LMFDB - Embedded newform 690.3.g.a.461.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(461,690)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("690.461");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.13
Character	$\chi$	$=$	690.461
Dual form			690.3.g.a.461.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(-1.34299 - 2.68261i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-3.79378 + 1.89928i) q^{6} -8.50482 q^{7} +2.82843i q^{8} +(-5.39274 + 7.20544i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(-1.34299 - 2.68261i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-3.79378 + 1.89928i) q^{6} -8.50482 q^{7} +2.82843i q^{8} +(-5.39274 + 7.20544i) q^{9} -3.16228 q^{10} -13.2166i q^{11} +(2.68599 + 5.36521i) q^{12} +3.60104 q^{13} +12.0276i q^{14} +(-5.99849 + 3.00302i) q^{15} +4.00000 q^{16} +0.776501i q^{17} +(10.1900 + 7.62649i) q^{18} -36.7798 q^{19} +4.47214i q^{20} +(11.4219 + 22.8151i) q^{21} -18.6911 q^{22} +4.79583i q^{23} +(7.58755 - 3.79856i) q^{24} -5.00000 q^{25} -5.09264i q^{26} +(26.5718 + 4.78975i) q^{27} +17.0096 q^{28} +25.4478i q^{29} +(4.24692 + 8.48314i) q^{30} +34.1895 q^{31} -5.65685i q^{32} +(-35.4549 + 17.7498i) q^{33} +1.09814 q^{34} +19.0174i q^{35} +(10.7855 - 14.4109i) q^{36} +33.7342 q^{37} +52.0144i q^{38} +(-4.83617 - 9.66016i) q^{39} +6.32456 q^{40} +41.1741i q^{41} +(32.2654 - 16.1530i) q^{42} +30.1714 q^{43} +26.4332i q^{44} +(16.1118 + 12.0585i) q^{45} +6.78233 q^{46} +6.22979i q^{47} +(-5.37197 - 10.7304i) q^{48} +23.3320 q^{49} +7.07107i q^{50} +(2.08305 - 1.04284i) q^{51} -7.20208 q^{52} -15.6386i q^{53} +(6.77372 - 37.5781i) q^{54} -29.5532 q^{55} -24.0553i q^{56} +(49.3949 + 98.6656i) q^{57} +35.9886 q^{58} -70.7460i q^{59} +(11.9970 - 6.00605i) q^{60} -71.2693 q^{61} -48.3513i q^{62} +(45.8643 - 61.2810i) q^{63} -8.00000 q^{64} -8.05217i q^{65} +(25.1020 + 50.1408i) q^{66} -107.782 q^{67} -1.55300i q^{68} +(12.8653 - 6.44077i) q^{69} +26.8946 q^{70} -110.094i q^{71} +(-20.3801 - 15.2530i) q^{72} +86.0156 q^{73} -47.7074i q^{74} +(6.71496 + 13.4130i) q^{75} +73.5595 q^{76} +112.405i q^{77} +(-13.6615 + 6.83937i) q^{78} +72.6189 q^{79} -8.94427i q^{80} +(-22.8367 - 77.7141i) q^{81} +58.2290 q^{82} +150.313i q^{83} +(-22.8438 - 45.6302i) q^{84} +1.73631 q^{85} -42.6687i q^{86} +(68.2664 - 34.1762i) q^{87} +37.3822 q^{88} +135.965i q^{89} +(17.0533 - 22.7856i) q^{90} -30.6262 q^{91} -9.59166i q^{92} +(-45.9163 - 91.7170i) q^{93} +8.81025 q^{94} +82.2420i q^{95} +(-15.1751 + 7.59711i) q^{96} +187.823 q^{97} -32.9965i q^{98} +(95.2313 + 71.2736i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7}+O(q^{10}) $ 56 * q - 8 * q^3 - 112 * q^4 + 16 * q^6 - 16 * q^7	$ 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7} + 16 q^{12} + 80 q^{13} - 40 q^{15} + 224 q^{16} - 32 q^{18} - 64 q^{19} + 56 q^{21} - 96 q^{22} - 32 q^{24} - 280 q^{25} + 40 q^{27} + 32 q^{28} - 80 q^{31} + 32 q^{33} + 192 q^{34} + 240 q^{37} - 56 q^{39} - 144 q^{43} - 32 q^{48} + 72 q^{49} - 24 q^{51} - 160 q^{52} + 16 q^{54} - 16 q^{57} + 80 q^{60} + 112 q^{61} - 64 q^{63} - 448 q^{64} + 160 q^{66} + 832 q^{67} + 64 q^{72} - 608 q^{73} + 40 q^{75} + 128 q^{76} - 320 q^{78} + 48 q^{79} - 32 q^{81} - 448 q^{82} - 112 q^{84} + 240 q^{85} + 200 q^{87} + 192 q^{88} + 80 q^{91} - 232 q^{93} + 160 q^{94} + 64 q^{96} - 448 q^{97} + 464 q^{99}+O(q^{100}) $ 56 * q - 8 * q^3 - 112 * q^4 + 16 * q^6 - 16 * q^7 + 16 * q^12 + 80 * q^13 - 40 * q^15 + 224 * q^16 - 32 * q^18 - 64 * q^19 + 56 * q^21 - 96 * q^22 - 32 * q^24 - 280 * q^25 + 40 * q^27 + 32 * q^28 - 80 * q^31 + 32 * q^33 + 192 * q^34 + 240 * q^37 - 56 * q^39 - 144 * q^43 - 32 * q^48 + 72 * q^49 - 24 * q^51 - 160 * q^52 + 16 * q^54 - 16 * q^57 + 80 * q^60 + 112 * q^61 - 64 * q^63 - 448 * q^64 + 160 * q^66 + 832 * q^67 + 64 * q^72 - 608 * q^73 + 40 * q^75 + 128 * q^76 - 320 * q^78 + 48 * q^79 - 32 * q^81 - 448 * q^82 - 112 * q^84 + 240 * q^85 + 200 * q^87 + 192 * q^88 + 80 * q^91 - 232 * q^93 + 160 * q^94 + 64 * q^96 - 448 * q^97 + 464 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	−1.34299	−	2.68261i	−0.447664	−	0.894202i
$3$	−1.34299	−	2.68261i	−0.447664	−	0.894202i
$4$	−2.00000			−0.500000
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	−3.79378	+	1.89928i	−0.632296	+	0.316546i
$7$	−8.50482			−1.21497			−0.607487	−	0.794329i	$-0.707822\pi$
$7$	−8.50482			−1.21497			−0.607487	+	0.794329i	$0.707822\pi$
$8$			2.82843i			0.353553i
$9$	−5.39274	+	7.20544i	−0.599194	+	0.800604i
$10$	−3.16228			−0.316228
