LMFDB - Embedded newform 690.3.b.a.599.5

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			599.5
Character	$\chi$	$=$	690.599
Dual form			690.3.b.a.599.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(-2.79936 - 1.07869i) q^{3} +2.00000 q^{4} +(4.72534 + 1.63438i) q^{5} +(3.95890 + 1.52550i) q^{6} +7.69411i q^{7} -2.82843 q^{8} +(6.67285 + 6.03929i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(-2.79936 - 1.07869i) q^{3} +2.00000 q^{4} +(4.72534 + 1.63438i) q^{5} +(3.95890 + 1.52550i) q^{6} +7.69411i q^{7} -2.82843 q^{8} +(6.67285 + 6.03929i) q^{9} +(-6.68264 - 2.31136i) q^{10} -16.6679i q^{11} +(-5.59872 - 2.15738i) q^{12} -13.7877i q^{13} -10.8811i q^{14} +(-11.4649 - 9.67239i) q^{15} +4.00000 q^{16} -26.8740 q^{17} +(-9.43684 - 8.54085i) q^{18} +31.7201 q^{19} +(9.45067 + 3.26875i) q^{20} +(8.29957 - 21.5386i) q^{21} +23.5720i q^{22} -4.79583 q^{23} +(7.91779 + 3.05100i) q^{24} +(19.6576 + 15.4460i) q^{25} +19.4987i q^{26} +(-12.1652 - 24.1041i) q^{27} +15.3882i q^{28} +26.0495i q^{29} +(16.2139 + 13.6788i) q^{30} -7.68297 q^{31} -5.65685 q^{32} +(-17.9795 + 46.6596i) q^{33} +38.0055 q^{34} +(-12.5751 + 36.3573i) q^{35} +(13.3457 + 12.0786i) q^{36} +39.6223i q^{37} -44.8590 q^{38} +(-14.8726 + 38.5967i) q^{39} +(-13.3653 - 4.62272i) q^{40} -64.5050i q^{41} +(-11.7374 + 30.4602i) q^{42} -58.0405i q^{43} -33.3359i q^{44} +(21.6610 + 39.4436i) q^{45} +6.78233 q^{46} +72.2219 q^{47} +(-11.1974 - 4.31476i) q^{48} -10.1994 q^{49} +(-27.8001 - 21.8439i) q^{50} +(75.2299 + 28.9887i) q^{51} -27.5753i q^{52} +20.7097 q^{53} +(17.2042 + 34.0884i) q^{54} +(27.2417 - 78.7616i) q^{55} -21.7622i q^{56} +(-88.7961 - 34.2162i) q^{57} -36.8396i q^{58} +30.3283i q^{59} +(-22.9299 - 19.3448i) q^{60} -7.15931 q^{61} +10.8654 q^{62} +(-46.4670 + 51.3417i) q^{63} +8.00000 q^{64} +(22.5342 - 65.1514i) q^{65} +(25.4269 - 65.9866i) q^{66} -88.3837i q^{67} -53.7479 q^{68} +(13.4253 + 5.17322i) q^{69} +(17.7839 - 51.4170i) q^{70} -71.2117i q^{71} +(-18.8737 - 17.0817i) q^{72} +28.2401i q^{73} -56.0344i q^{74} +(-38.3674 - 64.4433i) q^{75} +63.4402 q^{76} +128.245 q^{77} +(21.0331 - 54.5839i) q^{78} -23.1310 q^{79} +(18.9013 + 6.53751i) q^{80} +(8.05390 + 80.5986i) q^{81} +91.2238i q^{82} +139.074 q^{83} +(16.5991 - 43.0772i) q^{84} +(-126.989 - 43.9222i) q^{85} +82.0817i q^{86} +(28.0994 - 72.9220i) q^{87} +47.1440i q^{88} -44.9943i q^{89} +(-30.6333 - 55.7817i) q^{90} +106.084 q^{91} -9.59166 q^{92} +(21.5074 + 8.28755i) q^{93} -102.137 q^{94} +(149.888 + 51.8426i) q^{95} +(15.8356 + 6.10200i) q^{96} +59.4001i q^{97} +14.4241 q^{98} +(100.663 - 111.223i) 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
$3$	−2.79936	−	1.07869i	−0.933121	−	0.359564i
$3$	−2.79936	−	1.07869i	−0.933121	−	0.359564i
$4$	2.00000			0.500000
$5$	4.72534	+	1.63438i	0.945067	+	0.326875i
$5$	4.72534	+	1.63438i	0.945067	+	0.326875i
$6$	3.95890	+	1.52550i	0.659816	+	0.254250i
$7$			7.69411i			1.09916i	0.835441	+	0.549580i	$0.185212\pi$
$7$			7.69411i			1.09916i	−0.835441	+	0.549580i	$0.814788\pi$
$8$	−2.82843			−0.353553
$9$	6.67285	+	6.03929i	0.741428	+	0.671032i
$10$	−6.68264	−	2.31136i	−0.668264	−	0.231136i
$11$		−	16.6679i		−	1.51527i	−0.652680	−	0.757633i	$-0.726356\pi$
$11$		−	16.6679i		−	1.51527i	0.652680	−	0.757633i	$-0.273644\pi$
$12$	−5.59872	−	2.15738i	−0.466560	−	0.179782i
$13$		−	13.7877i		−	1.06059i	−0.847813	−	0.530295i	$-0.822081\pi$
$13$		−	13.7877i		−	1.06059i	0.847813	−	0.530295i	$-0.177919\pi$
$14$		−	10.8811i		−	0.777223i
$15$	−11.4649	−	9.67239i	−0.764329	−	0.644826i
$16$	4.00000			0.250000
$17$	−26.8740			−1.58082			−0.790411	−	0.612578i	$-0.790133\pi$
$17$	−26.8740			−1.58082			−0.790411	+	0.612578i	$0.790133\pi$
$18$	−9.43684	−	8.54085i	−0.524269	−	0.474492i
$19$	31.7201			1.66948			0.834740	−	0.550644i	$-0.185618\pi$
$19$	31.7201			1.66948			0.834740	+	0.550644i	$0.185618\pi$
$20$	9.45067	+	3.26875i	0.472534	+	0.163438i
$21$	8.29957	−	21.5386i	0.395218	−	1.02565i
$22$			23.5720i			1.07146i
$23$	−4.79583			−0.208514
$23$	−4.79583			−0.208514
$24$	7.91779	+	3.05100i	0.329908	+	0.127125i
$25$	19.6576	+	15.4460i	0.786305	+	0.617839i
$26$			19.4987i			0.749950i
$27$	−12.1652	−	24.1041i	−0.450563	−	0.892745i
$28$			15.3882i			0.549580i
$29$			26.0495i			0.898259i	0.893467	+	0.449129i	$0.148266\pi$
$29$			26.0495i			0.898259i	−0.893467	+	0.449129i	$0.851734\pi$
$30$	16.2139	+	13.6788i	0.540462	+	0.455961i
$31$	−7.68297			−0.247838			−0.123919	−	0.992292i	$-0.539546\pi$
$31$	−7.68297			−0.247838			−0.123919	+	0.992292i	$0.539546\pi$
$32$	−5.65685			−0.176777
$33$	−17.9795	+	46.6596i	−0.544835	+	1.41393i
$34$	38.0055			1.11781
$35$	−12.5751	+	36.3573i	−0.359288	+	1.03878i
$36$	13.3457	+	12.0786i	0.370714	+	0.335516i
$37$			39.6223i			1.07087i	0.844575	+	0.535437i	$0.179853\pi$
$37$			39.6223i			1.07087i	−0.844575	+	0.535437i	$0.820147\pi$
$38$	−44.8590			−1.18050
$39$	−14.8726	+	38.5967i	−0.381349	+	0.989658i
$40$	−13.3653	−	4.62272i	−0.334132	−	0.115568i
$41$		−	64.5050i		−	1.57329i	−0.617404	−	0.786646i	$-0.711816\pi$
$41$		−	64.5050i		−	1.57329i	0.617404	−	0.786646i	$-0.288184\pi$
$42$	−11.7374	+	30.4602i	−0.279461	+	0.725243i
$43$		−	58.0405i		−	1.34978i	−0.737919	−	0.674890i	$-0.764191\pi$
$43$		−	58.0405i		−	1.34978i	0.737919	−	0.674890i	$-0.235809\pi$
$44$		−	33.3359i		−	0.757633i
$45$	21.6610	+	39.4436i	0.481355	+	0.876526i
$46$	6.78233			0.147442
$47$	72.2219			1.53664			0.768318	−	0.640068i	$-0.221094\pi$
$47$	72.2219			1.53664			0.768318	+	0.640068i	$0.221094\pi$
$48$	−11.1974	−	4.31476i	−0.233280	−	0.0898909i
$49$	−10.1994			−0.208151
$50$	−27.8001	−	21.8439i	−0.556001	−	0.436878i
$51$	75.2299	+	28.9887i	1.47510	+	0.568406i
$52$		−	27.5753i		−	0.530295i
$53$	20.7097			0.390749			0.195375	−	0.980729i	$-0.437408\pi$
$53$	20.7097			0.390749			0.195375	+	0.980729i	$0.437408\pi$
$54$	17.2042	+	34.0884i	0.318596	+	0.631266i
$55$	27.2417	−	78.7616i	0.495303	−	1.43203i
$56$		−	21.7622i		−	0.388611i
$57$	−88.7961	−	34.2162i	−1.55783	−	0.600284i
$58$		−	36.8396i		−	0.635165i
$59$			30.3283i			0.514039i	0.966406	+	0.257019i	$0.0827405\pi$
$59$			30.3283i			0.514039i	−0.966406	+	0.257019i	$0.917260\pi$
$60$	−22.9299	−	19.3448i	−0.382165	−	0.322413i
$61$	−7.15931			−0.117366			−0.0586829	−	0.998277i	$-0.518690\pi$
$61$	−7.15931			−0.117366			−0.0586829	+	0.998277i	$0.518690\pi$
$62$	10.8654			0.175248
$63$	−46.4670	+	51.3417i	−0.737571	+	0.814947i
$64$	8.00000			0.125000
$65$	22.5342	−	65.1514i	0.346681	−	1.00233i
$66$	25.4269	−	65.9866i	0.385256	−	0.999797i
$67$		−	88.3837i		−	1.31916i	−0.751635	−	0.659580i	$-0.770734\pi$
$67$		−	88.3837i		−	1.31916i	0.751635	−	0.659580i	$-0.229266\pi$
$68$	−53.7479			−0.790411
$69$	13.4253	+	5.17322i	0.194569	+	0.0749742i
$70$	17.7839	−	51.4170i	0.254055	−	0.734528i
$71$		−	71.2117i		−	1.00298i	−0.865163	−	0.501491i	$-0.832785\pi$
$71$		−	71.2117i		−	1.00298i	0.865163	−	0.501491i	$-0.167215\pi$
$72$	−18.8737	−	17.0817i	−0.262134	−	0.237246i
$73$			28.2401i			0.386850i	0.981115	+	0.193425i	$0.0619596\pi$
$73$			28.2401i			0.386850i	−0.981115	+	0.193425i	$0.938040\pi$
$74$		−	56.0344i		−	0.757222i
$75$	−38.3674	−	64.4433i	−0.511565	−	0.859245i
$76$	63.4402			0.834740
$77$	128.245			1.66552
$78$	21.0331	−	54.5839i	0.269655	−	0.699794i
$79$	−23.1310			−0.292798			−0.146399	−	0.989226i	$-0.546768\pi$
$79$	−23.1310			−0.292798			−0.146399	+	0.989226i	$0.546768\pi$
$80$	18.9013	+	6.53751i	0.236267	+	0.0817189i
