		−	12.0538i		−	0.165120i	−0.996586	−	0.0825601i	$-0.973690\pi$
$73$		−	12.0538i		−	0.165120i	0.996586	−	0.0825601i	$-0.0263097\pi$
$74$			44.5410i			0.601905i
$75$	−69.8084	+	27.4186i	−0.930779	+	0.365582i
$76$	−38.3256			−0.504284
$77$	19.5206			0.253514
$78$	44.9991	−	47.0447i	0.576912	−	0.603137i
$79$	−101.853			−1.28928			−0.644639	−	0.764487i	$-0.722992\pi$
$79$	−101.853			−1.28928			−0.644639	+	0.764487i	$0.722992\pi$
$80$	16.8518	−	10.7710i	0.210648	−	0.134638i
$81$	−80.6803	+	7.18975i	−0.996053	+	0.0887623i
$82$		−	40.0298i		−	0.488168i
$83$	−146.715			−1.76765			−0.883826	−	0.467815i	$-0.845041\pi$
$83$	−146.715			−1.76765			−0.883826	+	0.467815i	$0.845041\pi$
$84$	−16.0556	+	16.7855i	−0.191139	+	0.199827i
$85$	−43.1717	+	27.5937i	−0.507903	+	0.324632i
$86$			38.0027i			0.441892i
$87$	−22.5713	+	23.5974i	−0.259441	+	0.271234i
$88$		−	14.2620i		−	0.162068i
$89$		−	126.637i		−	1.42289i	−0.702744	−	0.711443i	$-0.748042\pi$
$89$		−	126.637i		−	1.42289i	0.702744	−	0.711443i	$-0.251958\pi$
$90$	−36.6216	−	52.0467i	−0.406907	−	0.578297i
$91$	−59.4031			−0.652781
$92$	9.59166			0.104257
$93$	−1.99855	−	1.91165i	−0.0214897	−	0.0205554i
$94$	75.0609			0.798521
$95$	−80.7322	+	51.6009i	−0.849812	+	0.543167i
$96$	12.2637	+	11.7304i	0.127746	+	0.122192i
$97$			136.772i			1.41002i	0.709199	+	0.705009i	$0.249057\pi$
$97$			136.772i			1.41002i	−0.709199	+	0.705009i	$0.750943\pi$
$98$	−48.1015			−0.490832
$99$	−45.3365	+	2.01606i	−0.457944	+	0.0203643i
$100$	20.9961	−	45.3780i	0.209961	−	0.453780i
$101$		−	66.3835i		−	0.657263i	−0.944458	−	0.328631i	$-0.893413\pi$
$101$		−	66.3835i		−	0.657263i	0.944458	−	0.328631i	$-0.106587\pi$
$102$	−31.4175	−	30.0515i	−0.308015	−	0.294622i
$103$			96.5999i			0.937863i	0.883234	+	0.468932i	$0.155361\pi$
$103$			96.5999i			0.937863i	−0.883234	+	0.468932i	$0.844639\pi$
$104$			43.4006i			0.417313i
$105$	−11.2212	+	56.9753i	−0.106869	+	0.542622i
$106$	21.3845			0.201741
$107$	−157.136			−1.46856			−0.734280	−	0.678846i	$-0.762480\pi$
$107$	−157.136			−1.46856			−0.734280	+	0.678846i	$0.762480\pi$
$108$	35.5555	−	40.6424i	0.329218	−	0.376318i
$109$	−142.427			−1.30667			−0.653337	−	0.757067i	$-0.726631\pi$
$109$	−142.427			−1.30667			−0.653337	+	0.757067i	$0.726631\pi$
$110$	−19.2020	−	30.0425i	−0.174564	−	0.273114i
$111$	−65.3106	+	68.2794i	−0.588383	+	0.615130i
$112$		−	15.4853i		−	0.138261i
$113$	63.4870			0.561832			0.280916	−	0.959732i	$-0.409362\pi$
$113$	63.4870			0.561832			0.280916	+	0.959732i	$0.409362\pi$
$114$	−58.7515	−	56.1970i	−0.515364	−	0.492956i
$115$	20.2046	−	12.9140i	0.175693	−	0.112296i
$116$		−	21.7695i		−	0.187668i
$117$	137.963	−	6.13508i	1.17917	−	0.0524366i
$118$		−	33.7399i		−	0.285932i
$119$			39.6708i			0.333368i
$120$	41.6268	+	8.19836i	0.346890	+	0.0683196i
$121$	95.5745			0.789872
$122$	78.3113			0.641896
$123$	58.6958	−	61.3639i	0.477201	−	0.498894i
$124$	1.84374			0.0148689
$125$	−16.8681	−	123.857i	−0.134945	−	0.990853i
$126$	−49.2252	+	2.18899i	−0.390676	+	0.0173729i
$127$			195.570i			1.53992i	0.638090	+	0.769962i	$0.279725\pi$
$127$			195.570i			1.53992i	−0.638090	+	0.769962i	$0.720275\pi$
$128$	−11.3137			−0.0883883
$129$	−55.7235	+	58.2565i	−0.431965	+	0.451601i
$130$	58.4337	+	91.4224i	0.449490	+	0.703249i
$131$			67.9207i			0.518479i	0.965813	+	0.259239i	$0.0834719\pi$
$131$			67.9207i			0.518479i	−0.965813	+	0.259239i	$0.916528\pi$
$132$	20.9124	−	21.8630i	0.158427	−	0.165629i
$133$			74.1853i			0.557784i
$134$		−	61.6599i		−	0.460148i
$135$	20.1769	−	133.484i	0.149459	−	0.988768i
$136$	28.9839			0.213117
$137$	−95.4416			−0.696654			−0.348327	−	0.937373i	$-0.613250\pi$
$137$	−95.4416			−0.696654			−0.348327	+	0.937373i	$0.613250\pi$
$138$	14.7036	+	14.0643i	0.106548	+	0.101915i
$139$	20.1287			0.144811			0.0724053	−	0.997375i	$-0.476932\pi$
$139$	20.1287			0.144811			0.0724053	+	0.997375i	$0.476932\pi$
$140$	−20.8491	−	32.6194i	−0.148922	−	0.232996i
$141$	115.065	+	110.062i	0.816065	+	0.780582i
$142$			3.61076i			0.0254279i
$143$	77.3722			0.541064
$144$	1.59930	+	35.9645i	0.0111063	+	0.249753i
$145$	−29.3100	−	45.8570i	−0.202138	−	0.316255i
$146$			17.0466i			0.116758i
$147$	−73.7375	−	70.5314i	−0.501616	−	0.479805i
$148$		−	62.9904i		−	0.425611i
$149$			3.49799i			0.0234764i	0.999931	+	0.0117382i	$0.00373648\pi$
$149$			3.49799i			0.0234764i	−0.999931	+	0.0117382i	$0.996264\pi$
$150$	98.7241	−	38.7758i	0.658160	−	0.258505i
$151$	256.597			1.69932			0.849660	−	0.527331i	$-0.176807\pi$
$151$	256.597			1.69932			0.849660	+	0.527331i	$0.176807\pi$
$152$	54.2006			0.356583
$153$	−4.09715	−	92.1352i	−0.0267788	−	0.602191i
$154$	−27.6063			−0.179262
$155$	3.88380	−	2.48237i	0.0250568	−	0.0160153i
$156$	−63.6384	+	66.5312i	−0.407938	+	0.426482i
$157$		−	4.85732i		−	0.0309384i	−0.999880	−	0.0154692i	$-0.995076\pi$
$157$		−	4.85732i		−	0.0309384i	0.999880	−	0.0154692i	$-0.00492419\pi$
$158$	144.042			0.911657
$159$	32.7815	+	31.3562i	0.206173	+	0.197209i
$160$	−23.8321	+	15.2326i	−0.148951	+	0.0952035i
$161$		−	18.5662i		−	0.115318i
$162$	114.099	−	10.1678i	0.704316	−	0.0627644i
$163$		−	219.553i		−	1.34695i	−0.739210	−	0.673475i	$-0.764801\pi$
$163$		−	219.553i		−	1.34695i	0.739210	−	0.673475i	$-0.235199\pi$
$164$			56.6107i			0.345187i
$165$	14.6156	−	74.2099i	0.0885793	−	0.449757i
$166$	207.487			1.24992
$167$	−329.137			−1.97088			−0.985440	−	0.170025i	$-0.945615\pi$
$167$	−329.137			−1.97088			−0.985440	+	0.170025i	$0.945615\pi$
$168$	22.7061	−	23.7383i	0.135155	−	0.141299i
$169$	−66.4511			−0.393202
$170$	61.0540	−	39.0234i	0.359141	−	0.229549i
$171$	−7.66177	−	172.295i	−0.0448057	−	1.00757i
$172$		−	53.7439i		−	0.312465i
$173$	159.612			0.922611			0.461306	−	0.887241i	$-0.347381\pi$
$173$	159.612			0.922611			0.461306	+	0.887241i	$0.347381\pi$
$174$	31.9207	−	33.3717i	0.183452	−	0.191791i
$175$	−87.8363	−	40.6414i	−0.501922	−	0.232236i
$176$			20.1695i			0.114599i
$177$	49.4730	−	51.7219i	0.279508	−	0.292214i
$178$			179.091i			1.00613i
$179$			46.3952i			0.259191i	0.991567	+	0.129595i	$0.0413679\pi$
$179$			46.3952i			0.259191i	−0.991567	+	0.129595i	$0.958632\pi$
$180$	51.7907	+	73.6052i	0.287726	+	0.408918i
$181$	221.770			1.22525			0.612625	−	0.790373i	$-0.290113\pi$
$181$	221.770			1.22525			0.612625	+	0.790373i	$0.290113\pi$
$182$	84.0087			0.461586
$183$	120.048	+	114.828i	0.655999	+	0.627475i
$184$	−13.5647			−0.0737210
$185$	−84.8091	−	132.688i	−0.458428	−	0.717233i
$186$	2.82637	+	2.70348i	0.0151955	+	0.0145348i
$187$		−	51.6709i		−	0.276315i
$188$	−106.152			−0.564639
$189$	−78.6698	−	68.8234i	−0.416242	−	0.364145i
$190$	114.173	−	72.9746i	0.600908	−	0.384077i