$11$		−	13.2166i		−	1.20151i	−0.799434	−	0.600754i	$-0.794867\pi$
$11$		−	13.2166i		−	1.20151i	0.799434	−	0.600754i	$-0.205133\pi$
$12$	2.68599	+	5.36521i	0.223832	+	0.447101i
$13$	3.60104			0.277003			0.138501	−	0.990362i	$-0.455771\pi$
$13$	3.60104			0.277003			0.138501	+	0.990362i	$0.455771\pi$
$14$			12.0276i			0.859117i
$15$	−5.99849	+	3.00302i	−0.399899	+	0.200202i
$16$	4.00000			0.250000
$17$			0.776501i			0.0456765i	0.999739	+	0.0228383i	$0.00727028\pi$
$17$			0.776501i			0.0456765i	−0.999739	+	0.0228383i	$0.992730\pi$
$18$	10.1900	+	7.62649i	0.566113	+	0.423694i
$19$	−36.7798			−1.93578			−0.967888	−	0.251380i	$-0.919116\pi$
$19$	−36.7798			−1.93578			−0.967888	+	0.251380i	$0.919116\pi$
$20$			4.47214i			0.223607i
$21$	11.4219	+	22.8151i	0.543901	+	1.08643i
$22$	−18.6911			−0.849594
$23$			4.79583i			0.208514i
$23$			4.79583i			0.208514i
$24$	7.58755	−	3.79856i	0.316148	−	0.158273i
$25$	−5.00000			−0.200000
$26$		−	5.09264i		−	0.195871i
$27$	26.5718	+	4.78975i	0.984139	+	0.177398i
$28$	17.0096			0.607487
$29$			25.4478i			0.877511i	0.898607	+	0.438755i	$0.144581\pi$
$29$			25.4478i			0.877511i	−0.898607	+	0.438755i	$0.855419\pi$
$30$	4.24692	+	8.48314i	0.141564	+	0.282771i
$31$	34.1895			1.10289			0.551444	−	0.834212i	$-0.314077\pi$
$31$	34.1895			1.10289			0.551444	+	0.834212i	$0.314077\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−35.4549	+	17.7498i	−1.07439	+	0.537872i
$34$	1.09814			0.0322982
$35$			19.0174i			0.543353i
$36$	10.7855	−	14.4109i	0.299597	−	0.400302i
$37$	33.7342			0.911736			0.455868	−	0.890047i	$-0.349329\pi$
$37$	33.7342			0.911736			0.455868	+	0.890047i	$0.349329\pi$
$38$			52.0144i			1.36880i
$39$	−4.83617	−	9.66016i	−0.124004	−	0.247697i
$40$	6.32456			0.158114
$41$			41.1741i			1.00425i	0.864796	+	0.502124i	$0.167448\pi$
$41$			41.1741i			1.00425i	−0.864796	+	0.502124i	$0.832552\pi$
$42$	32.2654	−	16.1530i	0.768224	−	0.384596i
$43$	30.1714			0.701659			0.350830	−	0.936439i	$-0.385900\pi$
$43$	30.1714			0.701659			0.350830	+	0.936439i	$0.385900\pi$
$44$			26.4332i			0.600754i
$45$	16.1118	+	12.0585i	0.358041	+	0.267967i
$46$	6.78233			0.147442
$47$			6.22979i			0.132549i	0.997801	+	0.0662743i	$0.0211112\pi$
$47$			6.22979i			0.132549i	−0.997801	+	0.0662743i	$0.978889\pi$
$48$	−5.37197	−	10.7304i	−0.111916	−	0.223550i
$49$	23.3320			0.476164
$50$			7.07107i			0.141421i
$51$	2.08305	−	1.04284i	0.0408440	−	0.0204478i
$52$	−7.20208			−0.138501
$53$		−	15.6386i		−	0.295068i	−0.989057	−	0.147534i	$-0.952866\pi$
$53$		−	15.6386i		−	0.295068i	0.989057	−	0.147534i	$-0.0471336\pi$
$54$	6.77372	−	37.5781i	0.125439	−	0.695891i
$55$	−29.5532			−0.537331
$56$		−	24.0553i		−	0.429558i
$57$	49.3949	+	98.6656i	0.866578	+	1.73097i
$58$	35.9886			0.620494
$59$		−	70.7460i		−	1.19908i	−0.800343	−	0.599542i	$-0.795349\pi$
$59$		−	70.7460i		−	1.19908i	0.800343	−	0.599542i	$-0.204651\pi$
$60$	11.9970	−	6.00605i	0.199950	−	0.100101i
$61$	−71.2693			−1.16835			−0.584174	−	0.811628i	$-0.698582\pi$
$61$	−71.2693			−1.16835			−0.584174	+	0.811628i	$0.698582\pi$
$62$		−	48.3513i		−	0.779860i
$63$	45.8643	−	61.2810i	0.728005	−	0.972714i
$64$	−8.00000			−0.125000
$65$		−	8.05217i		−	0.123879i
$66$	25.1020	+	50.1408i	0.380333	+	0.759709i
$67$	−107.782			−1.60869			−0.804346	−	0.594162i	$-0.797484\pi$
$67$	−107.782			−1.60869			−0.804346	+	0.594162i	$0.797484\pi$
$68$		−	1.55300i		−	0.0228383i
$69$	12.8653	−	6.44077i	0.186454	−	0.0933444i
$70$	26.8946			0.384209
$71$		−	110.094i		−	1.55062i	−0.631581	−	0.775310i	$-0.717594\pi$
$71$		−	110.094i		−	1.55062i	0.631581	−	0.775310i	$-0.282406\pi$
$72$	−20.3801	−	15.2530i	−0.283056	−	0.211847i
$73$	86.0156			1.17830			0.589148	−	0.808025i	$-0.299464\pi$
$73$	86.0156			1.17830			0.589148	+	0.808025i	$0.299464\pi$
$74$		−	47.7074i		−	0.644695i
$75$	6.71496	+	13.4130i	0.0895328	+	0.178840i
$76$	73.5595			0.967888
$77$			112.405i			1.45980i
$78$	−13.6615	+	6.83937i	−0.175148	+	0.0876843i
$79$	72.6189			0.919227			0.459614	−	0.888119i	$-0.347988\pi$
$79$	72.6189			0.919227			0.459614	+	0.888119i	$0.347988\pi$
$80$		−	8.94427i		−	0.111803i
$81$	−22.8367	−	77.7141i	−0.281934	−	0.959434i
$82$	58.2290			0.710110
$83$			150.313i			1.81100i	0.424350	+	0.905498i	$0.360503\pi$
$83$			150.313i			1.81100i	−0.424350	+	0.905498i	$0.639497\pi$
$84$	−22.8438	−	45.6302i	−0.271950	−	0.543216i
$85$	1.73631			0.0204272
$86$		−	42.6687i		−	0.496148i
$87$	68.2664	−	34.1762i	0.784672	−	0.392830i
$88$	37.3822			0.424797
$89$			135.965i			1.52770i	0.645396	+	0.763849i	$0.276693\pi$