$81$	8.05390	+	80.5986i	0.0994309	+	0.995044i
$82$			91.2238i			1.11249i
$83$	139.074			1.67559			0.837793	−	0.545988i	$-0.183845\pi$
$83$	139.074			1.67559			0.837793	+	0.545988i	$0.183845\pi$
$84$	16.5991	−	43.0772i	0.197609	−	0.512824i
$85$	−126.989	−	43.9222i	−1.49398	−	0.516732i
$86$			82.0817i			0.954438i
$87$	28.0994	−	72.9220i	0.322981	−	0.838184i
$88$			47.1440i			0.535728i
$89$		−	44.9943i		−	0.505554i	−0.967525	−	0.252777i	$-0.918656\pi$
$89$		−	44.9943i		−	0.505554i	0.967525	−	0.252777i	$-0.0813440\pi$
$90$	−30.6333	−	55.7817i	−0.340370	−	0.619797i
$91$	106.084			1.16576
$92$	−9.59166			−0.104257
$93$	21.5074	+	8.28755i	0.231262	+	0.0891134i
$94$	−102.137			−1.08657
$95$	149.888	+	51.8426i	1.57777	+	0.545712i
$96$	15.8356	+	6.10200i	0.164954	+	0.0635625i
$97$			59.4001i			0.612372i	0.951972	+	0.306186i	$0.0990530\pi$
$97$			59.4001i			0.612372i	−0.951972	+	0.306186i	$0.900947\pi$
$98$	14.4241			0.147185
$99$	100.663	−	111.223i	1.01679	−	1.12346i
$100$	39.3152	+	30.8919i	0.393152	+	0.308919i
$101$		−	36.3941i		−	0.360338i	−0.983636	−	0.180169i	$-0.942336\pi$
$101$		−	36.3941i		−	0.360338i	0.983636	−	0.180169i	$-0.0576644\pi$
$102$	−106.391	−	40.9962i	−1.04305	−	0.401924i
$103$			4.70396i			0.0456696i	0.999739	+	0.0228348i	$0.00726917\pi$
$103$			4.70396i			0.0456696i	−0.999739	+	0.0228348i	$0.992731\pi$
$104$			38.9974i			0.374975i
$105$	74.4205	−	88.2126i	0.708767	−	0.840120i
$106$	−29.2879			−0.276301
$107$	143.867			1.34455			0.672276	−	0.740301i	$-0.265317\pi$
$107$	143.867			1.34455			0.672276	+	0.740301i	$0.265317\pi$
$108$	−24.3304	−	48.2082i	−0.225281	−	0.446372i
$109$	101.340			0.929721			0.464860	−	0.885384i	$-0.346105\pi$
$109$	101.340			0.929721			0.464860	+	0.885384i	$0.346105\pi$
$110$	−38.5256	+	111.386i	−0.350232	+	1.01260i
$111$	42.7402	−	110.917i	0.385047	−	0.999254i
$112$			30.7765i			0.274790i
$113$	44.1938			0.391096			0.195548	−	0.980694i	$-0.437351\pi$
$113$	44.1938			0.391096			0.195548	+	0.980694i	$0.437351\pi$
$114$	125.577	+	48.3890i	1.10155	+	0.424465i
$115$	−22.6619	−	7.83820i	−0.197060	−	0.0681582i
$116$			52.0990i			0.449129i
$117$	83.2677	−	92.0030i	0.711690	−	0.786351i
$118$		−	42.8907i		−	0.363480i
$119$		−	206.771i		−	1.73757i
$120$	32.4277	+	27.3577i	0.270231	+	0.227980i
$121$	−156.820			−1.29603
$122$	10.1248			0.0829902
$123$	−69.5810	+	180.573i	−0.565699	+	1.46807i
$124$	−15.3659			−0.123919
$125$	67.6443	+	105.115i	0.541155	+	0.840923i
$126$	65.7143	−	72.6081i	0.521542	−	0.576255i
$127$		−	221.597i		−	1.74486i	−0.488739	−	0.872430i	$-0.662543\pi$
$127$		−	221.597i		−	1.74486i	0.488739	−	0.872430i	$-0.337457\pi$
$128$	−11.3137			−0.0883883
$129$	−62.6078	+	162.476i	−0.485332	+	1.25951i
$130$	−31.8682	+	92.1379i	−0.245140	+	0.708753i
$131$		−	100.251i		−	0.765273i	−0.923899	−	0.382637i	$-0.875016\pi$
$131$		−	100.251i		−	0.765273i	0.923899	−	0.382637i	$-0.124984\pi$
$132$	−35.9591	+	93.3191i	−0.272417	+	0.706963i
$133$			244.058i			1.83502i
$134$			124.993i			0.932787i
$135$	−18.0894	−	133.783i	−0.133996	−	0.990982i
$136$	76.0110			0.558905
$137$	−154.818			−1.13006			−0.565030	−	0.825070i	$-0.691136\pi$
$137$	−154.818			−1.13006			−0.565030	+	0.825070i	$0.691136\pi$
$138$	−18.9862	−	7.31604i	−0.137581	−	0.0530148i
$139$	188.794			1.35823			0.679114	−	0.734033i	$-0.262364\pi$
$139$	188.794			1.35823			0.679114	+	0.734033i	$0.262364\pi$
$140$	−25.1502	+	72.7146i	−0.179644	+	0.519390i
$141$	−202.175	−	77.9051i	−1.43387	−	0.552519i
$142$			100.709i			0.709215i
$143$	−229.812			−1.60708
$144$	26.6914	+	24.1572i	0.185357	+	0.167758i
$145$	−42.5747	+	123.093i	−0.293619	+	0.848915i
$146$		−	39.9375i		−	0.273544i
$147$	28.5518	+	11.0020i	0.194230	+	0.0748435i
$148$			79.2446i			0.535437i
$149$		−	47.2917i		−	0.317394i	−0.987327	−	0.158697i	$-0.949271\pi$
$149$		−	47.2917i		−	0.317394i	0.987327	−	0.158697i	$-0.0507293\pi$
$150$	54.2596	+	91.1367i	0.361731	+	0.607578i
$151$	31.0861			0.205868			0.102934	−	0.994688i	$-0.467177\pi$
$151$	31.0861			0.205868			0.102934	+	0.994688i	$0.467177\pi$
$152$	−89.7180			−0.590250
$153$	−179.326	−	162.300i	−1.17206	−	1.06078i
$154$	−181.366			−1.17770
$155$	−36.3046	−	12.5569i	−0.234223	−	0.0810120i
$156$	−29.7453	+	77.1933i	−0.190675	+	0.494829i
$157$			47.1835i			0.300532i	0.988646	+	0.150266i	$0.0480130\pi$
$157$			47.1835i			0.300532i	−0.988646	+	0.150266i	$0.951987\pi$
$158$	32.7122			0.207039
$159$	−57.9739	−	22.3394i	−0.364616	−	0.140499i
$160$	−26.7305	−	9.24543i	−0.167066	−	0.0577840i
$161$		−	36.8997i		−	0.229191i
$162$	−11.3899	−	113.984i	−0.0703083	−	0.703603i
$163$		−	240.131i		−	1.47320i	−0.676331	−	0.736598i	$-0.736431\pi$
$163$		−	240.131i		−	1.47320i	0.676331	−	0.736598i	$-0.263569\pi$
$164$		−	129.010i		−	0.786646i
$165$	−161.219	+	191.097i	−0.977083	+	1.15816i
$166$	−196.680			−1.18482
$167$	81.2198			0.486346			0.243173	−	0.969983i	$-0.421812\pi$
$167$	81.2198			0.486346			0.243173	+	0.969983i	$0.421812\pi$
$168$	−23.4747	+	60.9204i	−0.139731	+	0.362621i
$169$	−21.0997			−0.124850
$170$	179.589	+	62.1154i	1.05641	+	0.365384i
$171$	211.664	+	191.567i	1.23780	+	1.12028i
$172$		−	116.081i		−	0.674890i
$173$	−31.4683			−0.181898			−0.0909488	−	0.995856i	$-0.528990\pi$
$173$	−31.4683			−0.181898			−0.0909488	+	0.995856i	$0.528990\pi$
$174$	−39.7385	+	103.127i	−0.228382	+	0.592685i
$175$	−118.843	+	151.248i	−0.679103	+	0.864274i
$176$		−	66.6717i		−	0.378817i
$177$	32.7149	−	84.8999i	0.184830	−	0.479660i
$178$			63.6316i			0.357481i
$179$			100.597i			0.561996i	0.959708	+	0.280998i	$0.0906653\pi$
$179$			100.597i			0.561996i	−0.959708	+	0.280998i	$0.909335\pi$
$180$	43.3220	+	78.8873i	0.240678	+	0.438263i
$181$	79.4785			0.439108			0.219554	−	0.975600i	$-0.429540\pi$
$181$	79.4785			0.439108			0.219554	+	0.975600i	$0.429540\pi$
$182$	−150.025			−0.824315
$183$	20.0415	+	7.72269i	0.109516	+	0.0422005i
$184$	13.5647			0.0737210
$185$	−64.7578	+	187.229i	−0.350042	+	1.01205i
$186$	−30.4161	−	11.7204i	−0.163527	−	0.0630127i
$187$			447.933i			2.39537i
$188$	144.444			0.768318
$189$	185.460	−	93.6004i	0.981269	−	0.495240i
$190$	−211.974	−	73.3166i	−1.11565	−	0.385877i
$191$			181.244i			0.948921i	0.880277	+	0.474461i	$0.157357\pi$
$191$			181.244i			0.948921i	−0.880277	+	0.474461i	$0.842643\pi$
$192$	−22.3949	−	8.62953i	−0.116640	−	0.0449455i
$193$		−	180.172i		−	0.933532i	−0.884381	−	0.466766i	$-0.845419\pi$
$193$		−	180.172i		−	0.933532i	0.884381	−	0.466766i	$-0.154581\pi$
$194$		−	84.0044i		−	0.433013i
$195$	−133.360	+	158.075i	−0.683896	+	0.810640i
$196$	−20.3988			−0.104075
$197$	273.165			1.38663			0.693313	−	0.720637i	$-0.256150\pi$
$197$	273.165			1.38663			0.693313	+	0.720637i	$0.256150\pi$
$198$	−142.358	+	157.293i	−0.718981	+	0.794407i
$199$	−1.98578			−0.00997879			−0.00498939	−	0.999988i	$-0.501588\pi$
$199$	−1.98578			−0.00997879			−0.00498939	+	0.999988i	$0.501588\pi$
$200$	−55.6001	−	43.6878i	−0.278001	−	0.218439i
$201$	−95.3387	+	247.418i	−0.474322	+	1.23093i
$202$			51.4691i			0.254797i
$203$	−200.428			−0.987329
$204$	150.460	+	57.9774i	0.737548	+	0.284203i
$205$	105.426	−	304.808i	0.514271	−	1.48687i
$206$		−	6.65241i		−	0.0322933i
$207$	−32.0019	−	28.9634i	−0.154598	−	0.139920i
$208$		−	55.1507i		−	0.265147i
$209$		−	528.709i		−	2.52971i
$210$	−105.246	+	124.751i	−0.501174	+	0.594054i
$211$	−216.942			−1.02816			−0.514081	−	0.857741i	$-0.671867\pi$
$211$	−216.942			−1.02816			−0.514081	+	0.857741i	$0.671867\pi$
$212$	41.4194			0.195375