$191$		−	14.2887i		−	0.0748099i	−0.999300	−	0.0374050i	$-0.988091\pi$
$191$		−	14.2887i		−	0.0748099i	0.999300	−	0.0374050i	$-0.0119091\pi$
$192$	−17.3434	−	16.5893i	−0.0903303	−	0.0864027i
$193$		−	283.329i		−	1.46802i	−0.679136	−	0.734012i	$-0.737645\pi$
$193$		−	283.329i		−	1.46802i	0.679136	−	0.734012i	$-0.262355\pi$
$194$		−	193.424i		−	0.997033i
$195$	−44.4767	+	225.828i	−0.228085	+	1.15809i
$196$	68.0258			0.347070
$197$	145.276			0.737439			0.368720	−	0.929541i	$-0.379796\pi$
$197$	145.276			0.737439			0.368720	+	0.929541i	$0.379796\pi$
$198$	64.1155	−	2.85115i	0.323816	−	0.0143997i
$199$	134.005			0.673390			0.336695	−	0.941614i	$-0.390691\pi$
$199$	134.005			0.673390			0.336695	+	0.941614i	$0.390691\pi$
$200$	−29.6930	+	64.1742i	−0.148465	+	0.320871i
$201$	90.4120	−	94.5219i	0.449811	−	0.470258i
$202$			93.8805i			0.464755i
$203$	−42.1383			−0.207578
$204$	44.4311	+	42.4992i	0.217799	+	0.208329i
$205$	76.2195	+	119.249i	0.371802	+	0.581704i
$206$		−	136.613i		−	0.663170i
$207$	1.91749	+	43.1199i	0.00926326	+	0.208309i
$208$		−	61.3777i		−	0.295085i
$209$		−	96.6259i		−	0.462325i
$210$	15.8692	−	80.5752i	0.0755677	−	0.383691i
$211$	−143.378			−0.679516			−0.339758	−	0.940513i	$-0.610345\pi$
$211$	−143.378			−0.679516			−0.339758	+	0.940513i	$0.610345\pi$
$212$	−30.2423			−0.142652
$213$	−5.29447	+	5.53514i	−0.0248567	+	0.0259866i
$214$	222.224			1.03843
$215$	−72.3598	−	113.211i	−0.336557	−	0.526561i
$216$	−50.2831	+	57.4770i	−0.232792	+	0.266097i
$217$		−	3.56885i		−	0.0164463i
$218$	201.423			0.923958
$219$	−24.9955	+	26.1317i	−0.114135	+	0.119323i
$220$	27.1558	+	42.4866i	0.123435	+	0.193121i
$221$			157.240i			0.711492i
$222$	92.3631	−	96.5616i	0.416050	−	0.434962i
$223$			87.2841i			0.391409i	0.980663	+	0.195704i	$0.0626993\pi$
$223$			87.2841i			0.391409i	−0.980663	+	0.195704i	$0.937301\pi$
$224$			21.8995i			0.0977655i
$225$	208.197	+	85.3178i	0.925319	+	0.379190i
$226$	−89.7841			−0.397275
$227$	−73.6779			−0.324572			−0.162286	−	0.986744i	$-0.551887\pi$
$227$	−73.6779			−0.324572			−0.162286	+	0.986744i	$0.551887\pi$
$228$	83.0872	+	79.4745i	0.364417	+	0.348572i
$229$	60.3596			0.263579			0.131789	−	0.991278i	$-0.457928\pi$
$229$	60.3596			0.263579			0.131789	+	0.991278i	$0.457928\pi$
$230$	−28.5737	+	18.2632i	−0.124233	+	0.0794052i
$231$	−42.3193	−	40.4792i	−0.183200	−	0.175235i
$232$			30.7867i			0.132701i
$233$	23.4620			0.100695			0.0503477	−	0.998732i	$-0.483967\pi$
$233$	23.4620			0.100695			0.0503477	+	0.998732i	$0.483967\pi$
$234$	−195.110	+	8.67632i	−0.833802	+	0.0370783i
$235$	−223.608	+	142.921i	−0.951521	+	0.608176i
$236$			47.7155i			0.202184i
$237$	220.810	+	211.209i	0.931687	+	0.891177i
$238$		−	56.1030i		−	0.235727i
$239$			63.7138i			0.266585i	0.991077	+	0.133293i	$0.0425550\pi$
$239$			63.7138i			0.266585i	−0.991077	+	0.133293i	$0.957445\pi$
$240$	−58.8691	−	11.5942i	−0.245288	−	0.0483093i
$241$	112.211			0.465606			0.232803	−	0.972524i	$-0.425210\pi$
$241$	112.211			0.465606			0.232803	+	0.972524i	$0.425210\pi$
$242$	−135.163			−0.558524
$243$	189.818	+	151.717i	0.781145	+	0.624350i
$244$	−110.749			−0.453889
$245$	143.295	−	91.5886i	0.584878	−	0.373831i
$246$	−83.0084	+	86.7817i	−0.337432	+	0.352771i
$247$			294.042i			1.19045i
$248$	−2.60744			−0.0105139
$249$	318.068	+	304.238i	1.27738	+	1.22184i
$250$	23.8551	+	175.160i	0.0954202	+	0.700639i
$251$		−	363.290i		−	1.44737i	−0.690130	−	0.723685i	$-0.742447\pi$
$251$		−	363.290i		−	1.44737i	0.690130	−	0.723685i	$-0.257553\pi$
$252$	69.6149	−	3.09570i	0.276250	−	0.0122845i
$253$			24.1823i			0.0955824i
$254$		−	276.578i		−	1.08889i
$255$	150.813	+	29.7025i	0.591424	+	0.116481i
$256$	16.0000			0.0625000
$257$	−30.3795			−0.118208			−0.0591040	−	0.998252i	$-0.518824\pi$
$257$	−30.3795			−0.118208			−0.0591040	+	0.998252i	$0.518824\pi$
$258$	78.8049	−	82.3871i	0.305445	−	0.319330i
$259$	−121.928			−0.470765
$260$	−82.6377	−	129.291i	−0.317837	−	0.497272i
$261$	97.8660	−	4.35200i	0.374966	−	0.0166743i
$262$		−	96.0544i		−	0.366620i
$263$	276.122			1.04989			0.524946	−	0.851135i	$-0.324085\pi$
$263$	276.122			1.04989			0.524946	+	0.851135i	$0.324085\pi$
$264$	−29.5745	+	30.9189i	−0.112025	+	0.117117i
$265$	−63.7047	+	40.7176i	−0.240395	+	0.153651i
$266$		−	104.914i		−	0.394413i
$267$	−262.602	+	274.539i	−0.983529	+	1.02824i
$268$			87.2002i			0.325374i
$269$			89.7539i			0.333658i	0.985986	+	0.166829i	$0.0533527\pi$
$269$			89.7539i			0.333658i	−0.985986	+	0.166829i	$0.946647\pi$
$270$	−28.5345	+	188.774i	−0.105683	+	0.699165i
$271$	−317.625			−1.17205			−0.586023	−	0.810294i	$-0.699307\pi$
$271$	−317.625			−1.17205			−0.586023	+	0.810294i	$0.699307\pi$
$272$	−40.9894			−0.150696
$273$	128.782	+	123.182i	0.471728	+	0.451217i
$274$	134.975			0.492609
$275$	114.406	+	52.9351i	0.416023	+	0.192491i
$276$	−20.7940	−	19.8899i	−0.0753407	−	0.0720648i
$277$			143.086i			0.516557i	0.966071	+	0.258279i	$0.0831552\pi$
$277$			143.086i			0.516557i	−0.966071	+	0.258279i	$0.916845\pi$
$278$	−28.4663			−0.102397
$279$	0.368587	+	8.28863i	0.00132110	+	0.0297084i
$280$	29.4850	+	46.1308i	0.105304	+	0.164753i
$281$		−	445.282i		−	1.58463i	−0.610111	−	0.792316i	$-0.708875\pi$
$281$		−	445.282i		−	1.58463i	0.610111	−	0.792316i	$-0.291125\pi$
$282$	−162.727	−	155.651i	−0.577045	−	0.551955i
$283$		−	418.790i		−	1.47982i	−0.672704	−	0.739912i	$-0.734867\pi$
$283$		−	418.790i		−	1.47982i	0.672704	−	0.739912i	$-0.265133\pi$
$284$		−	5.10639i		−	0.0179802i
$285$	282.024	+	55.5445i	0.989559	+	0.194893i
$286$	−109.421			−0.382590
$287$	109.579			0.381808
$288$	−2.26175	−	50.8614i	−0.00785331	−	0.176602i
$289$	−183.992			−0.636649
$290$	41.4506	+	64.8516i	0.142933	+	0.223626i
$291$	283.619	−	296.511i	0.974635	−	1.01894i
$292$		−	24.1076i		−	0.0825601i
$293$	−68.5934			−0.234107			−0.117054	−	0.993126i	$-0.537345\pi$
$293$	−68.5934			−0.234107			−0.117054	+	0.993126i	$0.537345\pi$
$294$	104.281	+	99.7464i	0.354696	+	0.339273i
$295$	64.2432	+	100.512i	0.217774	+	0.340718i
$296$			89.0819i			0.300953i
$297$	102.467	+	89.6420i	0.345006	+	0.301825i
$298$		−	4.94690i		−	0.0166004i
$299$		−	73.5892i		−	0.246118i
$300$	−139.617	+	54.8372i	−0.465390	+	0.182791i
$301$	−104.030			−0.345614
$302$	−362.883			−1.20160
$303$	−137.657	+	143.915i	−0.454314	+	0.474966i
$304$	−76.6512			−0.252142
$305$	−233.290	+	149.110i	−0.764886	+	0.488886i
$306$	5.79425	+	130.299i	0.0189354	+	0.425813i
$307$		−	402.815i		−	1.31210i	−0.754717	−	0.656050i	$-0.772226\pi$
$307$		−	402.815i		−	1.31210i	0.754717	−	0.656050i	$-0.227774\pi$
$308$	39.0412			0.126757
$309$	200.316	−	209.422i	0.648272	−	0.677740i