$89$			135.965i			1.52770i	−0.645396	+	0.763849i	$0.723307\pi$
$90$	17.0533	−	22.7856i	0.189482	−	0.253173i
$91$	−30.6262			−0.336552
$92$		−	9.59166i		−	0.104257i
$93$	−45.9163	−	91.7170i	−0.493723	−	0.986204i
$94$	8.81025			0.0937260
$95$			82.2420i			0.865706i
$96$	−15.1751	+	7.59711i	−0.158074	+	0.0791366i
$97$	187.823			1.93632			0.968160	−	0.250331i	$-0.0805396\pi$
$97$	187.823			1.93632			0.968160	+	0.250331i	$0.0805396\pi$
$98$		−	32.9965i		−	0.336699i
$99$	95.2313	+	71.2736i	0.961932	+	0.719936i
$100$	10.0000			0.100000
$101$		−	44.1749i		−	0.437375i	−0.975795	−	0.218687i	$-0.929822\pi$
$101$		−	44.1749i		−	0.437375i	0.975795	−	0.218687i	$-0.0701775\pi$
$102$	−1.47479	−	2.94587i	−0.0144587	−	0.0288811i
$103$	−50.1604			−0.486994			−0.243497	−	0.969902i	$-0.578295\pi$
$103$	−50.1604			−0.486994			−0.243497	+	0.969902i	$0.578295\pi$
$104$			10.1853i			0.0979353i
$105$	51.0161	−	25.5402i	0.485867	−	0.243240i
$106$	−22.1163			−0.208645
$107$			156.326i			1.46099i	0.682917	+	0.730496i	$0.260711\pi$
$107$			156.326i			1.46099i	−0.682917	+	0.730496i	$0.739289\pi$
$108$	−53.1435	−	9.57949i	−0.492070	−	0.0886990i
$109$	−199.822			−1.83322			−0.916612	−	0.399777i	$-0.869088\pi$
$109$	−199.822			−1.83322			−0.916612	+	0.399777i	$0.869088\pi$
$110$			41.7945i			0.379950i
$111$	−45.3048	−	90.4957i	−0.408152	−	0.815276i
$112$	−34.0193			−0.303744
$113$			9.47173i			0.0838207i	0.999121	+	0.0419103i	$0.0133444\pi$
$113$			9.47173i			0.0838207i	−0.999121	+	0.0419103i	$0.986656\pi$
$114$	139.534	−	69.8550i	1.22398	−	0.612763i
$115$	10.7238			0.0932505
$116$		−	50.8956i		−	0.438755i
$117$	−19.4195	+	25.9471i	−0.165978	+	0.221770i
$118$	−100.050			−0.847880
$119$		−	6.60401i		−	0.0554959i
$120$	−8.49383	−	16.9663i	−0.0707819	−	0.141386i
$121$	−53.6782			−0.443621
$122$			100.790i			0.826147i
$123$	110.454	−	55.2966i	0.897999	−	0.449565i
$124$	−68.3791			−0.551444
$125$			11.1803i			0.0894427i
$126$	−86.6644	−	64.8619i	−0.687813	−	0.514777i
$127$	87.0946			0.685784			0.342892	−	0.939375i	$-0.388594\pi$
$127$	87.0946			0.685784			0.342892	+	0.939375i	$0.388594\pi$
$128$			11.3137i			0.0883883i
$129$	−40.5199	−	80.9378i	−0.314108	−	0.627425i
$130$	−11.3875			−0.0875960
$131$			55.2935i			0.422088i	0.977477	+	0.211044i	$0.0676863\pi$
$131$			55.2935i			0.422088i	−0.977477	+	0.211044i	$0.932314\pi$
$132$	70.9098	−	35.4996i	0.537195	−	0.268936i
$133$	312.805			2.35192
$134$			152.427i			1.13752i
$135$	10.7102	−	59.4163i	0.0793348	−	0.440120i
$136$	−2.19628			−0.0161491
$137$			128.257i			0.936181i	0.883681	+	0.468090i	$0.155058\pi$
$137$			128.257i			0.936181i	−0.883681	+	0.468090i	$0.844942\pi$
$138$	−9.10862	−	18.1943i	−0.0660045	−	0.131843i
$139$	−142.423			−1.02463			−0.512313	−	0.858799i	$-0.671211\pi$
$139$	−142.423			−1.02463			−0.512313	+	0.858799i	$0.671211\pi$
$140$		−	38.0347i		−	0.271677i
$141$	16.7121	−	8.36656i	0.118525	−	0.0593373i
$142$	−155.696			−1.09645
$143$		−	47.5934i		−	0.332821i
$144$	−21.5710	+	28.8218i	−0.149798	+	0.200151i
$145$	56.9030			0.392435
$146$		−	121.644i		−	0.833181i
$147$	−31.3347	−	62.5906i	−0.213161	−	0.425786i
$148$	−67.4685			−0.455868
$149$			143.307i			0.961793i	0.876777	+	0.480897i	$0.159689\pi$
$149$			143.307i			0.961793i	−0.876777	+	0.480897i	$0.840311\pi$
$150$	18.9689	−	9.49639i	0.126459	−	0.0633093i
$151$	−146.838			−0.972439			−0.486219	−	0.873837i	$-0.661624\pi$
$151$	−146.838			−0.972439			−0.486219	+	0.873837i	$0.661624\pi$
$152$		−	104.029i		−	0.684400i
$153$	−5.59503	−	4.18747i	−0.0365688	−	0.0273691i
$154$	158.964			1.03224
$155$		−	76.4501i		−	0.493226i
$156$	9.67234	+	19.3203i	0.0620022	+	0.123848i
$157$	−200.244			−1.27544			−0.637720	−	0.770269i	$-0.720122\pi$
$157$	−200.244			−1.27544			−0.637720	+	0.770269i	$0.720122\pi$
$158$		−	102.699i		−	0.649992i
$159$	−41.9522	+	21.0025i	−0.263850	+	0.132091i
$160$	−12.6491			−0.0790569
$161$		−	40.7877i		−	0.253340i
$162$	−109.904	+	32.2959i	−0.678422	+	0.199358i
$163$	−185.503			−1.13805			−0.569027	−	0.822319i	$-0.692680\pi$
$163$	−185.503			−1.13805			−0.569027	+	0.822319i	$0.692680\pi$
$164$		−	82.3483i		−	0.502124i
$165$	39.6897	+	79.2795i	0.240544	+	0.480482i
$166$	212.574			1.28057
$167$			158.560i			0.949462i	0.880131	+	0.474731i	$0.157455\pi$
$167$			158.560i			0.949462i	−0.880131	+	0.474731i	$0.842545\pi$
$168$	−64.5308	+	32.3061i	−0.384112	+	0.192298i
$169$	−156.033			−0.923269
$170$		−	2.45551i		−	0.0144442i
$171$	198.344	−	265.014i	1.15990	−	1.54979i
$172$	−60.3427			−0.350830
$173$		−	55.2641i		−	0.319446i	−0.987162	−	0.159723i	$-0.948940\pi$