$213$	−76.8154	+	199.347i	−0.360636	+	0.935903i
$214$	−203.459			−0.950742
$215$	94.8601	−	274.261i	0.441210	−	1.27563i
$216$	34.4084	+	68.1767i	0.159298	+	0.315633i
$217$		−	59.1136i		−	0.272413i
$218$	−143.316			−0.657412
$219$	30.4623	−	79.0541i	0.139097	−	0.360978i
$220$	54.4834	−	157.523i	0.247652	−	0.716015i
$221$			370.529i			1.67660i
$222$	−60.4438	+	156.861i	−0.272269	+	0.706579i
$223$			256.080i			1.14834i	0.818736	+	0.574171i	$0.194675\pi$
$223$			256.080i			1.14834i	−0.818736	+	0.574171i	$0.805325\pi$
$224$		−	43.5245i		−	0.194306i
$225$	37.8897	+	221.787i	0.168399	+	0.985719i
$226$	−62.4995			−0.276547
$227$	215.303			0.948473			0.474237	−	0.880397i	$-0.342724\pi$
$227$	215.303			0.948473			0.474237	+	0.880397i	$0.342724\pi$
$228$	−177.592	−	68.4324i	−0.778913	−	0.300142i
$229$	−182.701			−0.797823			−0.398911	−	0.916989i	$-0.630612\pi$
$229$	−182.701			−0.797823			−0.398911	+	0.916989i	$0.630612\pi$
$230$	32.0488	+	11.0849i	0.139343	+	0.0481952i
$231$	−359.004	−	138.337i	−1.55413	−	0.598860i
$232$		−	73.6791i		−	0.317582i
$233$	135.492			0.581512			0.290756	−	0.956797i	$-0.406093\pi$
$233$	135.492			0.581512			0.290756	+	0.956797i	$0.406093\pi$
$234$	−117.758	+	130.112i	−0.503241	+	0.556034i
$235$	341.273	+	118.038i	1.45222	+	0.502289i
$236$			60.6566i			0.257019i
$237$	64.7521	+	24.9512i	0.273216	+	0.105279i
$238$			292.419i			1.22865i
$239$			301.405i			1.26111i	0.776145	+	0.630555i	$0.217173\pi$
$239$			301.405i			1.26111i	−0.776145	+	0.630555i	$0.782827\pi$
$240$	−45.8598	−	38.6896i	−0.191082	−	0.161207i
$241$	−88.1708			−0.365854			−0.182927	−	0.983127i	$-0.558557\pi$
$241$	−88.1708			−0.365854			−0.182927	+	0.983127i	$0.558557\pi$
$242$	221.777			0.916434
$243$	64.3952	−	234.312i	0.265001	−	0.964248i
$244$	−14.3186			−0.0586829
$245$	−48.1956	−	16.6697i	−0.196717	−	0.0680394i
$246$	98.4023	−	255.369i	0.400009	−	1.03808i
$247$		−	437.346i		−	1.77063i
$248$	21.7307			0.0876238
$249$	−389.318	−	150.018i	−1.56352	−	0.602480i
$250$	−95.6636	−	148.656i	−0.382654	−	0.594622i
$251$		−	176.705i		−	0.704003i	−0.936000	−	0.352001i	$-0.885501\pi$
$251$		−	176.705i		−	0.704003i	0.936000	−	0.352001i	$-0.114499\pi$
$252$	−92.9340	+	102.683i	−0.368786	+	0.407474i
$253$			79.9366i			0.315955i
$254$			313.386i			1.23380i
$255$	308.108	+	259.935i	1.20827	+	1.01935i
$256$	16.0000			0.0625000
$257$	257.023			1.00009			0.500044	−	0.866000i	$-0.333317\pi$
$257$	257.023			1.00009			0.500044	+	0.866000i	$0.333317\pi$
$258$	88.5408	−	229.776i	0.343181	−	0.890606i
$259$	−304.859			−1.17706
$260$	45.0685	−	130.303i	0.173340	−	0.501164i
$261$	−157.321	+	173.824i	−0.602761	+	0.665994i
$262$			141.776i			0.541130i
$263$	64.1622			0.243963			0.121981	−	0.992532i	$-0.461075\pi$
$263$	64.1622			0.243963			0.121981	+	0.992532i	$0.461075\pi$
$264$	50.8538	−	131.973i	0.192628	−	0.499898i
$265$	97.8603	+	33.8475i	0.369284	+	0.127726i
$266$		−	345.150i		−	1.29756i
$267$	−48.5350	+	125.955i	−0.181779	+	0.471743i
$268$		−	176.767i		−	0.659580i
$269$			417.123i			1.55064i	0.631568	+	0.775321i	$0.282412\pi$
$269$			417.123i			1.55064i	−0.631568	+	0.775321i	$0.717588\pi$
$270$	25.5823	+	189.197i	0.0947494	+	0.700730i
$271$	−375.668			−1.38623			−0.693115	−	0.720827i	$-0.743762\pi$
$271$	−375.668			−1.38623			−0.693115	+	0.720827i	$0.743762\pi$
$272$	−107.496			−0.395205
$273$	−296.967	−	114.432i	−1.08779	−	0.419164i
$274$	218.946			0.799074
$275$	257.452	−	327.652i	0.936190	−	1.19146i
$276$	26.8505	+	10.3464i	0.0972845	+	0.0374871i
$277$			361.975i			1.30677i	0.757027	+	0.653384i	$0.226651\pi$
$277$			361.975i			1.30677i	−0.757027	+	0.653384i	$0.773349\pi$
$278$	−266.995			−0.960412
$279$	−51.2673	−	46.3997i	−0.183754	−	0.166307i
$280$	35.5677	−	102.834i	0.127028	−	0.367264i
$281$		−	53.2019i		−	0.189330i	−0.995509	−	0.0946652i	$-0.969822\pi$
$281$		−	53.2019i		−	0.189330i	0.995509	−	0.0946652i	$-0.0301781\pi$
$282$	285.919	+	110.174i	1.01390	+	0.390690i
$283$		−	262.727i		−	0.928363i	−0.885740	−	0.464182i	$-0.846349\pi$
$283$		−	262.727i		−	0.928363i	0.885740	−	0.464182i	$-0.153651\pi$
$284$		−	142.423i		−	0.501491i
$285$	−363.669	−	306.809i	−1.27603	−	1.07652i
$286$	325.003			1.13637
$287$	496.309			1.72930
$288$	−37.7473	−	34.1634i	−0.131067	−	0.118623i
$289$	433.210			1.49900
$290$	60.2097	−	174.079i	0.207620	−	0.600274i
$291$	64.0744	−	166.282i	0.220187	−	0.571417i
$292$			56.4801i			0.193425i
$293$	−249.475			−0.851452			−0.425726	−	0.904852i	$-0.639981\pi$
$293$	−249.475			−0.851452			−0.425726	+	0.904852i	$0.639981\pi$
$294$	−40.3783	−	15.5592i	−0.137341	−	0.0529223i
$295$	−49.5679	+	143.311i	−0.168027	+	0.485801i
$296$		−	112.069i		−	0.378611i
$297$	−401.766	+	202.769i	−1.35275	+	0.682723i
$298$			66.8806i			0.224432i
$299$			66.1233i			0.221148i
$300$	−76.7347	−	128.887i	−0.255782	−	0.429622i
$301$	446.570			1.48362
$302$	−43.9624			−0.145571
$303$	−39.2580	+	101.880i	−0.129564	+	0.336239i
$304$	126.880			0.417370
$305$	−33.8302	−	11.7010i	−0.110919	−	0.0383640i
$306$	253.605	+	229.526i	0.828775	+	0.750086i
$307$		−	368.547i		−	1.20048i	−0.799820	−	0.600240i	$-0.795072\pi$
$307$		−	368.547i		−	1.20048i	0.799820	−	0.600240i	$-0.204928\pi$
$308$	256.490			0.832760
$309$	5.07412	−	13.1681i	0.0164211	−	0.0426152i
$310$	51.3425	+	17.7581i	0.165621	+	0.0572842i
$311$			446.781i			1.43660i	0.695735	+	0.718298i	$0.255079\pi$
$311$			446.781i			1.43660i	−0.695735	+	0.718298i	$0.744921\pi$
$312$	42.0661	−	109.168i	0.134827	−	0.349897i
$313$			55.1749i			0.176278i	0.996108	+	0.0881388i	$0.0280919\pi$
$313$			55.1749i			0.176278i	−0.996108	+	0.0881388i	$0.971908\pi$
$314$		−	66.7276i		−	0.212508i
$315$	−303.484	+	166.662i	−0.963441	+	0.529086i
$316$	−46.2621			−0.146399
$317$	−296.868			−0.936492			−0.468246	−	0.883598i	$-0.655114\pi$
$317$	−296.868			−0.936492			−0.468246	+	0.883598i	$0.655114\pi$
$318$	81.9875	+	31.5926i	0.257822	+	0.0993479i
$319$	434.191			1.36110
$320$	37.8027	+	13.0750i	0.118133	+	0.0408594i
$321$	−402.736	−	155.188i	−1.25463	−	0.483452i
$322$			52.1840i			0.162062i
$323$	−852.445			−2.63915
$324$	16.1078	+	161.197i	0.0497154	+	0.497522i
$325$	212.964	−	271.033i	0.655273	−	0.833947i
$326$			339.596i			1.04171i
$327$	−283.686	−	109.314i	−0.867542	−	0.334294i
$328$			182.448i			0.556243i
$329$			555.684i			1.68901i
$330$	227.998	−	270.252i	0.690902	−	0.818945i
$331$	−589.940			−1.78230			−0.891148	−	0.453712i	$-0.850100\pi$
$331$	−589.940			−1.78230			−0.891148	+	0.453712i	$0.850100\pi$
$332$	278.147			0.837793
$333$	−239.291	+	264.394i	−0.718591	+	0.793975i
$334$	−114.862			−0.343899
$335$	144.452	−	417.643i	0.431201	−	1.24669i
$336$	33.1983	−	86.1544i	0.0988044	−	0.256412i
$337$		−	58.6794i		−	0.174123i	−0.996203	−	0.0870614i	$-0.972252\pi$
$337$		−	58.6794i		−	0.174123i	0.996203	−	0.0870614i	$-0.0277476\pi$
$338$	29.8395			0.0882825
$339$	−123.715	−	47.6715i	−0.364940	−	0.140624i
$340$	−253.977	−	87.8444i	−0.746991	−	0.258366i
$341$			128.059i			0.375540i
$342$	−299.338	−	270.917i	−0.875256	−	0.792154i
$343$			298.536i			0.870368i
$344$			164.163i			0.477219i
$345$	54.9839	+	46.3872i	0.159374	+	0.134456i
$346$	44.5029			0.128621
$347$	202.744			0.584277			0.292138	−	0.956376i	$-0.405633\pi$
$347$	202.744			0.584277			0.292138	+	0.956376i	$0.405633\pi$
$348$	56.1987	−	145.844i	0.161491	−	0.419092i
$349$	−201.859			−0.578391			−0.289196	−	0.957270i	$-0.593388\pi$
$349$	−201.859			−0.578391			−0.289196	+	0.957270i	$0.593388\pi$
$350$	168.069	−	213.897i	0.480198	−	0.611134i