$310$	−5.49252	+	3.51061i	−0.0177178	+	0.0113245i
$311$		−	468.326i		−	1.50587i	−0.658094	−	0.752936i	$-0.728637\pi$
$311$		−	468.326i		−	1.50587i	0.658094	−	0.752936i	$-0.271363\pi$
$312$	89.9982	−	94.0893i	0.288456	−	0.301568i
$313$		−	555.209i		−	1.77383i	−0.461933	−	0.886915i	$-0.652844\pi$
$313$		−	555.209i		−	1.77383i	0.461933	−	0.886915i	$-0.347156\pi$
$314$			6.86929i			0.0218767i
$315$	142.474	−	100.249i	0.452300	−	0.318252i
$316$	−203.706			−0.644639
$317$	−441.805			−1.39371			−0.696854	−	0.717213i	$-0.745417\pi$
$317$	−441.805			−1.39371			−0.696854	+	0.717213i	$0.745417\pi$
$318$	−46.3601	−	44.3443i	−0.145786	−	0.139447i
$319$	54.8849			0.172053
$320$	33.7037	−	21.5421i	0.105324	−	0.0673190i
$321$	340.660	+	325.847i	1.06124	+	1.01510i
$322$			26.2566i			0.0815421i
$323$	196.368			0.607951
$324$	−161.361	+	14.3795i	−0.498026	+	0.0443812i
$325$	−348.149	−	161.087i	−1.07123	−	0.495652i
$326$			310.495i			0.952437i
$327$	308.772	+	295.347i	0.944258	+	0.903201i
$328$		−	80.0596i		−	0.244084i
$329$			205.474i			0.624542i
$330$	−20.6696	+	104.949i	−0.0626350	+	0.318026i
$331$	−5.74801			−0.0173656			−0.00868280	−	0.999962i	$-0.502764\pi$
$331$	−5.74801			−0.0173656			−0.00868280	+	0.999962i	$0.502764\pi$
$332$	−293.430			−0.883826
$333$	283.177	−	12.5926i	0.850382	−	0.0378156i
$334$	465.470			1.39362
$335$	117.405	+	183.686i	0.350462	+	0.548315i
$336$	−32.1113	+	33.5710i	−0.0955693	+	0.0999136i
$337$			168.422i			0.499768i	0.968276	+	0.249884i	$0.0803924\pi$
$337$			168.422i			0.499768i	−0.968276	+	0.249884i	$0.919608\pi$
$338$	93.9760			0.278036
$339$	−137.635	−	131.651i	−0.406004	−	0.388350i
$340$	−86.3434	+	55.1874i	−0.253951	+	0.162316i
$341$			4.64840i			0.0136317i
$342$	10.8354	+	243.662i	0.0316824	+	0.712462i
$343$		−	321.369i		−	0.936937i
$344$			76.0054i			0.220946i
$345$	−70.5816	−	13.9010i	−0.204584	−	0.0402927i
$346$	−225.725			−0.652385
$347$	−43.0406			−0.124036			−0.0620182	−	0.998075i	$-0.519754\pi$
$347$	−43.0406			−0.124036			−0.0620182	+	0.998075i	$0.519754\pi$
$348$	−45.1427	+	47.1947i	−0.129720	+	0.135617i
$349$	0.727200			0.00208367			0.00104183	−	0.999999i	$-0.499668\pi$
$349$	0.727200			0.00208367			0.00104183	+	0.999999i	$0.499668\pi$
$350$	124.219	+	57.4756i	0.354912	+	0.164216i
$351$	−311.817	−	272.789i	−0.888367	−	0.777178i
$352$		−	28.5239i		−	0.0810339i
$353$	629.821			1.78420			0.892098	−	0.451843i	$-0.149233\pi$
$353$	629.821			1.78420			0.892098	+	0.451843i	$0.149233\pi$
$354$	−69.9653	+	73.1458i	−0.197642	+	0.206626i
$355$	−6.87514	−	10.7565i	−0.0193666	−	0.0303000i
$356$		−	253.274i		−	0.711443i
$357$	82.2639	−	86.0034i	0.230431	−	0.240906i
$358$		−	65.6127i		−	0.183276i
$359$			583.627i			1.62570i	0.582471	+	0.812851i	$0.302086\pi$
$359$			583.627i			1.62570i	−0.582471	+	0.812851i	$0.697914\pi$
$360$	−73.2432	−	104.093i	−0.203453	−	0.289148i
$361$	6.21317			0.0172110
$362$	−313.631			−0.866383
$363$	−207.199	−	198.190i	−0.570795	−	0.545977i
$364$	−118.806			−0.326391
$365$	−32.4580	−	50.7821i	−0.0889259	−	0.139129i
$366$	−169.773	−	162.391i	−0.463861	−	0.443692i
$367$			373.566i			1.01789i	0.860799	+	0.508946i	$0.169965\pi$
$367$			373.566i			1.01789i	−0.860799	+	0.508946i	$0.830035\pi$
$368$	19.1833			0.0521286
$369$	−254.496	+	11.3172i	−0.689692	+	0.0306699i
$370$	119.938	+	187.649i	0.324157	+	0.507160i
$371$			58.5387i			0.157786i
$372$	−3.99709	−	3.82330i	−0.0107449	−	0.0102777i
$373$		−	216.748i		−	0.581094i	−0.956861	−	0.290547i	$-0.906163\pi$
$373$		−	216.748i		−	0.581094i	0.956861	−	0.290547i	$-0.0938372\pi$
$374$			73.0737i			0.195384i
$375$	−220.268	+	303.491i	−0.587383	+	0.809309i
$376$	150.122			0.399260
$377$	−167.020			−0.443024
$378$	111.256	+	97.3310i	0.294328	+	0.257489i
$379$	206.231			0.544145			0.272072	−	0.962277i	$-0.412291\pi$
$379$	206.231			0.544145			0.272072	+	0.962277i	$0.412291\pi$
$380$	−161.464	+	103.202i	−0.424906	+	0.271583i
$381$	405.547	−	423.982i	1.06443	−	1.11281i
$382$			20.2073i			0.0528986i
$383$	95.6645			0.249777			0.124888	−	0.992171i	$-0.460143\pi$
$383$	95.6645			0.249777			0.124888	+	0.992171i	$0.460143\pi$
$384$	24.5273	+	23.4608i	0.0638732	+	0.0610959i
$385$	82.2395	−	52.5643i	0.213609	−	0.136531i
$386$			400.687i			1.03805i
$387$	241.609	−	10.7441i	0.624313	−	0.0277625i
$388$			273.543i			0.705009i
$389$			173.495i			0.446003i	0.974818	+	0.223001i	$0.0715854\pi$
$389$			173.495i			0.446003i	−0.974818	+	0.223001i	$0.928415\pi$
$390$	62.8995	−	319.369i	0.161281	−	0.818895i
$391$	−49.1446			−0.125690
$392$	−96.2030			−0.245416
$393$	140.845	−	147.247i	0.358384	−	0.374675i
$394$	−205.451			−0.521448
$395$	−429.102	+	274.266i	−1.08634	+	0.694343i
$396$	−90.6730	+	4.03213i	−0.228972	+	0.0101821i
$397$		−	341.235i		−	0.859533i	−0.902940	−	0.429767i	$-0.858596\pi$
$397$		−	341.235i		−	0.859533i	0.902940	−	0.429767i	$-0.141404\pi$
$398$	−189.511			−0.476158
$399$	153.836	−	160.828i	0.385553	−	0.403079i
$400$	41.9923	−	90.7560i	0.104981	−	0.226890i
$401$			335.722i			0.837213i	0.908168	+	0.418606i	$0.137481\pi$
$401$			335.722i			0.837213i	−0.908168	+	0.418606i	$0.862519\pi$
$402$	−127.862	+	133.674i	−0.318064	+	0.332523i
$403$		−	14.1455i		−	0.0351006i
$404$		−	132.767i		−	0.328631i
$405$	−320.543	+	247.543i	−0.791463	+	0.611217i
$406$	59.5926			0.146780
$407$	158.810			0.390198
$408$	−62.8350	−	60.1029i	−0.154007	−	0.147311i
$409$	−132.366			−0.323634			−0.161817	−	0.986821i	$-0.551735\pi$
$409$	−132.366			−0.323634			−0.161817	+	0.986821i	$0.551735\pi$
$410$	−107.791	−	168.644i	−0.262904	−	0.411327i
$411$	206.911	+	197.914i	0.503432	+	0.481542i
$412$			193.200i			0.468932i
$413$	92.3609			0.223634
$414$	−2.71175	−	60.9807i	−0.00655011	−	0.147296i
$415$	−618.105	+	395.069i	−1.48941	+	0.951973i
$416$			86.8011i			0.208657i
$417$	−43.6375	−	41.7402i	−0.104646	−	0.100096i
$418$			136.650i			0.326913i
$419$		−	545.122i		−	1.30101i	−0.759504	−	0.650503i	$-0.774558\pi$
$419$		−	545.122i		−	1.30101i	0.759504	−	0.650503i	$-0.225442\pi$
$420$	−22.4425	+	113.951i	−0.0534345	+	0.271311i
$421$	41.9780			0.0997102			0.0498551	−	0.998756i	$-0.484124\pi$
$421$	41.9780			0.0997102			0.0498551	+	0.998756i	$0.484124\pi$
$422$	202.767			0.480490
$423$	−21.2212	−	477.213i	−0.0501682	−	1.12816i
$424$	42.7690			0.100870
$425$	−107.578	+	232.502i	−0.253124	+	0.547064i
$426$	7.48751	−	7.82787i	0.0175763	−	0.0183753i
$427$			214.372i			0.502042i
$428$	−314.272			−0.734280
$429$	−167.737	−	160.444i	−0.390996	−	0.373995i
$430$	102.332	+	160.104i	0.237982	+	0.372335i
$431$		−	106.166i		−	0.246324i	−0.992387	−	0.123162i	$-0.960696\pi$