$173$		−	55.2641i		−	0.319446i	0.987162	−	0.159723i	$-0.0510601\pi$
$174$	−48.3325	−	96.5433i	−0.277773	−	0.554847i
$175$	42.5241			0.242995
$176$		−	52.8663i		−	0.300377i
$177$	−189.783	+	95.0113i	−1.07222	+	0.536787i
$178$	192.284			1.08024
$179$		−	103.383i		−	0.577558i	−0.957396	−	0.288779i	$-0.906751\pi$
$179$		−	103.383i		−	0.577558i	0.957396	−	0.288779i	$-0.0932493\pi$
$180$	−32.2237	−	24.1171i	−0.179021	−	0.133984i
$181$	−161.443			−0.891949			−0.445974	−	0.895046i	$-0.647143\pi$
$181$	−161.443			−0.891949			−0.445974	+	0.895046i	$0.647143\pi$
$182$			43.3120i			0.237978i
$183$	95.7141	+	191.187i	0.523028	+	1.04474i
$184$	−13.5647			−0.0737210
$185$		−	75.4321i		−	0.407741i
$186$	−129.707	+	64.9354i	−0.697352	+	0.349115i
$187$	10.2627			0.0548807
$188$		−	12.4596i		−	0.0662743i
$189$	−225.988	−	40.7359i	−1.19570	−	0.215534i
$190$	116.308			0.612146
$191$			57.0826i			0.298862i	0.988772	+	0.149431i	$0.0477442\pi$
$191$			57.0826i			0.298862i	−0.988772	+	0.149431i	$0.952256\pi$
$192$	10.7439	+	21.4608i	0.0559580	+	0.111775i
$193$	−106.150			−0.549998			−0.274999	−	0.961445i	$-0.588678\pi$
$193$	−106.150			−0.549998			−0.274999	+	0.961445i	$0.588678\pi$
$194$		−	265.622i		−	1.36919i
$195$	−21.6008	+	10.8140i	−0.110773	+	0.0554564i
$196$	−46.6640			−0.238082
$197$			188.120i			0.954925i	0.878652	+	0.477463i	$0.158443\pi$
$197$			188.120i			0.954925i	−0.878652	+	0.477463i	$0.841557\pi$
$198$	100.796	−	134.677i	0.509071	−	0.680189i
$199$	−258.348			−1.29823			−0.649115	−	0.760691i	$-0.724860\pi$
$199$	−258.348			−1.29823			−0.649115	+	0.760691i	$0.724860\pi$
$200$		−	14.1421i		−	0.0707107i
$201$	144.751	+	289.137i	0.720154	+	1.43849i
$202$	−62.4727			−0.309271
$203$		−	216.429i		−	1.06615i
$204$	−4.16609	+	2.08567i	−0.0204220	+	0.0102239i
$205$	92.0682			0.449113
$206$			70.9376i			0.344357i
$207$	−34.5561	−	25.8627i	−0.166938	−	0.124940i
$208$	14.4042			0.0692507
$209$			486.103i			2.32585i
$210$	−36.1193	−	72.1476i	−0.171997	−	0.343560i
$211$	−8.22042			−0.0389593			−0.0194797	−	0.999810i	$-0.506201\pi$
$211$	−8.22042			−0.0389593			−0.0194797	+	0.999810i	$0.506201\pi$
$212$			31.2772i			0.147534i
$213$	−295.339	+	147.855i	−1.38657	+	0.694157i
$214$	221.078			1.03308
$215$		−	67.4652i		−	0.313792i
$216$	−13.5474	+	75.1563i	−0.0627197	+	0.347946i
$217$	−290.776			−1.33998
$218$			282.590i			1.29629i
$219$	−115.518	−	230.746i	−0.527481	−	1.05363i
$220$	59.1064			0.268665
$221$			2.79621i			0.0126525i
$222$	−127.980	+	64.0707i	−0.576487	+	0.288607i
$223$	134.067			0.601198			0.300599	−	0.953751i	$-0.402813\pi$
$223$	134.067			0.601198			0.300599	+	0.953751i	$0.402813\pi$
$224$			48.1105i			0.214779i
$225$	26.9637	−	36.0272i	0.119839	−	0.160121i
$226$	13.3951			0.0592702
$227$			252.146i			1.11078i	0.831591	+	0.555388i	$0.187430\pi$
$227$			252.146i			1.11078i	−0.831591	+	0.555388i	$0.812570\pi$
$228$	−98.7899	−	197.331i	−0.433289	−	0.865487i
$229$	−405.638			−1.77134			−0.885672	−	0.464312i	$-0.846302\pi$
$229$	−405.638			−1.77134			−0.885672	+	0.464312i	$0.846302\pi$
$230$		−	15.1658i		−	0.0659380i
$231$	301.538	−	150.959i	1.30536	−	0.653501i
$232$	−71.9773			−0.310247
$233$			176.120i			0.755879i	0.925830	+	0.377940i	$0.123367\pi$
$233$			176.120i			0.755879i	−0.925830	+	0.377940i	$0.876633\pi$
$234$	36.6947	+	27.4633i	0.156815	+	0.117364i
$235$	13.9302			0.0592776
$236$			141.492i			0.599542i
$237$	−97.5267	−	194.808i	−0.411505	−	0.821974i
$238$	−9.33948			−0.0392415
$239$		−	52.4894i		−	0.219621i	−0.993953	−	0.109810i	$-0.964976\pi$
$239$		−	52.4894i		−	0.219621i	0.993953	−	0.109810i	$-0.0350244\pi$
$240$	−23.9940	+	12.0121i	−0.0999748	+	0.0500504i
$241$	240.203			0.996692			0.498346	−	0.866978i	$-0.333941\pi$
$241$	240.203			0.996692			0.498346	+	0.866978i	$0.333941\pi$
$242$			75.9124i			0.313688i
$243$	−177.807	+	165.631i	−0.731715	+	0.681610i
$244$	142.539			0.584174
$245$		−	52.1720i		−	0.212947i
$246$	−78.2011	−	156.205i	−0.317891	−	0.634982i
$247$	−132.445			−0.536216
$248$			96.7026i			0.389930i
$249$	403.230	−	201.869i	1.61940	−	0.810718i
$250$	15.8114			0.0632456
$251$		−	207.455i		−	0.826514i	−0.910614	−	0.413257i	$-0.864391\pi$
$251$		−	207.455i		−	0.826514i	0.910614	−	0.413257i	$-0.135609\pi$
$252$	−91.7286	+	122.562i	−0.364002	+	0.486357i
$253$	63.3845			0.250532
$254$		−	123.170i		−	0.484922i
$255$	−2.33185	−	4.65783i	−0.00914451	−	0.0182660i
$256$	16.0000			0.0625000
$257$		−	97.7262i		−	0.380257i	−0.981759	−	0.190129i	$-0.939109\pi$
$257$		−	97.7262i		−	0.380257i	0.981759	−	0.190129i	$-0.0608905\pi$