$351$	−332.339	+	167.730i	−0.946836	+	0.477862i
$352$			94.2881i			0.267864i
$353$	212.494			0.601965			0.300982	−	0.953630i	$-0.402685\pi$
$353$	212.494			0.601965			0.300982	+	0.953630i	$0.402685\pi$
$354$	−46.2658	+	120.067i	−0.130694	+	0.339171i
$355$	116.387	−	336.499i	0.327850	−	0.947885i
$356$		−	89.9887i		−	0.252777i
$357$	−223.042	+	578.828i	−0.624768	+	1.62137i
$358$		−	142.266i		−	0.397391i
$359$			663.928i			1.84938i	0.380720	+	0.924690i	$0.375676\pi$
$359$			663.928i			1.84938i	−0.380720	+	0.924690i	$0.624324\pi$
$360$	−61.2665	−	111.563i	−0.170185	−	0.309899i
$361$	645.166			1.78716
$362$	−112.400			−0.310496
$363$	438.996	+	169.160i	1.20935	+	0.466006i
$364$	212.168			0.582878
$365$	−46.1549	+	133.444i	−0.126452	+	0.365599i
$366$	−28.3430	−	10.9215i	−0.0774398	−	0.0298402i
$367$		−	630.396i		−	1.71770i	−0.512227	−	0.858850i	$-0.671179\pi$
$367$		−	630.396i		−	1.71770i	0.512227	−	0.858850i	$-0.328821\pi$
$368$	−19.1833			−0.0521286
$369$	389.565	−	430.432i	1.05573	−	1.16648i
$370$	91.5814	−	264.781i	0.247517	−	0.715626i
$371$			159.343i			0.429495i
$372$	43.0148	+	16.5751i	0.115631	+	0.0445567i
$373$			383.897i			1.02921i	0.857426	+	0.514607i	$0.172062\pi$
$373$			383.897i			1.02921i	−0.857426	+	0.514607i	$0.827938\pi$
$374$		−	633.473i		−	1.69378i
$375$	−75.9740	−	367.223i	−0.202597	−	0.979262i
$376$	−204.274			−0.543283
$377$	359.162			0.952684
$378$	−262.280	+	132.371i	−0.693862	+	0.350188i
$379$	210.581			0.555621			0.277811	−	0.960636i	$-0.410391\pi$
$379$	210.581			0.555621			0.277811	+	0.960636i	$0.410391\pi$
$380$	299.777	+	103.685i	0.788886	+	0.272856i
$381$	−239.035	+	620.331i	−0.627388	+	1.62816i
$382$		−	256.318i		−	0.670989i
$383$	−566.239			−1.47843			−0.739216	−	0.673469i	$-0.764804\pi$
$383$	−566.239			−1.47843			−0.739216	+	0.673469i	$0.764804\pi$
$384$	31.6712	+	12.2040i	0.0824770	+	0.0317812i
$385$	606.001	+	209.601i	1.57403	+	0.544417i
$386$			254.801i			0.660107i
$387$	350.524	−	387.296i	0.905746	−	1.00076i
$388$			118.800i			0.306186i
$389$		−	120.478i		−	0.309713i	−0.987937	−	0.154856i	$-0.950509\pi$
$389$		−	120.478i		−	0.309713i	0.987937	−	0.154856i	$-0.0494915\pi$
$390$	188.599	−	223.551i	0.483587	−	0.573209i
$391$	128.883			0.329624
$392$	28.8482			0.0735924
$393$	−108.140	+	280.638i	−0.275164	+	0.714092i
$394$	−386.314			−0.980492
$395$	−109.302	−	37.8048i	−0.276714	−	0.0957085i
$396$	201.325	−	222.445i	0.508397	−	0.561731i
$397$			214.516i			0.540342i	0.962812	+	0.270171i	$0.0870802\pi$
$397$			214.516i			0.540342i	−0.962812	+	0.270171i	$0.912920\pi$
$398$	2.80831			0.00705607
$399$	263.263	−	683.207i	0.659808	−	1.71230i
$400$	78.6305	+	61.7839i	0.196576	+	0.154460i
$401$		−	630.643i		−	1.57268i	−0.617796	−	0.786338i	$-0.711974\pi$
$401$		−	630.643i		−	1.57268i	0.617796	−	0.786338i	$-0.288026\pi$
$402$	134.829	−	349.902i	0.335396	−	0.870402i
$403$			105.930i			0.262854i
$404$		−	72.7883i		−	0.180169i
$405$	−93.6711	+	394.019i	−0.231287	+	0.972886i
$406$	283.448			0.698147
$407$	660.422			1.62266
$408$	−212.782	−	81.9924i	−0.521525	−	0.200962i
$409$	−464.370			−1.13538			−0.567689	−	0.823243i	$-0.692163\pi$
$409$	−464.370			−1.13538			−0.567689	+	0.823243i	$0.692163\pi$
$410$	−149.094	+	431.063i	−0.363644	+	1.05137i
$411$	433.393	+	167.001i	1.05448	+	0.406329i
$412$			9.40793i			0.0228348i
$413$	−233.349			−0.565011
$414$	45.2575	+	40.9605i	0.109318	+	0.0989383i
$415$	657.170	+	227.299i	1.58354	+	0.547708i
$416$			77.9948i			0.187488i
$417$	−528.502	−	203.650i	−1.26739	−	0.488369i
$418$			747.707i			1.78877i
$419$		−	586.065i		−	1.39872i	−0.714769	−	0.699361i	$-0.753468\pi$
$419$		−	586.065i		−	1.39872i	0.714769	−	0.699361i	$-0.246532\pi$
$420$	148.841	−	176.425i	0.354383	−	0.420060i
$421$	−228.330			−0.542353			−0.271176	−	0.962530i	$-0.587413\pi$
$421$	−228.330			−0.542353			−0.271176	+	0.962530i	$0.587413\pi$
$422$	306.803			0.727021
$423$	481.926	+	436.169i	1.13931	+	1.03113i
$424$	−58.5759			−0.138151
$425$	−528.278	−	415.094i	−1.24301	−	0.976692i
$426$	108.633	−	281.920i	0.255008	−	0.661783i
$427$		−	55.0846i		−	0.129004i
$428$	287.734			0.672276
$429$	643.327	+	247.896i	1.49960	+	0.577846i
$430$	−134.152	+	387.864i	−0.311982	+	0.902009i
$431$		−	562.763i		−	1.30571i	−0.757481	−	0.652857i	$-0.773570\pi$
$431$		−	562.763i		−	1.30571i	0.757481	−	0.652857i	$-0.226430\pi$
$432$	−48.6608	−	96.4164i	−0.112641	−	0.223186i
$433$		−	402.222i		−	0.928919i	−0.885594	−	0.464459i	$-0.846249\pi$
$433$		−	402.222i		−	0.928919i	0.885594	−	0.464459i	$-0.153751\pi$
$434$			83.5993i			0.192625i
$435$	251.961	−	298.656i	0.579221	−	0.686566i
$436$	202.679			0.464860
$437$	−152.124			−0.348111
$438$	−43.0802	+	111.799i	−0.0983566	+	0.255250i
$439$	−146.580			−0.333896			−0.166948	−	0.985966i	$-0.553391\pi$
$439$	−146.580			−0.333896			−0.166948	+	0.985966i	$0.553391\pi$
$440$	−77.0511	+	222.771i	−0.175116	+	0.506299i
$441$	−68.0590	−	61.5971i	−0.154329	−	0.139676i
$442$		−	524.007i		−	1.18554i
$443$	−784.192			−1.77019			−0.885093	−	0.465414i	$-0.845905\pi$
$443$	−784.192			−1.77019			−0.885093	+	0.465414i	$0.845905\pi$
$444$	85.4805	−	221.834i	0.192524	−	0.499627i
$445$	73.5377	−	212.613i	0.165253	−	0.477783i
$446$		−	362.152i		−	0.812000i
$447$	−51.0131	+	132.387i	−0.114123	+	0.296167i
$448$			61.5529i			0.137395i
$449$		−	579.670i		−	1.29103i	−0.763750	−	0.645513i	$-0.776644\pi$
$449$		−	579.670i		−	1.29103i	0.763750	−	0.645513i	$-0.223356\pi$
$450$	−53.5841	−	313.654i	−0.119076	−	0.697009i
$451$	−1075.16			−2.38396
$452$	88.3877			0.195548
$453$	−87.0212	−	33.5323i	−0.192100	−	0.0740227i
$454$	−304.485			−0.670672
$455$	501.282	+	173.381i	1.10172	+	0.381057i
$456$	251.153	+	96.7780i	0.550775	+	0.212233i
$457$			72.8841i			0.159484i	0.996816	+	0.0797419i	$0.0254096\pi$
$457$			72.8841i			0.159484i	−0.996816	+	0.0797419i	$0.974590\pi$
$458$	258.379			0.564146
$459$	326.927	+	647.773i	0.712259	+	1.41127i
$460$	−45.3238	−	15.6764i	−0.0985301	−	0.0340791i
$461$			188.695i			0.409316i	0.978834	+	0.204658i	$0.0656082\pi$
$461$			188.695i			0.409316i	−0.978834	+	0.204658i	$0.934392\pi$
$462$	507.708	+	195.638i	1.09894	+	0.423458i
$463$			553.814i			1.19614i	0.801443	+	0.598072i	$0.204066\pi$
$463$			553.814i			1.19614i	−0.801443	+	0.598072i	$0.795934\pi$
$464$			104.198i			0.224565i
$465$	88.0847	+	74.3127i	0.189430	+	0.159812i
$466$	−191.615			−0.411191
$467$	−425.497			−0.911129			−0.455565	−	0.890203i	$-0.650563\pi$
$467$	−425.497			−0.911129			−0.455565	+	0.890203i	$0.650563\pi$
$468$	166.535	−	184.006i	0.355845	−	0.393175i
$469$	680.034			1.44997
$470$	−482.633	−	166.931i	−1.02688	−	0.355172i
$471$	50.8964	−	132.084i	0.108060	−	0.280432i
$472$		−	85.7814i		−	0.181740i
$473$	−967.416			−2.04528
$474$	−91.5734	−	35.2864i	−0.193193	−	0.0744438i
$475$	623.542	+	489.948i	1.31272	+	1.03147i
$476$		−	413.543i		−	0.868787i
$477$	138.193	+	125.072i	0.289712	+	0.262205i
$478$		−	426.251i		−	0.891739i
$479$		−	166.558i		−	0.347720i	−0.984770	−	0.173860i	$-0.944376\pi$
$479$		−	166.558i		−	0.347720i	0.984770	−	0.173860i	$-0.0556240\pi$
$480$	64.8555	+	54.7153i	0.135116	+	0.113990i
$481$	546.299			1.13576
$482$	124.692			0.258698
$483$	−39.8033	+	103.296i	−0.0824086	+	0.213862i
$484$	−313.640			−0.648016
$485$	−97.0822	+	280.686i	−0.200169	+	0.578733i
$486$	−91.0686	+	331.368i	−0.187384	+	0.681826i
$487$		−	332.759i		−	0.683284i	−0.939830	−	0.341642i	$-0.889017\pi$
$487$		−	332.759i		−	0.683284i	0.939830	−	0.341642i	$-0.110983\pi$