$431$		−	106.166i		−	0.246324i	0.992387	−	0.123162i	$-0.0393036\pi$
$432$	71.1111	−	81.2848i	0.164609	−	0.188159i
$433$		−	616.452i		−	1.42368i	−0.702343	−	0.711838i	$-0.747863\pi$
$433$		−	616.452i		−	1.42368i	0.702343	−	0.711838i	$-0.252137\pi$
$434$			5.04712i			0.0116293i
$435$	−31.5501	+	160.194i	−0.0725289	+	0.368262i
$436$	−284.855			−0.653337
$437$	−91.9016			−0.210301
$438$	35.3490	−	36.9558i	0.0807054	−	0.0843741i
$439$	649.727			1.48002			0.740008	−	0.672598i	$-0.234822\pi$
$439$	649.727			1.48002			0.740008	+	0.672598i	$0.234822\pi$
$440$	−38.4041	−	60.0851i	−0.0872820	−	0.136557i
$441$	13.5992	+	305.814i	0.0308372	+	0.693455i
$442$		−	222.371i		−	0.503101i
$443$	−215.853			−0.487252			−0.243626	−	0.969869i	$-0.578337\pi$
$443$	−215.853			−0.487252			−0.243626	+	0.969869i	$0.578337\pi$
$444$	−130.621	+	136.559i	−0.294192	+	0.307565i
$445$	−341.003	−	533.516i	−0.766298	−	1.19891i
$446$		−	123.438i		−	0.276768i
$447$	7.25366	−	7.58339i	0.0162274	−	0.0169651i
$448$		−	30.9705i		−	0.0691307i
$449$			655.202i			1.45925i	0.683849	+	0.729623i	$0.260305\pi$
$449$			655.202i			1.45925i	−0.683849	+	0.729623i	$0.739695\pi$
$450$	−294.435	−	120.658i	−0.654299	−	0.268128i
$451$	−142.726			−0.316465
$452$	126.974			0.280916
$453$	−556.284	−	532.097i	−1.22800	−	1.17461i
$454$	104.196			0.229507
$455$	−250.263	+	159.958i	−0.550029	+	0.351557i
$456$	−117.503	−	112.394i	−0.257682	−	0.246478i
$457$		−	96.6236i		−	0.211430i	−0.994396	−	0.105715i	$-0.966287\pi$
$457$		−	96.6236i		−	0.211430i	0.994396	−	0.105715i	$-0.0337132\pi$
$458$	−85.3613			−0.186378
$459$	−182.175	+	208.239i	−0.396896	+	0.453679i
$460$	40.4093	−	25.8281i	0.0878463	−	0.0561480i
$461$		−	732.435i		−	1.58880i	−0.607397	−	0.794398i	$-0.707786\pi$
$461$		−	732.435i		−	1.58880i	0.607397	−	0.794398i	$-0.292214\pi$
$462$	59.8485	+	57.2462i	0.129542	+	0.123910i
$463$			160.728i			0.347145i	0.984821	+	0.173572i	$0.0555311\pi$
$463$			160.728i			0.347145i	−0.984821	+	0.173572i	$0.944469\pi$
$464$		−	43.5390i		−	0.0938340i
$465$	−13.5674	−	2.67209i	−0.0291772	−	0.00574643i
$466$	−33.1803			−0.0712024
$467$	−614.619			−1.31610			−0.658050	−	0.752974i	$-0.728618\pi$
$467$	−614.619			−1.31610			−0.658050	+	0.752974i	$0.728618\pi$
$468$	275.927	−	12.2702i	0.589587	−	0.0262183i
$469$	168.790			0.359893
$470$	316.229	−	202.121i	0.672827	−	0.430045i
$471$	−10.0725	+	10.5303i	−0.0213853	+	0.0223574i
$472$		−	67.4799i		−	0.142966i
$473$	135.498			0.286466
$474$	−312.272	−	298.694i	−0.658802	−	0.630157i
$475$	−201.173	+	434.785i	−0.423521	+	0.915336i
$476$			79.3416i			0.166684i
$477$	−6.04581	−	135.956i	−0.0126746	−	0.285023i
$478$		−	90.1050i		−	0.188504i
$479$		−	328.068i		−	0.684902i	−0.939536	−	0.342451i	$-0.888743\pi$
$479$		−	328.068i		−	0.684902i	0.939536	−	0.342451i	$-0.111257\pi$
$480$	83.2535	+	16.3967i	0.173445	+	0.0341598i
$481$	−483.276			−1.00473
$482$	−158.690			−0.329233
$483$	−38.5001	+	40.2502i	−0.0797103	+	0.0833337i
$484$	191.149			0.394936
$485$	368.293	+	576.214i	0.759368	+	1.18807i
$486$	−268.443	−	214.560i	−0.552353	−	0.441482i
$487$		−	183.987i		−	0.377796i	−0.981997	−	0.188898i	$-0.939508\pi$
$487$		−	183.987i		−	0.377796i	0.981997	−	0.188898i	$-0.0604916\pi$
$488$	156.623			0.320948
$489$	−455.279	+	475.975i	−0.931041	+	0.973363i
$490$	−202.650	+	129.526i	−0.413571	+	0.264338i
$491$			152.142i			0.309862i	0.987925	+	0.154931i	$0.0495156\pi$
$491$			152.142i			0.309862i	−0.987925	+	0.154931i	$0.950484\pi$
$492$	117.392	−	122.728i	0.238601	−	0.249447i
$493$			111.540i			0.226247i
$494$		−	415.838i		−	0.841778i
$495$	−185.572	+	130.574i	−0.374893	+	0.263786i
$496$	3.68748			0.00743443
$497$	−9.88422			−0.0198878
$498$	−449.816	−	430.258i	−0.903245	−	0.863971i
$499$	320.913			0.643111			0.321556	−	0.946891i	$-0.395794\pi$
$499$	320.913			0.643111			0.321556	+	0.946891i	$0.395794\pi$
$500$	−33.7361	−	247.713i	−0.0674723	−	0.495427i
$501$	713.545	+	682.520i	1.42424	+	1.36231i
$502$			513.770i			1.02345i
$503$	783.001			1.55666			0.778331	−	0.627855i	$-0.216067\pi$
$503$	783.001			1.55666			0.778331	+	0.627855i	$0.216067\pi$
$504$	−98.4504	+	4.37798i	−0.195338	+	0.00868647i
$505$	−178.755	−	279.671i	−0.353970	−	0.553804i
$506$		−	34.1990i		−	0.0675869i
$507$	144.061	+	137.797i	0.284144	+	0.271790i
$508$			391.141i			0.769962i
$509$		−	15.4948i		−	0.0304417i	−0.999884	−	0.0152209i	$-0.995155\pi$
$509$		−	15.4948i		−	0.0304417i	0.999884	−	0.0152209i	$-0.00484514\pi$
$510$	−213.282	−	42.0057i	−0.418200	−	0.0823642i
$511$	−46.6640			−0.0913190
$512$	−22.6274			−0.0441942
$513$	−340.672	+	389.411i	−0.664078	+	0.759086i
$514$	42.9631			0.0835857
$515$	260.121	+	406.972i	0.505088	+	0.790236i
$516$	−111.447	+	116.513i	−0.215982	+	0.225800i
$517$		−	267.629i		−	0.517658i
$518$	172.432			0.332881
$519$	−346.027	−	330.981i	−0.666718	−	0.637729i
$520$	116.867	+	182.845i	0.224745	+	0.351625i
$521$		−	689.773i		−	1.32394i	−0.749530	−	0.661970i	$-0.769720\pi$
$521$		−	689.773i		−	1.32394i	0.749530	−	0.661970i	$-0.230280\pi$
$522$	−138.403	+	6.15465i	−0.265141	+	0.0117905i
$523$		−	59.6203i		−	0.113997i	−0.998374	−	0.0569984i	$-0.981847\pi$
$523$		−	59.6203i		−	0.113997i	0.998374	−	0.0569984i	$-0.0181530\pi$
$524$			135.841i			0.259239i
$525$	106.146	+	270.251i	0.202183	+	0.514763i
$526$	−390.495			−0.742386
$527$	−9.44673			−0.0179255
$528$	41.8247	−	43.7259i	0.0792135	−	0.0828143i
$529$	23.0000			0.0434783
$530$	90.0921	−	57.5834i	0.169985	−	0.108648i
$531$	−214.508	+	9.53892i	−0.403969	+	0.0179641i
$532$			148.371i			0.278892i
$533$	434.329			0.814876
$534$	371.376	−	388.257i	0.695460	−	0.727074i
$535$	−662.008	+	423.130i	−1.23740	+	0.790897i
$536$		−	123.320i		−	0.230074i
$537$	96.2081	−	100.581i	0.179158	−	0.187302i
$538$		−	126.931i		−	0.235932i
$539$			171.505i			0.318192i
$540$	40.3538	−	266.967i	0.0747293	−	0.494384i
$541$	−146.409			−0.270626			−0.135313	−	0.990803i	$-0.543204\pi$
$541$	−146.409			−0.270626			−0.135313	+	0.990803i	$0.543204\pi$
$542$	449.189			0.828762
$543$	−480.782	−	459.878i	−0.885419	−	0.846920i
$544$	57.9678			0.106558
$545$	−600.041	+	383.523i	−1.10099	+	0.703712i
$546$	−182.125	−	174.206i	−0.333562	−	0.319058i
$547$		−	750.940i		−	1.37283i	−0.727209	−	0.686416i	$-0.759183\pi$
$547$		−	750.940i		−	1.37283i	0.727209	−	0.686416i	$-0.240817\pi$
$548$	−190.883			−0.348327
$549$	−22.1401	−	497.878i	−0.0403280	−	0.906881i
$550$	−161.795	−	74.8616i	−0.294172	−	0.136112i
$551$			208.582i			0.378552i
$552$	29.4072	+	28.1286i	0.0532739	+	0.0509575i
$553$			394.305i			0.713029i
$554$		−	202.355i		−	0.365261i
$555$	−91.2907	+	463.524i	−0.164488	+	0.835179i
$556$	40.2574			0.0724053