$258$	−114.463	+	57.3038i	−0.443657	+	0.222108i
$259$	−286.904			−1.10774
$260$			16.1043i			0.0619397i
$261$	−183.363	−	137.233i	−0.702539	−	0.525799i
$262$	78.1968			0.298461
$263$		−	93.5480i		−	0.355696i	−0.984058	−	0.177848i	$-0.943086\pi$
$263$		−	93.5480i		−	0.355696i	0.984058	−	0.177848i	$-0.0569135\pi$
$264$	−50.2040	−	100.282i	−0.190167	−	0.379854i
$265$	−34.9690			−0.131958
$266$		−	442.374i		−	1.66306i
$267$	364.741	−	182.600i	1.36607	−	0.683895i
$268$	215.565			0.804346
$269$			213.987i			0.795492i	0.917496	+	0.397746i	$0.130207\pi$
$269$			213.987i			0.795492i	−0.917496	+	0.397746i	$0.869793\pi$
$270$	−84.0273	−	15.1465i	−0.311212	−	0.0560982i
$271$	287.786			1.06194			0.530970	−	0.847391i	$-0.321828\pi$
$271$	287.786			1.06194			0.530970	+	0.847391i	$0.321828\pi$
$272$			3.10601i			0.0114191i
$273$	41.1308	+	82.1580i	0.150662	+	0.300945i
$274$	181.382			0.661980
$275$			66.0829i			0.240302i
$276$	−25.7306	+	12.8815i	−0.0932270	+	0.0466722i
$277$	122.451			0.442060			0.221030	−	0.975267i	$-0.429058\pi$
$277$	122.451			0.442060			0.221030	+	0.975267i	$0.429058\pi$
$278$			201.417i			0.724520i
$279$	−184.375	+	246.351i	−0.660843	+	0.882977i
$280$	−53.7892			−0.192104
$281$		−	180.885i		−	0.643718i	−0.946788	−	0.321859i	$-0.895692\pi$
$281$		−	180.885i		−	0.643718i	0.946788	−	0.321859i	$-0.104308\pi$
$282$	−11.8321	−	23.6344i	−0.0419578	−	0.0838100i
$283$	156.462			0.552869			0.276435	−	0.961033i	$-0.410847\pi$
$283$	156.462			0.552869			0.276435	+	0.961033i	$0.410847\pi$
$284$			220.188i			0.775310i
$285$	220.623	−	110.450i	0.774116	−	0.387545i
$286$	−67.3073			−0.235340
$287$		−	350.179i		−	1.22013i
$288$	40.7601	+	30.5060i	0.141528	+	0.105923i
$289$	288.397			0.997914
$290$		−	80.4730i		−	0.277493i
$291$	−252.245	−	503.855i	−0.866821	−	1.73146i
$292$	−172.031			−0.589148
$293$		−	2.88676i		−	0.00985241i	−0.999988	−	0.00492620i	$-0.998432\pi$
$293$		−	2.88676i		−	0.00985241i	0.999988	−	0.00492620i	$-0.00156807\pi$
$294$	−88.5165	+	44.3140i	−0.301076	+	0.150728i
$295$	−158.193			−0.536247
$296$			95.4149i			0.322347i
$297$	63.3041	−	351.188i	0.213145	−	1.18245i
$298$	202.667			0.680090
$299$			17.2700i			0.0577591i
$300$	−13.4299	−	26.8261i	−0.0447664	−	0.0894202i
$301$	−256.602			−0.852498
$302$			207.661i			0.687618i
$303$	−118.504	+	59.3265i	−0.391101	+	0.195797i
$304$	−147.119			−0.483944
$305$			159.363i			0.522501i
$306$	−5.92198	+	7.91257i	−0.0193529	+	0.0258581i
$307$	−271.452			−0.884207			−0.442104	−	0.896964i	$-0.645768\pi$
$307$	−271.452			−0.884207			−0.442104	+	0.896964i	$0.645768\pi$
$308$		−	224.809i		−	0.729901i
$309$	67.3651	+	134.561i	0.218010	+	0.435471i
$310$	−108.117			−0.348764
$311$		−	198.082i		−	0.636918i	−0.947937	−	0.318459i	$-0.896835\pi$
$311$		−	198.082i		−	0.636918i	0.947937	−	0.318459i	$-0.103165\pi$
$312$	27.3231	−	13.6787i	0.0875740	−	0.0438421i
$313$	−67.5994			−0.215973			−0.107986	−	0.994152i	$-0.534440\pi$
$313$	−67.5994			−0.215973			−0.107986	+	0.994152i	$0.534440\pi$
$314$			283.188i			0.901872i
$315$	−137.028	−	102.556i	−0.435011	−	0.325574i
$316$	−145.238			−0.459614
$317$			397.841i			1.25502i	0.778609	+	0.627509i	$0.215926\pi$
$317$			397.841i			1.25502i	−0.778609	+	0.627509i	$0.784074\pi$
$318$	29.7021	+	59.3294i	0.0934028	+	0.186570i
$319$	336.333			1.05434
$320$			17.8885i			0.0559017i
$321$	419.361	−	209.945i	1.30642	−	0.654034i
$322$	−57.6825			−0.179138
$323$		−	28.5595i		−	0.0884196i
$324$	45.6734	+	155.428i	0.140967	+	0.479717i
$325$	−18.0052			−0.0554006
$326$			262.341i			0.804726i
$327$	268.359	+	536.042i	0.820669	+	1.63927i
$328$	−116.458			−0.355055
$329$		−	52.9832i		−	0.161043i
$330$	112.118	−	56.1297i	0.339752	−	0.170090i
$331$	−426.686			−1.28908			−0.644540	−	0.764570i	$-0.722951\pi$
$331$	−426.686			−1.28908			−0.644540	+	0.764570i	$0.722951\pi$
$332$		−	300.625i		−	0.905498i
$333$	−181.920	+	243.070i	−0.546307	+	0.729940i
$334$	224.238			0.671371
$335$			241.009i			0.719429i
$336$	45.6877	+	91.2603i	0.135975	+	0.271608i
$337$	−480.323			−1.42529			−0.712646	−	0.701524i	$-0.752503\pi$
$337$	−480.323			−1.42529			−0.712646	+	0.701524i	$0.752503\pi$
$338$			220.663i			0.652850i
$339$	25.4089	−	12.7205i	0.0749526	−	0.0375235i
$340$	−3.47262			−0.0102136
$341$		−	451.869i		−	1.32513i
$342$	−374.787	−	280.500i	−1.09587	−	0.820177i
$343$	218.302			0.636448
$344$			85.3375i			0.248074i
$345$	−14.4020	−	28.7677i	−0.0417449	−	0.0833847i
$346$	−78.1553			−0.225882
$347$		−	397.363i		−	1.14514i	−0.819857	−	0.572569i	$-0.805947\pi$