$488$	20.2496			0.0414951
$489$	−259.027	+	672.213i	−0.529708	+	1.37467i
$490$	68.1588	+	23.5745i	0.139100	+	0.0481111i
$491$			499.918i			1.01816i	0.860719	+	0.509081i	$0.170015\pi$
$491$			499.918i			1.01816i	−0.860719	+	0.509081i	$0.829985\pi$
$492$	−139.162	+	361.146i	−0.282849	+	0.734036i
$493$		−	700.053i		−	1.41999i
$494$			618.501i			1.25203i
$495$	657.444	−	361.044i	1.32817	−	0.729382i
$496$	−30.7319			−0.0619594
$497$	547.911			1.10244
$498$	550.578	+	212.157i	1.10558	+	0.426018i
$499$	−29.1297			−0.0583761			−0.0291881	−	0.999574i	$-0.509292\pi$
$499$	−29.1297			−0.0583761			−0.0291881	+	0.999574i	$0.509292\pi$
$500$	135.289	+	210.231i	0.270577	+	0.420462i
$501$	−227.364	−	87.6111i	−0.453820	−	0.174872i
$502$			249.898i			0.497805i
$503$	445.761			0.886204			0.443102	−	0.896471i	$-0.353878\pi$
$503$	445.761			0.886204			0.443102	+	0.896471i	$0.353878\pi$
$504$	131.429	−	145.216i	0.260771	−	0.288127i
$505$	59.4817	−	171.975i	0.117786	−	0.340544i
$506$		−	113.047i		−	0.223414i
$507$	59.0657	+	22.7601i	0.116500	+	0.0448916i
$508$		−	443.194i		−	0.872430i
$509$			208.350i			0.409333i	0.978832	+	0.204666i	$0.0656110\pi$
$509$			208.350i			0.409333i	−0.978832	+	0.204666i	$0.934389\pi$
$510$	−435.731	−	367.604i	−0.854374	−	0.720793i
$511$	−217.282			−0.425210
$512$	−22.6274			−0.0441942
$513$	−385.881	−	764.585i	−0.752206	−	1.49042i
$514$	−363.485			−0.707169
$515$	−7.68805	+	22.2278i	−0.0149283	+	0.0431608i
$516$	−125.216	+	324.953i	−0.242666	+	0.629754i
$517$		−	1203.79i		−	2.32841i
$518$	431.135			0.832307
$519$	88.0912	+	33.9446i	0.169732	+	0.0654038i
$520$	−63.7365	+	184.276i	−0.122570	+	0.354377i
$521$		−	823.005i		−	1.57966i	−0.613324	−	0.789832i	$-0.710168\pi$
$521$		−	823.005i		−	1.57966i	0.613324	−	0.789832i	$-0.289832\pi$
$522$	222.485	−	245.825i	0.426216	−	0.470929i
$523$			293.166i			0.560546i	0.959920	+	0.280273i	$0.0904250\pi$
$523$			293.166i			0.560546i	−0.959920	+	0.280273i	$0.909575\pi$
$524$		−	200.502i		−	0.382637i
$525$	495.834	−	295.203i	0.944447	−	0.562291i
$526$	−90.7391			−0.172508
$527$	206.472			0.391787
$528$	−71.9182	+	186.638i	−0.136209	+	0.353482i
$529$	23.0000			0.0434783
$530$	−138.395	−	47.8676i	−0.261123	−	0.0903161i
$531$	−183.161	+	202.376i	−0.344937	+	0.381123i
$532$			488.116i			0.917512i
$533$	−889.373			−1.66862
$534$	68.6388	−	178.128i	0.128537	−	0.333573i
$535$	679.820	+	235.133i	1.27069	+	0.439501i
$536$			249.987i			0.466393i
$537$	108.513	−	281.608i	0.202073	−	0.524410i
$538$		−	589.900i		−	1.09647i
$539$			170.003i			0.315404i
$540$	−36.1789	−	267.565i	−0.0669979	−	0.495491i
$541$	572.496			1.05822			0.529109	−	0.848554i	$-0.322526\pi$
$541$	572.496			1.05822			0.529109	+	0.848554i	$0.322526\pi$
$542$	531.275			0.980212
$543$	−222.489	−	85.7327i	−0.409740	−	0.157887i
$544$	152.022			0.279452
$545$	478.864	+	165.627i	0.878649	+	0.303903i
$546$	419.975	+	161.831i	0.769185	+	0.296394i
$547$		−	168.725i		−	0.308456i	−0.988035	−	0.154228i	$-0.950711\pi$
$547$		−	168.725i		−	0.308456i	0.988035	−	0.154228i	$-0.0492890\pi$
$548$	−309.637			−0.565030
$549$	−47.7730	−	43.2372i	−0.0870183	−	0.0787563i
$550$	−364.093	+	463.370i	−0.661987	+	0.842490i
$551$			826.293i			1.49962i
$552$	−37.9724	−	14.6321i	−0.0687906	−	0.0265074i
$553$		−	177.973i		−	0.321832i
$554$		−	511.909i		−	0.924024i
$555$	383.243	−	454.267i	0.690527	−	0.818500i
$556$	377.587			0.679114
$557$	−990.965			−1.77911			−0.889555	−	0.456828i	$-0.848986\pi$
$557$	−990.965			−1.77911			−0.889555	+	0.456828i	$0.848986\pi$
$558$	72.5029	+	65.6190i	0.129934	+	0.117597i
$559$	−800.243			−1.43156
$560$	−50.3003	+	145.429i	−0.0898220	+	0.259695i
$561$	483.182	−	1253.93i	0.861286	−	2.23516i
$562$			75.2388i			0.133877i
$563$	790.012			1.40322			0.701609	−	0.712562i	$-0.252465\pi$
$563$	790.012			1.40322			0.701609	+	0.712562i	$0.252465\pi$
$564$	−404.350	−	155.810i	−0.716933	−	0.276259i
$565$	208.831	+	72.2294i	0.369612	+	0.127840i
$566$			371.552i			0.656452i
$567$	−620.135	+	61.9676i	−1.09371	+	0.109290i
$568$			201.417i			0.354608i
$569$		−	133.372i		−	0.234398i	−0.993108	−	0.117199i	$-0.962609\pi$
$569$		−	133.372i		−	0.234398i	0.993108	−	0.117199i	$-0.0373915\pi$
$570$	514.306	+	433.894i	0.902291	+	0.761218i
$571$	1030.36			1.80449			0.902244	−	0.431227i	$-0.141919\pi$
$571$	1030.36			1.80449			0.902244	+	0.431227i	$0.141919\pi$
$572$	−459.624			−0.803538
$573$	195.506	−	507.367i	0.341198	−	0.885458i
$574$	−701.887			−1.22280
$575$	−94.2746	−	74.0763i	−0.163956	−	0.128828i
$576$	53.3828	+	48.3143i	0.0926785	+	0.0838791i
$577$			967.625i			1.67699i	0.544907	+	0.838497i	$0.316565\pi$
$577$			967.625i			1.67699i	−0.544907	+	0.838497i	$0.683435\pi$
$578$	−612.651			−1.05995
$579$	−194.349	+	504.365i	−0.335664	+	0.871098i
$580$	−85.1494	+	246.185i	−0.146809	+	0.424458i
$581$			1070.05i			1.84174i
$582$	−90.6148	+	235.159i	−0.155696	+	0.404053i
$583$		−	345.188i		−	0.592089i
$584$		−	79.8750i		−	0.136772i
$585$	543.836	−	298.654i	0.929634	−	0.510520i
$586$	352.811			0.602067
$587$	−947.013			−1.61331			−0.806655	−	0.591023i	$-0.798724\pi$
$587$	−947.013			−1.61331			−0.806655	+	0.591023i	$0.798724\pi$
$588$	57.1036	+	22.0040i	0.0971149	+	0.0374217i
$589$	−243.705			−0.413760
$590$	70.0996	−	202.673i	0.118813	−	0.343514i
$591$	−764.688	−	294.661i	−1.29389	−	0.498580i
$592$			158.489i			0.267718i
$593$	−579.653			−0.977492			−0.488746	−	0.872426i	$-0.662546\pi$
$593$	−579.653			−0.977492			−0.488746	+	0.872426i	$0.662546\pi$
$594$	568.182	−	286.758i	0.956536	−	0.482758i
$595$	337.942	−	977.064i	0.567970	−	1.64212i
$596$		−	94.5834i		−	0.158697i
$597$	5.55891	+	2.14204i	0.00931141	+	0.00358801i
$598$		−	93.5125i		−	0.156375i
$599$		−	537.808i		−	0.897843i	−0.893571	−	0.448922i	$-0.851808\pi$
$599$		−	537.808i		−	0.897843i	0.893571	−	0.448922i	$-0.148192\pi$
$600$	108.519	+	182.273i	0.180865	+	0.303789i
$601$	29.8675			0.0496964			0.0248482	−	0.999691i	$-0.492090\pi$
$601$	29.8675			0.0496964			0.0248482	+	0.999691i	$0.492090\pi$
$602$	−631.546			−1.04908
$603$	533.775	−	589.771i	0.885199	−	0.978062i
$604$	62.1722			0.102934
$605$	−741.027	−	256.303i	−1.22484	−	0.423641i
$606$	55.5192	−	144.081i	0.0916159	−	0.237757i
$607$			828.617i			1.36510i	0.730838	+	0.682551i	$0.239130\pi$
$607$			828.617i			1.36510i	−0.730838	+	0.682551i	$0.760870\pi$
$608$	−179.436			−0.295125
$609$	561.070	+	216.200i	0.921297	+	0.355008i
$610$	47.8431	+	16.5477i	0.0784313	+	0.0271274i
$611$		−	995.771i		−	1.62974i
$612$	−358.652	−	324.599i	−0.586032	−	0.530391i
$613$		−	255.509i		−	0.416817i	−0.978042	−	0.208409i	$-0.933172\pi$
$613$		−	255.509i		−	0.416817i	0.978042	−	0.208409i	$-0.0668284\pi$
$614$			521.204i			0.848867i
$615$	−623.918	+	739.546i	−1.01450	+	1.20251i
$616$	−362.732			−0.588850
$617$	591.174			0.958142			0.479071	−	0.877776i	$-0.340974\pi$
$617$	591.174			0.958142			0.479071	+	0.877776i	$0.340974\pi$
$618$	−7.17589	+	18.6225i	−0.0116115	+	0.0301335i
$619$	−1201.44			−1.94094			−0.970472	−	0.241215i	$-0.922454\pi$
$619$	−1201.44			−1.94094			−0.970472	+	0.241215i	$0.922454\pi$
$620$	−72.6092	−	25.1137i	−0.117112	−	0.0405060i
$621$	58.3422	+	115.599i	0.0939488	+	0.186150i
$622$		−	631.844i		−	1.01583i
$623$	346.192			0.555685
$624$	−59.4905	+	154.387i	−0.0953374	+	0.247414i
$625$	147.844	+	607.262i	0.236551	+	0.971619i
$626$		−	78.0291i		−	0.124647i
$627$	−570.313	+	1480.05i	−0.909591	+	2.36052i
$628$			94.3670i			0.150266i