$557$	579.005			1.03951			0.519753	−	0.854317i	$-0.326024\pi$
$557$	579.005			1.03951			0.519753	+	0.854317i	$0.326024\pi$
$558$	−0.521260	−	11.7219i	−0.000934158	−	0.0210070i
$559$	−412.335			−0.737629
$560$	−41.6981	−	65.2388i	−0.0744610	−	0.116498i
$561$	−107.148	+	112.019i	−0.190995	+	0.199677i
$562$			629.724i			1.12050i
$563$	15.5541			0.0276272			0.0138136	−	0.999905i	$-0.495603\pi$
$563$	15.5541			0.0276272			0.0138136	+	0.999905i	$0.495603\pi$
$564$	230.130	+	220.124i	0.408033	+	0.390291i
$565$	267.468	−	170.955i	0.473395	−	0.302576i
$566$			592.259i			1.04639i
$567$	27.8338	+	312.339i	0.0490896	+	0.550862i
$568$			7.22152i			0.0127139i
$569$			858.739i			1.50921i	0.656181	+	0.754604i	$0.272171\pi$
$569$			858.739i			1.50921i	−0.656181	+	0.754604i	$0.727829\pi$
$570$	−398.843	−	78.5518i	−0.699724	−	0.137810i
$571$	807.796			1.41470			0.707352	−	0.706862i	$-0.249890\pi$
$571$	807.796			1.41470			0.707352	+	0.706862i	$0.249890\pi$
$572$	154.744			0.270532
$573$	−29.6300	+	30.9769i	−0.0517103	+	0.0540609i
$574$	−154.968			−0.269979
$575$	50.3470	−	108.813i	0.0875600	−	0.189239i
$576$	3.19860	+	71.9289i	0.00555313	+	0.124877i
$577$		−	1032.87i		−	1.79007i	−0.445999	−	0.895033i	$-0.647152\pi$
$577$		−	1032.87i		−	1.79007i	0.445999	−	0.895033i	$-0.352848\pi$
$578$	260.204			0.450179
$579$	−587.529	+	614.237i	−1.01473	+	1.06086i
$580$	−58.6201	−	91.7140i	−0.101069	−	0.158128i
$581$			567.981i			0.977592i
$582$	−401.097	+	419.330i	−0.689171	+	0.720499i
$583$		−	76.2463i		−	0.130783i
$584$			34.0932i			0.0583788i
$585$	564.714	−	397.349i	0.965323	−	0.679230i
$586$	97.0057			0.165539
$587$	235.989			0.402026			0.201013	−	0.979589i	$-0.435577\pi$
$587$	235.989			0.402026			0.201013	+	0.979589i	$0.435577\pi$
$588$	−147.475	−	141.063i	−0.250808	−	0.239903i
$589$	−17.6656			−0.0299925
$590$	−90.8536	−	142.145i	−0.153989	−	0.240924i
$591$	−314.947	−	301.253i	−0.532905	−	0.509734i
$592$		−	125.981i		−	0.212806i
$593$	−361.012			−0.608789			−0.304395	−	0.952546i	$-0.598454\pi$
$593$	−361.012			−0.608789			−0.304395	+	0.952546i	$0.598454\pi$
$594$	−144.910	−	126.773i	−0.243956	−	0.213422i
$595$	106.824	+	167.131i	0.179536	+	0.280893i
$596$			6.99598i			0.0117382i
$597$	−290.512	−	277.881i	−0.486620	−	0.465462i
$598$			104.071i			0.174032i
$599$		−	727.245i		−	1.21410i	−0.794664	−	0.607049i	$-0.792353\pi$
$599$		−	727.245i		−	1.21410i	0.794664	−	0.607049i	$-0.207647\pi$
$600$	197.448	−	77.5516i	0.329080	−	0.129253i
$601$	222.405			0.370058			0.185029	−	0.982733i	$-0.440762\pi$
$601$	222.405			0.370058			0.185029	+	0.982733i	$0.440762\pi$
$602$	147.121			0.244386
$603$	−392.014	+	17.4324i	−0.650105	+	0.0289095i
$604$	513.195			0.849660
$605$	402.652	−	257.359i	0.665540	−	0.425387i
$606$	194.677	−	203.526i	0.321249	−	0.335852i
$607$			339.105i			0.558657i	0.960196	+	0.279329i	$0.0901119\pi$
$607$			339.105i			0.558657i	−0.960196	+	0.279329i	$0.909888\pi$
$608$	108.401			0.178291
$609$	91.3529	+	87.3808i	0.150005	+	0.143482i
$610$	329.922	−	210.874i	0.540856	−	0.345694i
$611$			814.422i			1.33293i
$612$	−8.19430	−	184.270i	−0.0133894	−	0.301095i
$613$			411.286i			0.670940i	0.942051	+	0.335470i	$0.108895\pi$
$613$			411.286i			0.670940i	−0.942051	+	0.335470i	$0.891105\pi$
$614$			569.666i			0.927795i
$615$	82.0446	−	416.577i	0.133406	−	0.677362i
$616$	−55.2126			−0.0896309
$617$	268.904			0.435825			0.217912	−	0.975968i	$-0.430075\pi$
$617$	268.904			0.435825			0.217912	+	0.975968i	$0.430075\pi$
$618$	−283.290	+	296.167i	−0.458397	+	0.479235i
$619$	−242.398			−0.391597			−0.195798	−	0.980644i	$-0.562730\pi$
$619$	−242.398			−0.391597			−0.195798	+	0.980644i	$0.562730\pi$
$620$	7.76760	−	4.96475i	0.0125284	−	0.00800766i
$621$	85.2592	−	97.4570i	0.137293	−	0.156936i
$622$			662.313i			1.06481i
$623$	−490.251			−0.786920
$624$	−127.277	+	133.062i	−0.203969	+	0.213241i
$625$	−404.581	−	476.381i	−0.647329	−	0.762210i
$626$			785.184i			1.25429i
$627$	−200.370	+	209.478i	−0.319569	+	0.334096i
$628$		−	9.71464i		−	0.0154692i
$629$			322.743i			0.513105i
$630$	−201.489	+	141.774i	−0.319824	+	0.225038i
$631$	19.5182			0.0309322			0.0154661	−	0.999880i	$-0.495077\pi$
$631$	19.5182			0.0309322			0.0154661	+	0.999880i	$0.495077\pi$
$632$	288.084			0.455828
$633$	310.833	+	297.318i	0.491047	+	0.469696i
$634$	624.807			0.985500
$635$	526.624	+	823.930i	0.829329	+	1.29753i
$636$	65.5630	+	62.7123i	0.103087	+	0.0986043i
$637$		−	521.908i		−	0.819322i
$638$	−77.6190			−0.121660
$639$	22.9561	−	1.02083i	0.0359250	−	0.00159754i
$640$	−47.6642	+	30.4651i	−0.0744753	+	0.0476017i
$641$			889.107i			1.38706i	0.720426	+	0.693531i	$0.243946\pi$
$641$			889.107i			1.38706i	−0.720426	+	0.693531i	$0.756054\pi$
$642$	−481.765	−	460.818i	−0.750413	−	0.717785i
$643$			78.9605i			0.122800i	0.998113	+	0.0614001i	$0.0195566\pi$
$643$			78.9605i			0.122800i	−0.998113	+	0.0614001i	$0.980443\pi$
$644$		−	37.1324i		−	0.0576590i
$645$	−77.8899	+	395.482i	−0.120760	+	0.613151i
$646$	−277.706			−0.429886
$647$	−844.151			−1.30472			−0.652358	−	0.757911i	$-0.726220\pi$
$647$	−844.151			−1.30472			−0.652358	+	0.757911i	$0.726220\pi$
$648$	228.198	−	20.3357i	0.352158	−	0.0313822i
$649$	−120.299			−0.185361
$650$	492.358	+	227.811i	0.757473	+	0.350479i
$651$	−7.40060	+	7.73701i	−0.0113680	+	0.0118848i
$652$		−	439.106i		−	0.673475i
$653$	1045.45			1.60099			0.800497	−	0.599336i	$-0.204569\pi$
$653$	1045.45			1.60099			0.800497	+	0.599336i	$0.204569\pi$
$654$	−436.670	−	417.683i	−0.667691	−	0.638660i
$655$	182.894	+	286.147i	0.279228	+	0.436866i
$656$			113.221i			0.172593i
$657$	108.377	−	4.81940i	0.164957	−	0.00733547i
$658$		−	290.585i		−	0.441618i
$659$		−	1221.83i		−	1.85407i	−0.374976	−	0.927035i	$-0.622349\pi$
$659$		−	1221.83i		−	1.85407i	0.374976	−	0.927035i	$-0.377651\pi$
$660$	29.2312	−	148.420i	0.0442897	−	0.224879i
$661$	−431.226			−0.652384			−0.326192	−	0.945303i	$-0.605766\pi$
$661$	−431.226			−0.652384			−0.326192	+	0.945303i	$0.605766\pi$
$662$	8.12892			0.0122793
$663$	326.063	−	340.884i	0.491799	−	0.514154i
$664$	414.973			0.624960
$665$	199.763	+	312.540i	0.300396	+	0.469985i
$666$	−400.473	+	17.8086i	−0.601311	+	0.0267396i
$667$		−	52.2014i		−	0.0782630i
$668$	−658.274			−0.985440
$669$	180.998	−	189.226i	0.270550	−	0.282849i
$670$	−166.035	−	259.771i	−0.247814	−	0.387717i
$671$		−	279.218i		−	0.416122i
$672$	45.4122	−	47.4765i	0.0675777	−	0.0706496i
$673$			1314.26i			1.95284i	0.215880	+	0.976420i	$0.430738\pi$
$673$			1314.26i			1.95284i	−0.215880	+	0.976420i	$0.569262\pi$
$674$		−	238.184i		−	0.353389i
$675$	−274.435	−	616.693i	−0.406571	−	0.913619i