$347$		−	397.363i		−	1.14514i	0.819857	−	0.572569i	$-0.194053\pi$
$348$	−136.533	+	68.3524i	−0.392336	+	0.196415i
$349$	504.033			1.44422			0.722110	−	0.691778i	$-0.243172\pi$
$349$	504.033			1.44422			0.722110	+	0.691778i	$0.243172\pi$
$350$		−	60.1382i		−	0.171823i
$351$	95.6859	+	17.2481i	0.272609	+	0.0491398i
$352$	−74.7643			−0.212399
$353$		−	567.131i		−	1.60660i	−0.595572	−	0.803302i	$-0.703075\pi$
$353$		−	567.131i		−	1.60660i	0.595572	−	0.803302i	$-0.296925\pi$
$354$	134.366	+	268.394i	0.379566	+	0.758176i
$355$	−246.178			−0.693458
$356$		−	271.930i		−	0.763849i
$357$	−17.7159	+	8.86913i	−0.0496245	+	0.0248435i
$358$	−146.206			−0.408395
$359$			296.132i			0.824881i	0.910984	+	0.412441i	$0.135324\pi$
$359$			296.132i			0.824881i	−0.910984	+	0.412441i	$0.864676\pi$
$360$	−34.1067	+	45.5712i	−0.0947408	+	0.126587i
$361$	991.751			2.74723
$362$			228.315i			0.630703i
$363$	72.0894	+	143.997i	0.198593	+	0.396687i
$364$	61.2524			0.168276
$365$		−	192.337i		−	0.526950i
$366$	270.380	−	135.360i	0.738742	−	0.369837i
$367$	−28.7924			−0.0784535			−0.0392268	−	0.999230i	$-0.512489\pi$
$367$	−28.7924			−0.0784535			−0.0392268	+	0.999230i	$0.512489\pi$
$368$			19.1833i			0.0521286i
$369$	−296.678	−	222.041i	−0.804004	−	0.601738i
$370$	−106.677			−0.288316
$371$			133.004i			0.358500i
$372$	91.8326	+	183.434i	0.246862	+	0.493102i
$373$	−215.231			−0.577026			−0.288513	−	0.957476i	$-0.593161\pi$
$373$	−215.231			−0.577026			−0.288513	+	0.957476i	$0.593161\pi$
$374$		−	14.5136i		−	0.0388065i
$375$	29.9924	−	15.0151i	0.0799798	−	0.0400403i
$376$	−17.6205			−0.0468630
$377$			91.6385i			0.243073i
$378$	−57.6093	+	319.595i	−0.152406	+	0.845491i
$379$	−557.330			−1.47053			−0.735264	−	0.677781i	$-0.762942\pi$
$379$	−557.330			−1.47053			−0.735264	+	0.677781i	$0.762942\pi$
$380$		−	164.484i		−	0.432853i
$381$	−116.967	−	233.640i	−0.307001	−	0.613229i
$382$	80.7270			0.211327
$383$		−	27.7534i		−	0.0724631i	−0.999343	−	0.0362316i	$-0.988465\pi$
$383$		−	27.7534i		−	0.0724631i	0.999343	−	0.0362316i	$-0.0115354\pi$
$384$	30.3502	−	15.1942i	0.0790370	−	0.0395683i
$385$	251.345			0.652843
$386$			150.118i			0.388907i
$387$	−162.706	+	217.398i	−0.420430	+	0.561751i
$388$	−375.646			−0.968160
$389$			352.556i			0.906312i	0.891431	+	0.453156i	$0.149702\pi$
$389$			352.556i			0.906312i	−0.891431	+	0.453156i	$0.850298\pi$
$390$	15.2933	+	30.5481i	0.0392136	+	0.0783285i
$391$	−3.72397			−0.00952422
$392$			65.9929i			0.168349i
$393$	148.331	−	74.2587i	0.377431	−	0.188953i
$394$	266.042			0.675234
$395$		−	162.381i		−	0.411091i
$396$	−190.463	−	142.547i	−0.480966	−	0.359968i
$397$	0.224835			0.000566334			0.000283167	−	1.00000i	$-0.499910\pi$
$397$	0.224835			0.000566334			0.000283167		1.00000i	$0.499910\pi$
$398$			365.359i			0.917987i
$399$	−420.095	−	839.133i	−1.05287	−	2.10309i
$400$	−20.0000			−0.0500000
$401$		−	442.929i		−	1.10456i	−0.833658	−	0.552280i	$-0.813758\pi$
$401$		−	442.929i		−	1.10456i	0.833658	−	0.552280i	$-0.186242\pi$
$402$	408.902	−	204.709i	1.01717	−	0.509225i
$403$	123.118			0.305503
$404$			88.3497i			0.218687i
$405$	−173.774	+	51.0644i	−0.429072	+	0.126085i
$406$	−306.077			−0.753884
$407$		−	445.852i		−	1.09546i
$408$	2.94958	+	5.89175i	0.00722937	+	0.0144406i
$409$	69.2653			0.169353			0.0846764	−	0.996409i	$-0.473014\pi$
$409$	69.2653			0.169353			0.0846764	+	0.996409i	$0.473014\pi$
$410$		−	130.204i		−	0.317571i
$411$	344.062	−	172.248i	0.837134	−	0.419095i
$412$	100.321			0.243497
$413$			601.682i			1.45686i
$414$	−36.5754	+	48.8697i	−0.0883463	+	0.118043i
$415$	336.109			0.809902
$416$		−	20.3706i		−	0.0489677i
$417$	191.273	+	382.065i	0.458688	+	0.916222i
$418$	687.453			1.64463
$419$		−	776.330i		−	1.85282i	−0.376522	−	0.926408i	$-0.622880\pi$
$419$		−	776.330i		−	1.85282i	0.376522	−	0.926408i	$-0.377120\pi$
$420$	−102.032	+	51.0804i	−0.242934	+	0.121620i
$421$	−700.311			−1.66345			−0.831723	−	0.555190i	$-0.812645\pi$
$421$	−700.311			−1.66345			−0.831723	+	0.555190i	$0.812645\pi$
$422$			11.6254i			0.0275484i
$423$	−44.8883	−	33.5956i	−0.106119	−	0.0794223i
$424$	44.2327			0.104322
$425$		−	3.88251i		−	0.00913531i
$426$	209.099	+	417.672i	0.490843	+	0.980451i
$427$	606.133			1.41951
$428$		−	312.652i		−	0.730496i
$429$	−127.674	+	63.9176i	−0.297609	+	0.148992i
$430$	−95.4102			−0.221884
$431$			554.331i			1.28615i	0.765803	+	0.643075i	$0.222342\pi$
$431$			554.331i			1.28615i	−0.765803	+	0.643075i	$0.777658\pi$
$432$	106.287	+	19.1590i	0.246035	+	0.0443495i