$629$		−	1064.81i		−	1.69286i
$630$	429.191	−	235.696i	0.681256	−	0.374120i
$631$	129.923			0.205900			0.102950	−	0.994687i	$-0.467172\pi$
$631$	129.923			0.205900			0.102950	+	0.994687i	$0.467172\pi$
$632$	65.4245			0.103520
$633$	607.300	+	234.014i	0.959400	+	0.369690i
$634$	419.835			0.662200
$635$	362.174	−	1047.12i	0.570352	−	1.64901i
$636$	−115.948	−	44.6787i	−0.182308	−	0.0702496i
$637$			140.626i			0.220763i
$638$	−614.039			−0.962444
$639$	430.068	−	475.185i	0.673033	−	0.743639i
$640$	−53.4611	−	18.4909i	−0.0835329	−	0.0288920i
$641$			395.927i			0.617670i	0.951116	+	0.308835i	$0.0999391\pi$
$641$			395.927i			0.617670i	−0.951116	+	0.308835i	$0.900061\pi$
$642$	569.555	+	219.469i	0.887157	+	0.341852i
$643$			787.933i			1.22540i	0.790315	+	0.612701i	$0.209917\pi$
$643$			787.933i			1.22540i	−0.790315	+	0.612701i	$0.790083\pi$
$644$		−	73.7993i		−	0.114595i
$645$	−561.391	+	665.431i	−0.870373	+	1.03168i
$646$	1205.54			1.86616
$647$	−752.984			−1.16381			−0.581904	−	0.813257i	$-0.697692\pi$
$647$	−752.984			−1.16381			−0.581904	+	0.813257i	$0.697692\pi$
$648$	−22.7799	−	227.967i	−0.0351541	−	0.351801i
$649$	505.510			0.778906
$650$	−301.176	+	383.298i	−0.463348	+	0.589689i
$651$	−63.7653	+	165.480i	−0.0979498	+	0.254194i
$652$		−	480.262i		−	0.736598i
$653$	36.4462			0.0558135			0.0279067	−	0.999611i	$-0.491116\pi$
$653$	36.4462			0.0558135			0.0279067	+	0.999611i	$0.491116\pi$
$654$	401.193	+	154.593i	0.613445	+	0.236381i
$655$	163.848	−	473.719i	0.250149	−	0.723235i
$656$		−	258.020i		−	0.393323i
$657$	−170.550	+	188.442i	−0.259589	+	0.286822i
$658$		−	785.855i		−	1.19431i
$659$			683.468i			1.03713i	0.855038	+	0.518565i	$0.173533\pi$
$659$			683.468i			1.03713i	−0.855038	+	0.518565i	$0.826467\pi$
$660$	−322.438	+	382.194i	−0.488542	+	0.579081i
$661$	−499.832			−0.756176			−0.378088	−	0.925770i	$-0.623418\pi$
$661$	−499.832			−0.756176			−0.378088	+	0.925770i	$0.623418\pi$
$662$	834.302			1.26027
$663$	399.686	−	1037.25i	0.602845	−	1.56447i
$664$	−393.360			−0.592409
$665$	−398.883	+	1153.26i	−0.599824	+	1.73422i
$666$	338.408	−	373.909i	0.508120	−	0.561425i
$667$		−	124.929i		−	0.187300i
$668$	162.440			0.243173
$669$	276.231	−	716.861i	0.412902	−	1.07154i
$670$	−204.286	+	590.636i	−0.304905	+	0.881546i
$671$			119.331i			0.177840i
$672$	−46.9495	+	121.841i	−0.0698653	+	0.181311i
$673$		−	61.0956i		−	0.0907810i	−0.998969	−	0.0453905i	$-0.985547\pi$
$673$		−	61.0956i		−	0.0907810i	0.998969	−	0.0453905i	$-0.0144532\pi$
$674$			82.9852i			0.123123i
$675$	133.172	−	661.733i	0.197293	−	0.980345i
$676$	−42.1994			−0.0624252
$677$	−905.990			−1.33824			−0.669121	−	0.743153i	$-0.733329\pi$
$677$	−905.990			−1.33824			−0.669121	+	0.743153i	$0.733329\pi$
$678$	174.959	+	67.4177i	0.258051	+	0.0994361i
$679$	−457.031			−0.673095
$680$	359.178	+	124.231i	0.528203	+	0.182692i
$681$	−602.712	−	232.246i	−0.885040	−	0.341036i
$682$		−	181.103i		−	0.265547i
$683$	244.248			0.357611			0.178806	−	0.983884i	$-0.442777\pi$
$683$	244.248			0.357611			0.178806	+	0.983884i	$0.442777\pi$
$684$	423.327	+	383.134i	0.618900	+	0.560138i
$685$	−731.569	−	253.032i	−1.06798	−	0.369389i
$686$		−	422.194i		−	0.615443i
$687$	511.447	+	197.078i	0.744465	+	0.286868i
$688$		−	232.162i		−	0.337445i
$689$		−	285.538i		−	0.414424i
$690$	−77.7590	−	65.6014i	−0.112694	−	0.0950744i
$691$	919.272			1.33035			0.665175	−	0.746688i	$-0.268357\pi$
$691$	919.272			1.33035			0.665175	+	0.746688i	$0.268357\pi$
$692$	−62.9366			−0.0909488
$693$	855.760	+	774.509i	1.23486	+	1.11762i
$694$	−286.723			−0.413146
$695$	892.114	+	308.560i	1.28362	+	0.443971i
$696$	−79.4770	+	206.255i	−0.114191	+	0.296343i
$697$			1733.50i			2.48709i
$698$	285.471			0.408984
$699$	−379.292	−	146.154i	−0.542621	−	0.209091i
$700$	−237.686	+	302.496i	−0.339552	+	0.432137i
$701$			310.828i			0.443407i	0.975114	+	0.221703i	$0.0711617\pi$
$701$			310.828i			0.443407i	−0.975114	+	0.221703i	$0.928838\pi$
$702$	469.999	−	237.206i	0.669514	−	0.337900i
$703$			1256.82i			1.78780i
$704$		−	133.343i		−	0.189408i
$705$	−828.020	−	698.559i	−1.17450	−	0.990863i
$706$	−300.511			−0.425653
$707$	280.021			0.396069
$708$	65.4297	−	169.800i	0.0924149	−	0.239830i
$709$	−479.118			−0.675766			−0.337883	−	0.941188i	$-0.609711\pi$
$709$	−479.118			−0.675766			−0.337883	+	0.941188i	$0.609711\pi$
$710$	−164.596	+	475.882i	−0.231825	+	0.670256i
$711$	−154.350	−	139.695i	−0.217089	−	0.196477i
$712$			127.263i			0.178740i
$713$	36.8462			0.0516777
$714$	315.429	−	818.586i	0.441778	−	1.14648i
$715$	−1085.94	−	375.599i	−1.51880	−	0.525314i
$716$			201.194i			0.280998i
$717$	325.123	−	843.742i	0.453449	−	1.17677i
$718$		−	938.935i		−	1.30771i
$719$			1121.51i			1.55982i	0.625895	+	0.779908i	$0.284734\pi$
$719$			1121.51i			1.55982i	−0.625895	+	0.779908i	$0.715266\pi$
$720$	86.6440	+	157.775i	0.120339	+	0.219131i
$721$	−36.1928			−0.0501981
$722$	−912.402			−1.26372
$723$	246.822	+	95.1090i	0.341386	+	0.131548i
$724$	158.957			0.219554
$725$	−402.360	+	512.071i	−0.554979	+	0.706305i
$726$	−620.834	−	239.229i	−0.855143	−	0.329516i
$727$			552.754i			0.760322i	0.924920	+	0.380161i	$0.124131\pi$
$727$			552.754i			0.760322i	−0.924920	+	0.380161i	$0.875869\pi$
$728$	−300.050			−0.412157
$729$	−433.016	+	586.462i	−0.593986	+	0.804475i
$730$	65.2729	−	188.718i	0.0894150	−	0.258518i
$731$			1559.78i			2.13376i
$732$	40.0830	+	15.4454i	0.0547582	+	0.0211002i
$733$		−	73.2361i		−	0.0999128i	−0.998751	−	0.0499564i	$-0.984092\pi$
$733$		−	73.2361i		−	0.0999128i	0.998751	−	0.0499564i	$-0.0159082\pi$
$734$			891.514i			1.21460i
$735$	116.935	+	98.6525i	0.159096	+	0.134221i
$736$	27.1293			0.0368605
$737$	−1473.17			−1.99888
$738$	−550.927	+	608.723i	−0.746514	+	0.824828i
$739$	−503.948			−0.681933			−0.340966	−	0.940075i	$-0.610754\pi$
$739$	−503.948			−0.681933			−0.340966	+	0.940075i	$0.610754\pi$
$740$	−129.516	+	374.458i	−0.175021	+	0.506024i
$741$	−471.762	+	1224.29i	−0.636655	+	1.65221i
$742$		−	225.345i		−	0.303699i
$743$	−310.256			−0.417572			−0.208786	−	0.977961i	$-0.566951\pi$
$743$	−310.256			−0.417572			−0.208786	+	0.977961i	$0.566951\pi$
$744$	−60.8321	−	23.4407i	−0.0817636	−	0.0315063i
$745$	77.2925	−	223.469i	0.103748	−	0.299959i
$746$		−	542.912i		−	0.727764i
$747$	928.018	+	839.907i	1.24233	+	1.12437i
$748$			895.867i			1.19768i
$749$			1106.93i			1.47788i
$750$	107.443	+	519.332i	0.143258	+	0.692443i
$751$	413.103			0.550070			0.275035	−	0.961434i	$-0.411311\pi$
$751$	413.103			0.550070			0.275035	+	0.961434i	$0.411311\pi$
$752$	288.888			0.384159
$753$	−190.610	+	494.660i	−0.253134	+	0.656919i
$754$	−507.932			−0.673649
$755$	146.892	+	50.8064i	0.194559	+	0.0672933i
$756$	370.920	−	187.201i	0.490634	−	0.247620i
$757$			941.341i			1.24351i	0.783210	+	0.621757i	$0.213581\pi$
$757$			941.341i			1.24351i	−0.783210	+	0.621757i	$0.786419\pi$
$758$	−297.806			−0.392884
$759$	86.2269	−	223.771i	0.113606	−	0.294824i
$760$	−423.948	−	146.633i	−0.557826	−	0.192938i
$761$			27.9347i			0.0367079i	0.999832	+	0.0183539i	$0.00584256\pi$
$761$			27.9347i			0.0367079i	−0.999832	+	0.0183539i	$0.994157\pi$
$762$	338.046	−	877.280i	0.443631	−	1.15129i
$763$			779.718i			1.02191i
$764$			362.488i			0.474461i
$765$	−582.117	−	1060.01i	−0.760937	−	1.38563i
$766$	800.783			1.04541
$767$	418.156			0.545184
$768$	−44.7898	−	17.2591i	−0.0583200	−	0.0224727i
$769$	−699.658			−0.909829			−0.454914	−	0.890535i	$-0.650330\pi$
$769$	−699.658			−0.909829			−0.454914	+	0.890535i	$0.650330\pi$