$676$	−132.902			−0.196601
$677$	572.358			0.845432			0.422716	−	0.906262i	$-0.361077\pi$
$677$	572.358			0.845432			0.422716	+	0.906262i	$0.361077\pi$
$678$	194.646	+	186.182i	0.287088	+	0.274605i
$679$	529.487			0.779804
$680$	122.108	−	78.0467i	0.179571	−	0.114775i
$681$	159.728	+	152.783i	0.234550	+	0.224351i
$682$		−	6.57383i		−	0.00963905i
$683$	1159.23			1.69726			0.848628	−	0.528990i	$-0.177429\pi$
$683$	1159.23			1.69726			0.848628	+	0.528990i	$0.177429\pi$
$684$	−15.3235	−	344.590i	−0.0224028	−	0.503787i
$685$	−402.092	+	257.001i	−0.586995	+	0.375185i
$686$			454.485i			0.662514i
$687$	−130.855	−	125.166i	−0.190473	−	0.182192i
$688$		−	107.488i		−	0.156232i
$689$			232.025i			0.336756i
$690$	99.8175	+	19.6590i	0.144663	+	0.0284913i
$691$	982.871			1.42239			0.711195	−	0.702995i	$-0.248155\pi$
$691$	982.871			1.42239			0.711195	+	0.702995i	$0.248155\pi$
$692$	319.223			0.461306
$693$	7.80483	+	175.512i	0.0112624	+	0.253264i
$694$	60.8686			0.0877069
$695$	84.8014	−	54.2017i	0.122016	−	0.0779881i
$696$	63.8413	−	66.7434i	0.0917261	−	0.0958957i
$697$		−	290.055i		−	0.416147i
$698$	−1.02842			−0.00147338
$699$	−50.8640	−	48.6524i	−0.0727668	−	0.0696029i
$700$	−175.673	−	81.2828i	−0.250961	−	0.116118i
$701$		−	354.669i		−	0.505948i	−0.967473	−	0.252974i	$-0.918591\pi$
$701$		−	354.669i		−	0.505948i	0.967473	−	0.252974i	$-0.0814087\pi$
$702$	440.976	+	385.783i	0.628170	+	0.549548i
$703$			603.537i			0.858516i
$704$			40.3389i			0.0572996i
$705$	781.136	+	153.844i	1.10799	+	0.218219i
$706$	−890.701			−1.26162
$707$	−256.992			−0.363496
$708$	98.9459	−	103.444i	0.139754	−	0.146107i
$709$	1097.20			1.54754			0.773769	−	0.633467i	$-0.218369\pi$
$709$	1097.20			1.54754			0.773769	+	0.633467i	$0.218369\pi$
$710$	9.72292	+	15.2120i	0.0136942	+	0.0214253i
$711$	−40.7234	−	915.771i	−0.0572762	−	1.28800i
$712$			358.183i			0.503066i
$713$	4.42113			0.00620074
$714$	−116.339	+	121.627i	−0.162939	+	0.170346i
$715$	325.966	−	208.345i	0.455896	−	0.291391i
$716$			92.7904i			0.129595i
$717$	132.121	−	138.127i	0.184269	−	0.192646i
$718$		−	825.374i		−	1.14955i
$719$		−	702.947i		−	0.977674i	−0.872375	−	0.488837i	$-0.837421\pi$
$719$		−	702.947i		−	0.977674i	0.872375	−	0.488837i	$-0.162579\pi$
$720$	103.581	+	147.210i	0.143863	+	0.204459i
$721$	373.969			0.518681
$722$	−8.78675			−0.0121700
$723$	−243.266	−	232.688i	−0.336467	−	0.321837i
$724$	443.541			0.612625
$725$	−246.964	−	114.269i	−0.340640	−	0.157612i
$726$	293.023	+	280.282i	0.403613	+	0.386064i
$727$			783.325i			1.07748i	0.842473	+	0.538738i	$0.181099\pi$
$727$			783.325i			1.07748i	−0.842473	+	0.538738i	$0.818901\pi$
$728$	168.017			0.230793
$729$	−96.9019	−	722.531i	−0.132924	−	0.991126i
$730$	45.9025	+	71.8167i	0.0628801	+	0.0983791i
$731$			275.367i			0.376699i
$732$	240.096	+	229.656i	0.327999	+	0.313738i
$733$		−	111.554i		−	0.152188i	−0.997101	−	0.0760938i	$-0.975755\pi$
$733$		−	111.554i		−	0.152188i	0.997101	−	0.0760938i	$-0.0242448\pi$
$734$		−	528.302i		−	0.719758i
$735$	−500.577	−	98.5883i	−0.681058	−	0.134134i
$736$	−27.1293			−0.0368605
$737$	−219.848			−0.298301
$738$	359.912	−	16.0049i	0.487686	−	0.0216869i
$739$	457.432			0.618988			0.309494	−	0.950901i	$-0.399840\pi$
$739$	457.432			0.618988			0.309494	+	0.950901i	$0.399840\pi$
$740$	−169.618	−	265.376i	−0.229214	−	0.358617i
$741$	609.745	−	637.462i	0.822868	−	0.860273i
$742$		−	82.7862i		−	0.111572i
$743$	−975.746			−1.31325			−0.656626	−	0.754216i	$-0.728017\pi$
$743$	−975.746			−1.31325			−0.656626	+	0.754216i	$0.728017\pi$
$744$	5.65274	+	5.40696i	0.00759777	+	0.00726742i
$745$	9.41925	+	14.7369i	0.0126433	+	0.0197811i
$746$			306.528i			0.410895i
$747$	−58.6604	−	1319.13i	−0.0785280	−	1.76591i
$748$		−	103.342i		−	0.138158i
$749$			608.323i			0.812181i
$750$	311.507	−	429.201i	0.415342	−	0.572268i
$751$	−897.353			−1.19488			−0.597438	−	0.801915i	$-0.703815\pi$
$751$	−897.353			−1.19488			−0.597438	+	0.801915i	$0.703815\pi$
$752$	−212.304			−0.282320
$753$	−753.342	+	787.587i	−1.00045	+	1.04593i
$754$	236.202			0.313265
$755$	1081.03	−	690.955i	1.43183	−	0.915172i
$756$	−157.340	−	137.647i	−0.208121	−	0.182072i
$757$		−	809.753i		−	1.06969i	−0.844951	−	0.534843i	$-0.820371\pi$
$757$		−	809.753i		−	1.06969i	0.844951	−	0.534843i	$-0.179629\pi$
$758$	−291.655			−0.384769
$759$	50.1461	−	52.4256i	0.0660686	−	0.0690719i
$760$	228.345	−	145.949i	0.300454	−	0.192039i
$761$		−	814.133i		−	1.06982i	−0.844909	−	0.534910i	$-0.820345\pi$
$761$		−	814.133i		−	1.06982i	0.844909	−	0.534910i	$-0.179655\pi$
$762$	−573.531	+	599.602i	−0.752665	+	0.786879i
$763$			551.382i			0.722650i
$764$		−	28.5774i		−	0.0374050i
$765$	−265.359	−	377.129i	−0.346875	−	0.492979i
$766$	−135.290			−0.176619
$767$	366.083			0.477292
$768$	−34.6869	−	33.1786i	−0.0451652	−	0.0432014i
$769$	538.649			0.700454			0.350227	−	0.936665i	$-0.386104\pi$
$769$	538.649			0.700454			0.350227	+	0.936665i	$0.386104\pi$
$770$	−116.304	+	74.3372i	−0.151044	+	0.0965418i
$771$	65.8605	+	62.9969i	0.0854222	+	0.0817080i
$772$		−	566.658i		−	0.734012i
$773$	642.229			0.830826			0.415413	−	0.909633i	$-0.363637\pi$
$773$	642.229			0.830826			0.415413	+	0.909633i	$0.363637\pi$
$774$	−341.687	+	15.1944i	−0.441456	+	0.0196311i
$775$	9.67785	−	20.9163i	0.0124876	−	0.0269888i
$776$		−	386.849i		−	0.498516i
$777$	264.331	+	252.838i	0.340195	+	0.325403i
$778$		−	245.359i		−	0.315372i
$779$		−	542.409i		−	0.696289i
$780$	−88.9533	+	451.656i	−0.114043	+	0.579046i
$781$	12.8741			0.0164842
$782$	69.5010			0.0888759
$783$	−221.191	−	193.507i	−0.282492	−	0.247135i
$784$	136.052			0.173535
$785$	−13.0796	−	20.4637i	−0.0166619	−	0.0260684i
$786$	−199.185	+	208.239i	−0.253416	+	0.264935i
$787$		−	443.245i		−	0.563209i	−0.959531	−	0.281604i	$-0.909133\pi$
$787$		−	443.245i		−	0.563209i	0.959531	−	0.281604i	$-0.0908666\pi$
$788$	290.551			0.368720
$789$	−598.612	−	572.584i	−0.758697	−	0.725709i
$790$	606.842	−	387.870i	0.768155	−	0.490975i
$791$		−	245.778i		−	0.310718i
$792$	128.231	−	5.70229i	0.161908	−	0.00719986i
$793$			849.688i			1.07149i
$794$			482.579i			0.607782i
$795$	222.542	+	43.8294i	0.279927	+	0.0551314i
$796$	268.009			0.336695
$797$	363.471			0.456049			0.228025	−	0.973655i	$-0.426773\pi$
$797$	363.471			0.456049			0.228025	+	0.973655i	$0.426773\pi$
$798$	−217.556	+	227.446i	−0.272627	+	0.285020i
$799$	543.890			0.680713
$800$	−59.3861	+	128.348i	−0.0742326	+	0.160435i
$801$	1138.61	−	50.6326i	1.42148	−	0.0632117i
$802$		−	474.783i		−	0.591999i
$803$	60.7796			0.0756906
$804$	180.824	−	189.044i	0.224906	−	0.235129i
$805$	−49.9943	−	78.2186i	−0.0621047	−	0.0971660i