$433$	423.019			0.976950			0.488475	−	0.872578i	$-0.337553\pi$
$433$	423.019			0.976950			0.488475	+	0.872578i	$0.337553\pi$
$434$			411.219i			0.947510i
$435$	−76.4203	−	152.648i	−0.175679	−	0.350916i
$436$	399.643			0.916612
$437$		−	176.390i		−	0.403637i
$438$	−326.324	+	163.368i	−0.745032	+	0.372985i
$439$	436.088			0.993366			0.496683	−	0.867932i	$-0.334551\pi$
$439$	436.088			0.993366			0.496683	+	0.867932i	$0.334551\pi$
$440$		−	83.5890i		−	0.189975i
$441$	−125.824	+	168.117i	−0.285314	+	0.381219i
$442$	3.95444			0.00894670
$443$		−	425.568i		−	0.960649i	−0.877091	−	0.480325i	$-0.840519\pi$
$443$		−	425.568i		−	0.960649i	0.877091	−	0.480325i	$-0.159481\pi$
$444$	90.6097	+	180.991i	0.204076	+	0.407638i
$445$	304.027			0.683207
$446$		−	189.600i		−	0.425111i
$447$	384.437	−	192.460i	0.860037	−	0.430560i
$448$	68.0386			0.151872
$449$			355.131i			0.790938i	0.918479	+	0.395469i	$0.129418\pi$
$449$			355.131i			0.790938i	−0.918479	+	0.395469i	$0.870582\pi$
$450$	−50.9501	−	38.1324i	−0.113223	−	0.0847388i
$451$	544.181			1.20661
$452$		−	18.9435i		−	0.0419103i
$453$	197.203	+	393.909i	0.435326	+	0.869556i
$454$	356.589			0.785438
$455$			68.4823i			0.150510i
$456$	−279.068	+	139.710i	−0.611992	+	0.306382i
$457$	−398.620			−0.872255			−0.436127	−	0.899885i	$-0.643650\pi$
$457$	−398.620			−0.872255			−0.436127	+	0.899885i	$0.643650\pi$
$458$			573.658i			1.25253i
$459$	−3.71924	+	20.6330i	−0.00810293	+	0.0449521i
$460$	−21.4476			−0.0466252
$461$			573.580i			1.24421i	0.782935	+	0.622104i	$0.213722\pi$
$461$			573.580i			1.24421i	−0.782935	+	0.622104i	$0.786278\pi$
$462$	−213.488	−	426.438i	−0.462095	−	0.923027i
$463$	−268.662			−0.580263			−0.290131	−	0.956987i	$-0.593699\pi$
$463$	−268.662			−0.580263			−0.290131	+	0.956987i	$0.593699\pi$
$464$			101.791i			0.219378i
$465$	−205.085	+	102.672i	−0.441044	+	0.220800i
$466$	249.071			0.534487
$467$			562.394i			1.20427i	0.798394	+	0.602135i	$0.205683\pi$
$467$			562.394i			1.20427i	−0.798394	+	0.602135i	$0.794317\pi$
$468$	38.8389	−	51.8941i	0.0829892	−	0.110885i
$469$	916.670			1.95452
$470$		−	19.7003i		−	0.0419156i
$471$	268.926	+	537.175i	0.570968	+	1.14050i
$472$	200.100			0.423940
$473$		−	398.762i		−	0.843049i
$474$	−275.500	+	137.924i	−0.581224	+	0.290978i
$475$	183.899			0.387155
$476$			13.2080i			0.0277479i
$477$	112.683	+	84.3350i	0.236233	+	0.176803i
$478$	−74.2312			−0.155295
$479$		−	502.529i		−	1.04912i	−0.851373	−	0.524561i	$-0.824230\pi$
$479$		−	502.529i		−	1.04912i	0.851373	−	0.524561i	$-0.175770\pi$
$480$	16.9877	+	33.9326i	0.0353910	+	0.0706929i
$481$	121.478			0.252554
$482$		−	339.698i		−	0.704768i
$483$	−109.417	+	54.7776i	−0.226537	+	0.113411i
$484$	107.356			0.221811
$485$		−	419.985i		−	0.865949i
$486$	234.238	+	251.457i	0.481971	+	0.517401i
$487$	266.197			0.546606			0.273303	−	0.961928i	$-0.411884\pi$
$487$	266.197			0.546606			0.273303	+	0.961928i	$0.411884\pi$
$488$		−	201.580i		−	0.413074i
$489$	249.129	+	497.631i	0.509466	+	1.01765i
$490$	−73.7823			−0.150576
$491$			13.7295i			0.0279624i	0.999902	+	0.0139812i	$0.00445049\pi$
$491$			13.7295i			0.0279624i	−0.999902	+	0.0139812i	$0.995550\pi$
$492$	−220.908	+	110.593i	−0.449000	+	0.224783i
$493$	−19.7603			−0.0400817
$494$			187.306i			0.379162i
$495$	159.373	−	212.944i	0.321965	−	0.430189i
$496$	136.758			0.275722
$497$			936.330i			1.88396i
$498$	−285.486	−	570.253i	−0.573265	−	1.14509i
$499$	305.888			0.613002			0.306501	−	0.951870i	$-0.400842\pi$
$499$	305.888			0.613002			0.306501	+	0.951870i	$0.400842\pi$
$500$		−	22.3607i		−	0.0447214i
$501$	425.354	−	212.945i	0.849010	−	0.425040i
$502$	−293.386			−0.584434
$503$		−	787.569i		−	1.56574i	−0.622183	−	0.782872i	$-0.713754\pi$
$503$		−	787.569i		−	1.56574i	0.622183	−	0.782872i	$-0.286246\pi$
$504$	173.329	+	129.724i	0.343906	+	0.257389i
$505$	−98.7780			−0.195600
$506$		−	89.6393i		−	0.177153i
$507$	209.551	+	418.574i	0.413315	+	0.825589i
$508$	−174.189			−0.342892
$509$			785.384i			1.54299i	0.636233	+	0.771497i	$0.280492\pi$
$509$			785.384i			1.54299i	−0.636233	+	0.771497i	$0.719508\pi$
$510$	−6.58717	+	3.29774i	−0.0129160	+	0.00646615i
$511$	−731.547			−1.43160
$512$		−	22.6274i		−	0.0441942i
$513$	−977.303	−	176.166i	−1.90507	−	0.343403i
$514$	−138.206			−0.268883
$515$			112.162i			0.217791i
$516$	81.0398	+	161.876i	0.157054	+	0.313713i
$517$	82.3365			0.159258
$518$			405.743i			0.783288i
$519$	−148.252	+	74.2193i	−0.285649	+	0.143004i
$520$	22.7750			0.0437980
$521$			858.879i			1.64852i	0.566211	+	0.824260i	$0.308409\pi$