$770$	−857.014	−	296.420i	−1.11301	−	0.384961i
$771$	−719.499	−	277.248i	−0.933203	−	0.359595i
$772$		−	360.343i		−	0.466766i
$773$	1255.17			1.62376			0.811881	−	0.583823i	$-0.198444\pi$
$773$	1255.17			1.62376			0.811881	+	0.583823i	$0.198444\pi$
$774$	−495.715	+	547.719i	−0.640459	+	0.707647i
$775$	−151.029	−	118.671i	−0.194876	−	0.153124i
$776$		−	168.009i		−	0.216506i
$777$	853.409	+	328.848i	1.09834	+	0.423228i
$778$			170.382i			0.219000i
$779$		−	2046.11i		−	2.62658i
$780$	−266.719	+	316.149i	−0.341948	+	0.405320i
$781$	−1186.95			−1.51978
$782$	−182.268			−0.233079
$783$	627.900	−	316.897i	0.801916	−	0.404722i
$784$	−40.7976			−0.0520377
$785$	−77.1157	+	222.958i	−0.0982365	+	0.284023i
$786$	152.933	−	396.882i	0.194571	−	0.504939i
$787$		−	1188.27i		−	1.50987i	−0.655800	−	0.754935i	$-0.727669\pi$
$787$		−	1188.27i		−	1.50987i	0.655800	−	0.754935i	$-0.272331\pi$
$788$	546.330			0.693313
$789$	−179.613	−	69.2112i	−0.227647	−	0.0877202i
$790$	154.576	+	53.4641i	0.195666	+	0.0676761i
$791$			340.032i			0.429877i
$792$	−284.717	+	314.585i	−0.359491	+	0.397203i
$793$			98.7102i			0.124477i
$794$		−	303.371i		−	0.382079i
$795$	−237.435	−	200.312i	−0.298661	−	0.251965i
$796$	−3.97156			−0.00498939
$797$	−383.572			−0.481270			−0.240635	−	0.970616i	$-0.577356\pi$
$797$	−383.572			−0.481270			−0.240635	+	0.970616i	$0.577356\pi$
$798$	−372.311	+	966.201i	−0.466555	+	1.21078i
$799$	−1940.89			−2.42915
$800$	−111.200	−	87.3756i	−0.139000	−	0.109219i
$801$	271.734	−	300.241i	0.339243	−	0.374832i
$802$			891.864i			1.11205i
$803$	470.703			0.586181
$804$	−190.677	+	494.836i	−0.237161	+	0.615467i
$805$	60.3080	−	174.363i	0.0749168	−	0.216600i
$806$		−	149.808i		−	0.185866i
$807$	449.946	−	1167.68i	0.557554	−	1.44694i
$808$			102.938i			0.127399i
$809$			748.595i			0.925334i	0.886532	+	0.462667i	$0.153107\pi$
$809$			748.595i			0.925334i	−0.886532	+	0.462667i	$0.846893\pi$
$810$	132.471	−	557.227i	0.163544	−	0.687934i
$811$	790.431			0.974638			0.487319	−	0.873224i	$-0.337975\pi$
$811$	790.431			0.974638			0.487319	+	0.873224i	$0.337975\pi$
$812$	−400.856			−0.493665
$813$	1051.63	+	405.230i	1.29352	+	0.498438i
$814$	−933.978			−1.14739
$815$	392.464	−	1134.70i	0.481551	−	1.39227i
$816$	300.920	+	115.955i	0.368774	+	0.142101i
$817$		−	1841.05i		−	2.25343i
$818$	656.718			0.802834
$819$	707.882	+	640.671i	0.864325	+	0.782261i
$820$	210.851	−	609.616i	0.257135	−	0.743434i
$821$		−	1076.43i		−	1.31113i	−0.755140	−	0.655563i	$-0.772431\pi$
$821$		−	1076.43i		−	1.31113i	0.755140	−	0.655563i	$-0.227569\pi$
$822$	−612.910	−	236.175i	−0.745632	−	0.287318i
$823$		−	156.761i		−	0.190475i	−0.995455	−	0.0952377i	$-0.969639\pi$
$823$		−	156.761i		−	0.190475i	0.995455	−	0.0952377i	$-0.0303611\pi$
$824$		−	13.3048i		−	0.0161466i
$825$	−1074.14	+	639.505i	−1.30198	+	0.775157i
$826$	330.006			0.399523
$827$	−731.147			−0.884095			−0.442048	−	0.896992i	$-0.645748\pi$
$827$	−731.147			−0.884095			−0.442048	+	0.896992i	$0.645748\pi$
$828$	−64.0037	−	57.9269i	−0.0772992	−	0.0699600i
$829$	−147.303			−0.177688			−0.0888439	−	0.996046i	$-0.528317\pi$
$829$	−147.303			−0.177688			−0.0888439	+	0.996046i	$0.528317\pi$
$830$	−929.379	−	321.449i	−1.11973	−	0.387288i
$831$	390.459	−	1013.30i	0.469866	−	1.21937i
$832$		−	110.301i		−	0.132574i
$833$	274.098			0.329049
$834$	747.414	+	288.005i	0.896180	+	0.345329i
$835$	383.791	+	132.744i	0.459630	+	0.158975i
$836$		−	1057.42i		−	1.26485i
$837$	93.4648	+	185.191i	0.111666	+	0.221256i
$838$			828.821i			0.989046i
$839$			932.751i			1.11174i	0.831269	+	0.555871i	$0.187615\pi$
$839$			932.751i			1.11174i	−0.831269	+	0.555871i	$0.812385\pi$
$840$	−210.493	+	249.503i	−0.250587	+	0.297027i
$841$	162.423			0.193131
$842$	322.908			0.383501
$843$	−57.3884	+	148.931i	−0.0680764	+	0.176668i
$844$	−433.885			−0.514081
$845$	−99.7032	−	34.4849i	−0.117992	−	0.0408105i
$846$	−681.546	−	616.836i	−0.805610	−	0.729121i
$847$		−	1206.59i		−	1.42455i
$848$	82.8388			0.0976873
$849$	−283.401	+	735.467i	−0.333806	+	0.866275i
$850$	747.098	+	587.032i	0.878939	+	0.690626i
$851$		−	190.022i		−	0.223293i
$852$	−153.631	+	398.695i	−0.180318	+	0.467952i
$853$		−	592.947i		−	0.695131i	−0.937656	−	0.347566i	$-0.887008\pi$
$853$		−	592.947i		−	0.695131i	0.937656	−	0.347566i	$-0.112992\pi$
$854$			77.9014i			0.0912194i
$855$	687.089	+	1251.16i	0.803613	+	1.46334i
$856$	−406.918			−0.475371
$857$	−127.840			−0.149171			−0.0745855	−	0.997215i	$-0.523763\pi$
$857$	−127.840			−0.149171			−0.0745855	+	0.997215i	$0.523763\pi$
$858$	−909.801	−	350.578i	−1.06037	−	0.408599i
$859$	−171.883			−0.200097			−0.100049	−	0.994983i	$-0.531900\pi$
$859$	−171.883			−0.200097			−0.100049	+	0.994983i	$0.531900\pi$
$860$	189.720	−	548.522i	0.220605	−	0.637816i
$861$	−1389.35	−	535.364i	−1.61364	−	0.621793i
$862$			795.867i			0.923279i
$863$	60.4223			0.0700143			0.0350071	−	0.999387i	$-0.488855\pi$
$863$	60.4223			0.0700143			0.0350071	+	0.999387i	$0.488855\pi$
$864$	68.8167	+	136.353i	0.0796490	+	0.157816i
$865$	−148.698	−	51.4311i	−0.171906	−	0.0594579i
$866$			568.828i			0.656845i
$867$	−1212.71	−	467.299i	−1.39874	−	0.538984i
$868$		−	118.227i		−	0.136206i
$869$			385.547i			0.443667i
$870$	−356.327	+	422.363i	−0.409571	+	0.485475i
$871$	−1218.60			−1.39909
$872$	−286.632			−0.328706
$873$	−358.735	+	396.368i	−0.410922	+	0.454030i
$874$	215.136			0.246151
$875$	−808.770	+	520.463i	−0.924308	+	0.594815i
$876$	60.9246	−	158.108i	0.0695486	−	0.180489i
$877$		−	295.791i		−	0.337275i	−0.985678	−	0.168638i	$-0.946063\pi$
$877$		−	295.791i		−	0.337275i	0.985678	−	0.168638i	$-0.0539368\pi$
$878$	207.296			0.236100
$879$	698.372	+	269.107i	0.794507	+	0.306151i
$880$	108.967	−	315.046i	0.123826	−	0.358007i
$881$			1056.63i			1.19935i	0.800243	+	0.599676i	$0.204704\pi$
$881$			1056.63i			1.19935i	−0.800243	+	0.599676i	$0.795296\pi$
$882$	96.2500	+	87.1115i	0.109127	+	0.0987658i
$883$		−	1207.51i		−	1.36751i	−0.729712	−	0.683755i	$-0.760346\pi$
$883$		−	1207.51i		−	1.36751i	0.729712	−	0.683755i	$-0.239654\pi$
$884$			741.058i			0.838301i
$885$	293.347	−	347.712i	0.331466	−	0.392895i
$886$	1109.02			1.25171
$887$	1677.87			1.89163			0.945813	−	0.324712i	$-0.105267\pi$
$887$	1677.87			1.89163			0.945813	+	0.324712i	$0.105267\pi$
$888$	−120.888	+	313.721i	−0.136135	+	0.353290i
$889$	1704.99			1.91788
$890$	−103.998	+	300.681i	−0.116852	+	0.337844i
$891$	1343.41	−	134.242i	1.50776	−	0.150664i
$892$			512.160i			0.574171i
$893$	2290.89			2.56538
$894$	72.1435	−	187.223i	0.0806974	−	0.209422i
$895$	−164.414	+	475.356i	−0.183703	+	0.531124i
$896$		−	87.0490i		−	0.0971529i
$897$	71.3266	−	185.103i	0.0795169	−	0.206358i
$898$			819.778i			0.912893i
$899$		−	200.137i		−	0.222622i
$900$	75.7794	+	443.574i	0.0841993	+	0.492859i
$901$	−556.552			−0.617704
$902$	1520.51			1.68571
$903$	−1250.11	−	481.711i	−1.38440	−	0.533457i
$904$	−124.999			−0.138273
$905$	375.563	+	129.898i	0.414986	+	0.143534i
$906$	123.067	+	47.4218i	0.135835	+	0.0523420i
$907$			844.746i			0.931363i	0.884952	+	0.465682i	$0.154191\pi$
$907$			844.746i			0.931363i	−0.884952	+	0.465682i	$0.845809\pi$
$908$	430.607			0.474237
$909$	219.795	−	242.853i	0.241798	−	0.267165i
$910$	−708.920	−	245.198i	−0.779033	−	0.269448i
$911$		−	536.985i		−	0.589446i	−0.955583	−	0.294723i	$-0.904773\pi$
$911$		−	536.985i		−	0.589446i	0.955583	−	0.294723i	$-0.0952273\pi$
$912$	−355.184	−	136.865i	−0.389457	−	0.150071i