$806$			20.0048i			0.0248199i
$807$	186.120	−	194.580i	0.230631	−	0.241115i
$808$			187.761i			0.232378i
$809$		−	2.55737i		−	0.00316115i	−0.999999	−	0.00158058i	$-0.999497\pi$
$809$		−	2.55737i		−	0.00316115i	0.999999	−	0.00158058i	$-0.000503113\pi$
$810$	453.316	−	350.078i	0.559649	−	0.432196i
$811$	−799.167			−0.985409			−0.492705	−	0.870197i	$-0.663992\pi$
$811$	−799.167			−0.985409			−0.492705	+	0.870197i	$0.663992\pi$
$812$	−84.2767			−0.103789
$813$	688.588	+	658.647i	0.846971	+	0.810144i
$814$	−224.592			−0.275911
$815$	−591.203	−	924.967i	−0.725403	−	1.13493i
$816$	88.8621	+	84.9984i	0.108900	+	0.104165i
$817$			514.942i			0.630284i
$818$	187.194			0.228844
$819$	−23.7509	−	534.100i	−0.0289998	−	0.652137i
$820$	152.439	+	238.498i	0.185901	+	0.290852i
$821$			311.233i			0.379090i	0.981872	+	0.189545i	$0.0607014\pi$
$821$			311.233i			0.379090i	−0.981872	+	0.189545i	$0.939299\pi$
$822$	−292.616	−	279.893i	−0.355980	−	0.340502i
$823$		−	974.714i		−	1.18434i	−0.805812	−	0.592171i	$-0.798271\pi$
$823$		−	974.714i		−	1.18434i	0.805812	−	0.592171i	$-0.201729\pi$
$824$		−	273.226i		−	0.331585i
$825$	−138.255	−	352.000i	−0.167581	−	0.426666i
$826$	−130.618			−0.158133
$827$	757.458			0.915911			0.457955	−	0.888975i	$-0.348582\pi$
$827$	757.458			0.915911			0.457955	+	0.888975i	$0.348582\pi$
$828$	3.83499	+	86.2397i	0.00463163	+	0.104154i
$829$	120.760			0.145669			0.0728347	−	0.997344i	$-0.476795\pi$
$829$	120.760			0.145669			0.0728347	+	0.997344i	$0.476795\pi$
$830$	874.133	−	558.712i	1.05317	−	0.673147i
$831$	296.713	−	310.201i	0.357055	−	0.373286i
$832$		−	122.755i		−	0.147542i
$833$	−348.542			−0.418418
$834$	61.7128	+	59.0295i	0.0739962	+	0.0707788i
$835$	−1386.64	+	886.287i	−1.66065	+	1.06142i
$836$		−	193.252i		−	0.231162i
$837$	16.3888	−	18.7335i	0.0195804	−	0.0223817i
$838$			770.918i			0.919950i
$839$		−	989.255i		−	1.17909i	−0.807736	−	0.589544i	$-0.799307\pi$
$839$		−	989.255i		−	1.17909i	0.807736	−	0.589544i	$-0.200693\pi$
$840$	31.7384	−	161.150i	0.0377839	−	0.191846i
$841$	722.522			0.859123
$842$	−59.3659			−0.0705058
$843$	−923.365	+	965.339i	−1.09533	+	1.14512i
$844$	−286.756			−0.339758
$845$	−279.956	+	178.937i	−0.331309	+	0.211760i
$846$	30.0113	+	674.882i	0.0354743	+	0.797732i
$847$		−	369.999i		−	0.436835i
$848$	−60.4845			−0.0713261
$849$	−868.430	+	907.907i	−1.02289	+	1.06938i
$850$	152.138	−	328.808i	0.178985	−	0.386833i
$851$		−	151.046i		−	0.177492i
$852$	−10.5889	+	11.0703i	−0.0124283	+	0.0129933i
$853$			871.455i			1.02164i	0.859689	+	0.510818i	$0.170657\pi$
$853$			871.455i			1.02164i	−0.859689	+	0.510818i	$0.829343\pi$
$854$		−	303.168i		−	0.354997i
$855$	−496.228	−	705.241i	−0.580384	−	0.824843i
$856$	444.448			0.519215
$857$	−509.107			−0.594057			−0.297028	−	0.954869i	$-0.595996\pi$
$857$	−509.107			−0.594057			−0.297028	+	0.954869i	$0.595996\pi$
$858$	237.216	+	226.902i	0.276476	+	0.264455i
$859$	727.905			0.847386			0.423693	−	0.905806i	$-0.360734\pi$
$859$	727.905			0.847386			0.423693	+	0.905806i	$0.360734\pi$
$860$	−144.720	−	226.421i	−0.168279	−	0.263280i
$861$	−237.559	−	227.230i	−0.275911	−	0.263914i
$862$			150.141i			0.174178i
$863$	−739.499			−0.856893			−0.428447	−	0.903567i	$-0.640939\pi$
$863$	−739.499			−0.856893			−0.428447	+	0.903567i	$0.640939\pi$
$864$	−100.566	+	114.954i	−0.116396	+	0.133049i
$865$	672.438	−	429.796i	0.777385	−	0.496874i
$866$			871.795i			1.00669i
$867$	398.881	+	381.537i	0.460070	+	0.440066i
$868$		−	7.13770i		−	0.00822316i
$869$		−	513.580i		−	0.591001i
$870$	44.6185	−	226.548i	0.0512857	−	0.260400i
$871$	669.018			0.768104
$872$	402.846			0.461979
$873$	−1229.73	+	54.6848i	−1.40863	+	0.0626400i
$874$	129.968			0.148705
$875$	−479.488	+	65.3017i	−0.547987	+	0.0746305i
$876$	−49.9910	+	52.2635i	−0.0570674	+	0.0596615i
$877$			1033.13i			1.17803i	0.808122	+	0.589016i	$0.200484\pi$
$877$			1033.13i			1.17803i	−0.808122	+	0.589016i	$0.799516\pi$
$878$	−918.853			−1.04653
$879$	148.706	+	142.240i	0.169176	+	0.161820i
$880$	54.3116	+	84.9732i	0.0617177	+	0.0965604i
$881$		−	201.330i		−	0.228525i	−0.993451	−	0.114262i	$-0.963550\pi$
$881$		−	201.330i		−	0.228525i	0.993451	−	0.114262i	$-0.0364505\pi$
$882$	−19.2322	−	432.486i	−0.0218052	−	0.490347i
$883$			831.521i			0.941699i	0.882213	+	0.470850i	$0.156053\pi$
$883$			831.521i			0.941699i	−0.882213	+	0.470850i	$0.843947\pi$
$884$			314.479i			0.355746i
$885$	69.1530	−	351.121i	0.0781390	−	0.396747i
$886$	305.262			0.344539
$887$	279.411			0.315007			0.157504	−	0.987518i	$-0.449655\pi$
$887$	279.411			0.315007			0.157504	+	0.987518i	$0.449655\pi$
$888$	184.726	−	193.123i	0.208025	−	0.217481i
$889$	757.115			0.851648
$890$	482.251	+	754.505i	0.541855	+	0.847759i
$891$	−36.2533	−	406.820i	−0.0406884	−	0.456588i
$892$			174.568i			0.195704i
$893$	1017.09			1.13896
$894$	−10.2582	+	10.7245i	−0.0114745	+	0.0119961i
$895$	124.931	+	195.461i	0.139588	+	0.218392i
$896$			43.7990i			0.0488828i
$897$	−152.599	+	159.536i	−0.170122	+	0.177855i
$898$		−	926.595i		−	1.03184i
$899$		−	10.0343i		−	0.0111616i
$900$	416.393	+	170.636i	0.462659	+	0.189595i
$901$	154.952			0.171977
$902$	201.845			0.223775
$903$	225.529	+	215.723i	0.249756	+	0.238896i
$904$	−179.568			−0.198637
$905$	934.310	−	597.175i	1.03239	−	0.659862i
$906$	786.705	+	752.499i	0.868328	+	0.830572i
$907$		−	336.814i		−	0.371350i	−0.982611	−	0.185675i	$-0.940553\pi$
$907$		−	336.814i		−	0.371350i	0.982611	−	0.185675i	$-0.0594471\pi$
$908$	−147.356			−0.162286
$909$	596.862	−	26.5418i	0.656614	−	0.0291989i
$910$	353.925	−	226.215i	0.388929	−	0.248588i
$911$			777.421i			0.853371i	0.904400	+	0.426685i	$0.140319\pi$
$911$			777.421i			0.853371i	−0.904400	+	0.426685i	$0.859681\pi$
$912$	166.174	+	158.949i	0.182209	+	0.174286i
$913$		−	739.792i		−	0.810286i
$914$			136.646i			0.149504i
$915$	814.961	+	160.506i	0.890668	+	0.175416i
$916$	120.719			0.131789
$917$	262.943			0.286742
$918$	257.635	−	294.494i	0.280648	−	0.320799i
$919$	−1057.46			−1.15066			−0.575330	−	0.817921i	$-0.695127\pi$
$919$	−1057.46			−1.15066			−0.575330	+	0.817921i	$0.695127\pi$
$920$	−57.1474	+	36.5264i	−0.0621167	+	0.0397026i
$921$	−835.303	+	873.273i	−0.906952	+	0.948179i
$922$			1035.82i			1.12345i
$923$	−39.1773			−0.0424456
$924$	−84.6385	−	80.9584i	−0.0916001	−	0.0876173i
$925$	−714.595	−	330.639i	−0.772535	−	0.357448i
$926$		−	227.304i		−	0.245468i
$927$	−868.541	+	38.6231i	−0.936938	+	0.0416646i
$928$			61.5734i			0.0663507i
$929$			925.514i			0.996247i	0.867106	+	0.498124i	$0.165977\pi$
$929$			925.514i			0.996247i	−0.867106	+	0.498124i	$0.834023\pi$
$930$	19.1872	+	3.77891i	0.0206314	+	0.00406334i