$913$		−	2318.07i		−	2.53896i
$914$		−	103.074i		−	0.112772i
$915$	82.0811	+	69.2477i	0.0897061	+	0.0756805i
$916$	−365.403			−0.398911
$917$	771.341			0.841157
$918$	−462.345	−	916.089i	−0.503643	−	0.997918i
$919$	−210.848			−0.229432			−0.114716	−	0.993398i	$-0.536596\pi$
$919$	−210.848			−0.229432			−0.114716	+	0.993398i	$0.536596\pi$
$920$	64.0976	+	22.1698i	0.0696713	+	0.0240976i
$921$	−397.548	+	1031.70i	−0.431649	+	1.12019i
$922$		−	266.855i		−	0.289430i
$923$	−981.843			−1.06375
$924$	−718.008	−	276.673i	−0.777065	−	0.299430i
$925$	−612.005	+	778.880i	−0.661627	+	0.842033i
$926$		−	783.212i		−	0.845801i
$927$	−28.4086	+	31.3889i	−0.0306458	+	0.0338607i
$928$		−	147.358i		−	0.158791i
$929$			522.829i			0.562787i	0.959593	+	0.281393i	$0.0907965\pi$
$929$			522.829i			0.562787i	−0.959593	+	0.281393i	$0.909203\pi$
$930$	−124.571	−	105.094i	−0.133947	−	0.113004i
$931$	−323.526			−0.347504
$932$	270.985			0.290756
$933$	481.939	−	1250.70i	0.516548	−	1.34052i
$934$	601.744			0.644266
$935$	−732.092	+	2116.64i	−0.782986	+	2.26378i
$936$	−235.517	+	260.224i	−0.251620	+	0.278017i
$937$			1249.72i			1.33374i	0.745172	+	0.666872i	$0.232367\pi$
$937$			1249.72i			1.33374i	−0.745172	+	0.666872i	$0.767633\pi$
$938$	−961.714			−1.02528
$939$	59.5167	−	154.454i	0.0633830	−	0.164488i
$940$	682.546	+	236.076i	0.726112	+	0.251144i
$941$		−	541.307i		−	0.575247i	−0.957744	−	0.287623i	$-0.907135\pi$
$941$		−	541.307i		−	0.575247i	0.957744	−	0.287623i	$-0.0928651\pi$
$942$	−71.9784	+	186.795i	−0.0764102	+	0.198296i
$943$			309.355i			0.328054i
$944$			121.313i			0.128510i
$945$	1029.34	−	139.182i	1.08925	−	0.147283i
$946$	1368.13			1.44623
$947$	1102.89			1.16462			0.582310	−	0.812967i	$-0.302149\pi$
$947$	1102.89			1.16462			0.582310	+	0.812967i	$0.302149\pi$
$948$	129.504	+	49.9025i	0.136608	+	0.0526397i
$949$	389.365			0.410289
$950$	−881.822	−	692.891i	−0.928233	−	0.729359i
$951$	831.041	+	320.229i	0.873860	+	0.336729i
$952$			584.838i			0.614325i
$953$	955.559			1.00269			0.501343	−	0.865249i	$-0.332840\pi$
$953$	955.559			1.00269			0.501343	+	0.865249i	$0.332840\pi$
$954$	−195.434	−	176.878i	−0.204858	−	0.185407i
$955$	−296.221	+	856.439i	−0.310179	+	0.896794i
$956$			602.811i			0.630555i
$957$	−1215.46	−	468.358i	−1.27007	−	0.489403i
$958$			235.549i			0.245875i
$959$		−	1191.19i		−	1.24212i
$960$	−91.7195	−	77.3791i	−0.0955412	−	0.0806033i
$961$	−901.972			−0.938577
$962$	−772.584			−0.803102
$963$	960.004	+	868.855i	0.996889	+	0.902238i
$964$	−176.342			−0.182927
$965$	294.468	−	851.372i	0.305149	−	0.882250i
$966$	56.2904	−	146.082i	0.0582717	−	0.151224i
$967$		−	295.569i		−	0.305656i	−0.988253	−	0.152828i	$-0.951162\pi$
$967$		−	295.569i		−	0.305656i	0.988253	−	0.152828i	$-0.0488381\pi$
$968$	443.554			0.458217
$969$	2386.30	+	919.525i	2.46264	+	0.948942i
$970$	137.295	−	396.949i	0.141541	−	0.409226i
$971$		−	667.702i		−	0.687644i	−0.939035	−	0.343822i	$-0.888278\pi$
$971$		−	667.702i		−	0.687644i	0.939035	−	0.343822i	$-0.111722\pi$
$972$	128.790	−	468.625i	0.132500	−	0.482124i
$973$			1452.60i			1.49291i
$974$			470.593i			0.483155i
$975$	−888.523	+	528.996i	−0.911306	+	0.542560i
$976$	−28.6373			−0.0293415
$977$	−1296.04			−1.32655			−0.663277	−	0.748374i	$-0.730835\pi$
$977$	−1296.04			−1.32655			−0.663277	+	0.748374i	$0.730835\pi$
$978$	366.319	−	950.653i	0.374560	−	0.972038i
$979$	−749.963			−0.766050
$980$	−96.3911	−	33.3393i	−0.0983583	−	0.0340197i
$981$	676.224	+	612.019i	0.689321	+	0.623873i
$982$		−	706.990i		−	0.719949i
$983$	−1094.14			−1.11306			−0.556532	−	0.830826i	$-0.687868\pi$
$983$	−1094.14			−1.11306			−0.556532	+	0.830826i	$0.687868\pi$
$984$	196.805	−	510.737i	0.200005	−	0.519042i
$985$	1290.80	+	446.455i	1.31045	+	0.453254i
$986$			990.025i			1.00408i
$987$	599.411	−	1555.56i	0.607306	−	1.57605i
$988$		−	874.693i		−	0.885317i
$989$			278.353i			0.281449i
$990$	−929.766	+	510.593i	−0.939158	+	0.515751i
$991$	−326.015			−0.328976			−0.164488	−	0.986379i	$-0.552597\pi$
$991$	−326.015			−0.328976			−0.164488	+	0.986379i	$0.552597\pi$
$992$	43.4614			0.0438119
$993$	1651.46	+	636.363i	1.66310	+	0.640849i
$994$	−774.863			−0.779540
$995$	−9.38347	−	3.24551i	−0.00943063	−	0.00326182i
$996$	−778.635	−	300.035i	−0.781762	−	0.301240i
$997$			1813.34i			1.81880i	0.415922	+	0.909400i	$0.363459\pi$
$997$			1813.34i			1.81880i	−0.415922	+	0.909400i	$0.636541\pi$
$998$	41.1956			0.0412781
$999$	955.060	−	482.013i	0.956016	−	0.482496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.b.a.599.5	✓	88
3.2	odd	2	inner	690.3.b.a.599.83	yes	88
5.4	even	2	inner	690.3.b.a.599.84	yes	88
15.14	odd	2	inner	690.3.b.a.599.6	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.b.a.599.5	✓	88	1.1	even	1	trivial
690.3.b.a.599.6	yes	88	15.14	odd	2	inner
690.3.b.a.599.83	yes	88	3.2	odd	2	inner
690.3.b.a.599.84	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)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(-2.79936 - 1.07869i) q^{3} +2.00000 q^{4} +(4.72534 + 1.63438i) q^{5} +(3.95890 + 1.52550i) q^{6} +7.69411i q^{7} -2.82843 q^{8} +(6.67285 + 6.03929i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(-2.79936 - 1.07869i) q^{3} +2.00000 q^{4} +(4.72534 + 1.63438i) q^{5} +(3.95890 + 1.52550i) q^{6} +7.69411i q^{7} -2.82843 q^{8} +(6.67285 + 6.03929i) q^{9} +(-6.68264 - 2.31136i) q^{10} -16.6679i q^{11} +(-5.59872 - 2.15738i) q^{12} -13.7877i q^{13} -10.8811i q^{14} +(-11.4649 - 9.67239i) q^{15} +4.00000 q^{16} -26.8740 q^{17} +(-9.43684 - 8.54085i) q^{18} +31.7201 q^{19} +(9.45067 + 3.26875i) q^{20} +(8.29957 - 21.5386i) q^{21} +23.5720i q^{22} -4.79583 q^{23} +(7.91779 + 3.05100i) q^{24} +(19.6576 + 15.4460i) q^{25} +19.4987i q^{26} +(-12.1652 - 24.1041i) q^{27} +15.3882i q^{28} +26.0495i q^{29} +(16.2139 + 13.6788i) q^{30} -7.68297 q^{31} -5.65685 q^{32} +(-17.9795 + 46.6596i) q^{33} +38.0055 q^{34} +(-12.5751 + 36.3573i) q^{35} +(13.3457 + 12.0786i) q^{36} +39.6223i q^{37} -44.8590 q^{38} +(-14.8726 + 38.5967i) q^{39} +(-13.3653 - 4.62272i) q^{40} -64.5050i q^{41} +(-11.7374 + 30.4602i) q^{42} -58.0405i q^{43} -33.3359i q^{44} +(21.6610 + 39.4436i) q^{45} +6.78233 q^{46} +72.2219 q^{47} +(-11.1974 - 4.31476i) q^{48} -10.1994 q^{49} +(-27.8001 - 21.8439i) q^{50} +(75.2299 + 28.9887i) q^{51} -27.5753i q^{52} +20.7097 q^{53} +(17.2042 + 34.0884i) q^{54} +(27.2417 - 78.7616i) q^{55} -21.7622i q^{56} +(-88.7961 - 34.2162i) q^{57} -36.8396i q^{58} +30.3283i q^{59} +(-22.9299 - 19.3448i) q^{60} -7.15931 q^{61} +10.8654 q^{62} +(-46.4670 + 51.3417i) q^{63} +8.00000 q^{64} +(22.5342 - 65.1514i) q^{65} +(25.4269 - 65.9866i) q^{66} -88.3837i q^{67} -53.7479 q^{68} +(13.4253 + 5.17322i) q^{69} +(17.7839 - 51.4170i) q^{70} -71.2117i q^{71} +(-18.8737 - 17.0817i) q^{72} +28.2401i q^{73} -56.0344i q^{74} +(-38.3674 - 64.4433i) q^{75} +63.4402 q^{76} +128.245 q^{77} +(21.0331 - 54.5839i) q^{78} -23.1310 q^{79} +(18.9013 + 6.53751i) q^{80} +(8.05390 + 80.5986i) q^{81} +91.2238i q^{82} +139.074 q^{83} +(16.5991 - 43.0772i) q^{84} +(-126.989 - 43.9222i) q^{85} +82.0817i q^{86} +(28.0994 - 72.9220i) q^{87} +47.1440i q^{88} -44.9943i q^{89} +(-30.6333 - 55.7817i) q^{90} +106.084 q^{91} -9.59166 q^{92} +(21.5074 + 8.28755i) q^{93} -102.137 q^{94} +(149.888 + 51.8426i) q^{95} +(15.8356 + 6.10200i) q^{96} +59.4001i q^{97} +14.4241 q^{98} +(100.663 - 111.223i) 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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