$931$	−651.783			−0.700089
$932$	46.9241			0.0503477
$933$	−971.151	+	1015.30i	−1.04089	+	1.08821i
$934$	869.202			0.930623
$935$	−139.137	−	217.688i	−0.148810	−	0.232821i
$936$	−390.219	+	17.3526i	−0.416901	+	0.0185391i
$937$			1620.41i			1.72936i	0.502327	+	0.864678i	$0.332477\pi$
$937$			1620.41i			1.72936i	−0.502327	+	0.864678i	$0.667523\pi$
$938$	−238.705			−0.254483
$939$	−1151.32	+	1203.65i	−1.22611	+	1.28184i
$940$	−447.215	+	285.843i	−0.475761	+	0.304088i
$941$			414.992i			0.441012i	0.975386	+	0.220506i	$0.0707709\pi$
$941$			414.992i			0.441012i	−0.975386	+	0.220506i	$0.929229\pi$
$942$	14.2446	−	14.8921i	0.0151217	−	0.0158091i
$943$			135.748i			0.143953i
$944$			95.4310i			0.101092i
$945$	−516.758	−	78.1113i	−0.546834	−	0.0826574i
$946$	−191.624			−0.202562
$947$	−1534.67			−1.62056			−0.810279	−	0.586044i	$-0.800684\pi$
$947$	−1534.67			−1.62056			−0.810279	+	0.586044i	$0.800684\pi$
$948$	441.620	+	422.418i	0.465844	+	0.445588i
$949$	−184.958			−0.194898
$950$	284.501	−	614.879i	0.299475	−	0.647241i
$951$	957.802	+	916.156i	1.00715	+	0.963361i
$952$		−	112.206i		−	0.117863i
$953$	450.043			0.472238			0.236119	−	0.971724i	$-0.424124\pi$
$953$	450.043			0.472238			0.236119	+	0.971724i	$0.424124\pi$
$954$	8.55006	+	192.271i	0.00896233	+	0.201541i
$955$	−38.4761	−	60.1977i	−0.0402891	−	0.0630343i
$956$			127.428i			0.133293i
$957$	−118.986	−	113.813i	−0.124333	−	0.118927i
$958$			463.958i			0.484299i
$959$			369.485i			0.385281i
$960$	−117.738	−	23.1885i	−0.122644	−	0.0241546i
$961$	−960.150			−0.999116
$962$	683.455			0.710452
$963$	−62.8269	−	1412.83i	−0.0652408	−	1.46711i
$964$	224.422			0.232803
$965$	−762.937	−	1193.65i	−0.790608	−	1.23695i
$966$	54.4473	−	56.9223i	0.0563637	−	0.0589258i
$967$			1438.54i			1.48763i	0.668383	+	0.743817i	$0.266987\pi$
$967$			1438.54i			1.48763i	−0.668383	+	0.743817i	$0.733013\pi$
$968$	−270.326			−0.279262
$969$	−425.712	−	407.202i	−0.439331	−	0.420229i
$970$	−520.846	−	814.889i	−0.536954	−	0.840092i
$971$			1003.17i			1.03313i	0.856247	+	0.516566i	$0.172790\pi$
$971$			1003.17i			1.03313i	−0.856247	+	0.516566i	$0.827210\pi$
$972$	379.636	+	303.434i	0.390572	+	0.312175i
$973$		−	77.9245i		−	0.0800869i
$974$			260.197i			0.267142i
$975$	420.723	+	1071.17i	0.431510	+	1.09864i
$976$	−221.498			−0.226944
$977$	−172.538			−0.176600			−0.0883001	−	0.996094i	$-0.528143\pi$
$977$	−172.538			−0.176600			−0.0883001	+	0.996094i	$0.528143\pi$
$978$	643.862	−	673.130i	0.658345	−	0.688272i
$979$	638.549			0.652246
$980$	286.590	−	183.177i	0.292439	−	0.186916i
$981$	−56.9461	−	1280.58i	−0.0580490	−	1.30538i
$982$		−	215.162i		−	0.219106i
$983$	−1095.53			−1.11448			−0.557240	−	0.830351i	$-0.688140\pi$
$983$	−1095.53			−1.11448			−0.557240	+	0.830351i	$0.688140\pi$
$984$	−166.017	+	173.563i	−0.168716	+	0.176386i
$985$	612.040	−	391.192i	0.621361	−	0.397150i
$986$		−	157.741i		−	0.159981i
$987$	426.085	−	445.454i	0.431697	−	0.451321i
$988$			588.084i			0.595227i
$989$		−	128.873i		−	0.130307i
$990$	262.439	−	184.659i	0.265089	−	0.186525i
$991$	47.1726			0.0476010			0.0238005	−	0.999717i	$-0.492423\pi$
$991$	47.1726			0.0476010			0.0238005	+	0.999717i	$0.492423\pi$
$992$	−5.21488			−0.00525694
$993$	12.4613	+	11.9195i	0.0125491	+	0.0120035i
$994$	13.9784			0.0140628
$995$	564.556	−	360.842i	0.567393	−	0.362656i
$996$	636.136	+	608.476i	0.638691	+	0.610920i
$997$			619.847i			0.621712i	0.950457	+	0.310856i	$0.100616\pi$
$997$			619.847i			0.621712i	−0.950457	+	0.310856i	$0.899384\pi$
$998$	−453.839			−0.454748
$999$	−640.021	−	559.915i	−0.640661	−	0.560475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.b.a.599.9	✓	88
3.2	odd	2	inner	690.3.b.a.599.79	yes	88
5.4	even	2	inner	690.3.b.a.599.80	yes	88
15.14	odd	2	inner	690.3.b.a.599.10	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.b.a.599.9	✓	88	1.1	even	1	trivial
690.3.b.a.599.10	yes	88	15.14	odd	2	inner
690.3.b.a.599.79	yes	88	3.2	odd	2	inner
690.3.b.a.599.80	yes	88	5.4	even	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)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(-2.16793 - 2.07367i) q^{3} +2.00000 q^{4} +(4.21296 - 2.69276i) q^{5} +(3.06591 + 2.93261i) q^{6} -3.87132i q^{7} -2.82843 q^{8} +(0.399825 + 8.99111i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(-2.16793 - 2.07367i) q^{3} +2.00000 q^{4} +(4.21296 - 2.69276i) q^{5} +(3.06591 + 2.93261i) q^{6} -3.87132i q^{7} -2.82843 q^{8} +(0.399825 + 8.99111i) q^{9} +(-5.95803 + 3.80814i) q^{10} +5.04237i q^{11} +(-4.33586 - 4.14733i) q^{12} -15.3444i q^{13} +5.47487i q^{14} +(-14.7173 - 2.89856i) q^{15} +4.00000 q^{16} -10.2474 q^{17} +(-0.565438 - 12.7154i) q^{18} -19.1628 q^{19} +(8.42592 - 5.38552i) q^{20} +(-8.02782 + 8.39274i) q^{21} -7.13098i q^{22} +4.79583 q^{23} +(6.13183 + 5.86521i) q^{24} +(10.4981 - 22.6890i) q^{25} +21.7003i q^{26} +(17.7778 - 20.3212i) q^{27} -7.74264i q^{28} -10.8847i q^{29} +(20.8134 + 4.09918i) q^{30} +0.921869 q^{31} -5.65685 q^{32} +(10.4562 - 10.9315i) q^{33} +14.4920 q^{34} +(-10.4245 - 16.3097i) q^{35} +(0.799650 + 17.9822i) q^{36} -31.4952i q^{37} +27.1003 q^{38} +(-31.8192 + 33.2656i) q^{39} +(-11.9161 + 7.61628i) q^{40} +28.3053i q^{41} +(11.3530 - 11.8691i) q^{42} -26.8720i q^{43} +10.0847i q^{44} +(25.8954 + 36.8026i) q^{45} -6.78233 q^{46} -53.0761 q^{47} +(-8.67171 - 8.29466i) q^{48} +34.0129 q^{49} +(-14.8465 + 32.0871i) q^{50} +(22.2155 + 21.2496i) q^{51} -30.6888i q^{52} -15.1211 q^{53} +(-25.1416 + 28.7385i) q^{54} +(13.5779 + 21.2433i) q^{55} +10.9497i q^{56} +(41.5436 + 39.7372i) q^{57} +15.3934i q^{58} +23.8577i q^{59} +(-29.4346 - 5.79711i) q^{60} -55.3744 q^{61} -1.30372 q^{62} +(34.8075 - 1.54785i) q^{63} +8.00000 q^{64} +(-41.3188 - 64.6454i) q^{65} +(-14.7873 + 15.4595i) q^{66} +43.6001i q^{67} -20.4947 q^{68} +(-10.3970 - 9.94495i) q^{69} +(14.7425 + 23.0654i) q^{70} -2.55319i q^{71} +(-1.13088 - 25.4307i) q^{72} -12.0538i q^{73} +44.5410i q^{74} +(-69.8084 + 27.4186i) q^{75} -38.3256 q^{76} +19.5206 q^{77} +(44.9991 - 47.0447i) q^{78} -101.853 q^{79} +(16.8518 - 10.7710i) q^{80} +(-80.6803 + 7.18975i) q^{81} -40.0298i q^{82} -146.715 q^{83} +(-16.0556 + 16.7855i) q^{84} +(-43.1717 + 27.5937i) q^{85} +38.0027i q^{86} +(-22.5713 + 23.5974i) q^{87} -14.2620i q^{88} -126.637i q^{89} +(-36.6216 - 52.0467i) q^{90} -59.4031 q^{91} +9.59166 q^{92} +(-1.99855 - 1.91165i) q^{93} +75.0609 q^{94} +(-80.7322 + 51.6009i) q^{95} +(12.2637 + 11.7304i) q^{96} +136.772i q^{97} -48.1015 q^{98} +(-45.3365 + 2.01606i) 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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