$521$			858.879i			1.64852i	−0.566211	+	0.824260i	$0.691591\pi$
$522$	−194.077	+	259.314i	−0.371796	+	0.496770i
$523$	−7.44546			−0.0142361			−0.00711803	−	0.999975i	$-0.502266\pi$
$523$	−7.44546			−0.0142361			−0.00711803	+	0.999975i	$0.502266\pi$
$524$		−	110.587i		−	0.211044i
$525$	−57.1096	−	114.075i	−0.108780	−	0.217287i
$526$	−132.297			−0.251515
$527$			26.5482i			0.0503761i
$528$	−141.820	+	70.9991i	−0.268598	+	0.134468i
$529$	−23.0000			−0.0434783
$530$			49.4536i			0.0933087i
$531$	509.756	+	381.515i	0.959992	+	0.718483i
$532$	−625.611			−1.17596
$533$			148.270i			0.278179i
$534$	−258.235	−	515.821i	−0.483587	−	0.965957i
$535$	349.556			0.653375
$536$		−	304.854i		−	0.568758i
$537$	−277.336	+	138.842i	−0.516454	+	0.258552i
$538$	302.624			0.562497
$539$		−	308.370i		−	0.572114i
$540$	−21.4204	+	118.833i	−0.0396674	+	0.220060i
$541$	−90.9543			−0.168123			−0.0840613	−	0.996461i	$-0.526789\pi$
$541$	−90.9543			−0.168123			−0.0840613	+	0.996461i	$0.526789\pi$
$542$		−	406.990i		−	0.750905i
$543$	216.816	+	433.087i	0.399294	+	0.797582i
$544$	4.39255			0.00807455
$545$			446.814i			0.819843i
$546$	116.189	−	58.1677i	0.212800	−	0.106534i
$547$	487.663			0.891522			0.445761	−	0.895152i	$-0.352933\pi$
$547$	487.663			0.891522			0.445761	+	0.895152i	$0.352933\pi$
$548$		−	256.514i		−	0.468090i
$549$	384.337	−	513.526i	0.700067	−	0.935385i
$550$	93.4554			0.169919
$551$		−	935.964i		−	1.69866i
$552$	18.2172	+	36.3886i	0.0330022	+	0.0659214i
$553$	−617.611			−1.11684
$554$		−	173.171i		−	0.312584i
$555$	−202.354	+	101.305i	−0.364603	+	0.182531i
$556$	284.846			0.512313
$557$		−	571.368i		−	1.02579i	−0.858450	−	0.512897i	$-0.828572\pi$
$557$		−	571.368i		−	1.02579i	0.858450	−	0.512897i	$-0.171428\pi$
$558$	348.392	+	260.746i	0.624359	+	0.467287i
$559$	108.648			0.194362
$560$			76.0695i			0.135838i
$561$	−13.7827	−	27.5308i	−0.0245681	−	0.0490744i
$562$	−255.810			−0.455177
$563$		−	239.855i		−	0.426031i	−0.977049	−	0.213015i	$-0.931672\pi$
$563$		−	239.855i		−	0.426031i	0.977049	−	0.213015i	$-0.0683285\pi$
$564$	−33.4241	+	16.7331i	−0.0592626	+	0.0296686i
$565$	21.1794			0.0374857
$566$		−	221.271i		−	0.390938i
$567$	194.222	+	660.945i	0.342543	+	1.16569i
$568$	311.393			0.548227
$569$			71.0260i			0.124826i	0.998050	+	0.0624130i	$0.0198796\pi$
$569$			71.0260i			0.124826i	−0.998050	+	0.0624130i	$0.980120\pi$
$570$	−156.201	−	312.008i	−0.274036	−	0.547382i
$571$	751.566			1.31623			0.658114	−	0.752919i	$-0.271355\pi$
$571$	751.566			1.31623			0.658114	+	0.752919i	$0.271355\pi$
$572$			95.1869i			0.166411i
$573$	153.130	−	76.6616i	0.267243	−	0.133790i
$574$	−495.227			−0.862766
$575$		−	23.9792i		−	0.0417029i
$576$	43.1419	−	57.6435i	0.0748992	−	0.100076i
$577$	99.6649			0.172729			0.0863647	−	0.996264i	$-0.472475\pi$
$577$	99.6649			0.172729			0.0863647	+	0.996264i	$0.472475\pi$
$578$		−	407.855i		−	0.705632i
$579$	142.558	+	284.757i	0.246214	+	0.491809i
$580$	−113.806			−0.196217
$581$		−	1278.38i		−	2.20032i
$582$	−712.559	+	356.728i	−1.22433	+	0.612935i
$583$	−206.689			−0.354527
$584$			243.289i			0.416590i
$585$	58.0194	+	43.4233i	0.0991784	+	0.0742278i
$586$	−4.08249			−0.00696671
$587$		−	150.122i		−	0.255744i	−0.991791	−	0.127872i	$-0.959185\pi$
$587$		−	150.122i		−	0.255744i	0.991791	−	0.127872i	$-0.0408147\pi$
$588$	62.6695	+	125.181i	0.106581	+	0.212893i
$589$	−1257.48			−2.13494
$590$			223.718i			0.379184i
$591$	504.652	−	252.644i	0.853896	−	0.427486i
$592$	134.937			0.227934
$593$		−	482.976i		−	0.814461i	−0.913325	−	0.407231i	$-0.866495\pi$
$593$		−	482.976i		−	0.814461i	0.913325	−	0.407231i	$-0.133505\pi$
$594$	−496.655	−	89.5255i	−0.836119	−	0.150716i
$595$	−14.7670			−0.0248185
$596$		−	286.614i		−	0.480897i
$597$	346.959	+	693.045i	0.581171	+	1.16088i
$598$	24.4234			0.0408419
$599$			531.979i			0.888112i	0.895999	+	0.444056i	$0.146461\pi$
$599$			531.979i			0.888112i	−0.895999	+	0.444056i	$0.853539\pi$
$600$	−37.9378	+	18.9928i	−0.0632296	+	0.0316546i
$601$	312.027			0.519180			0.259590	−	0.965719i	$-0.416413\pi$
$601$	312.027			0.519180			0.259590	+	0.965719i	$0.416413\pi$
$602$			362.890i			0.602807i
$603$	581.242	−	776.619i	0.963917	−	1.28793i
$604$	293.676			0.486219
$605$			120.028i			0.198393i
$606$	83.9004	+	167.590i	0.138449	+	0.276550i
$607$	137.992			0.227335			0.113667	−	0.993519i	$-0.463740\pi$
$607$	137.992			0.227335			0.113667	+	0.993519i	$0.463740\pi$
$608$			208.058i			0.342200i
$609$	−580.594	+	290.663i	−0.953356	+	0.477279i
$610$	225.373			0.369464
$611$			22.4337i			0.0367164i
$612$	11.1901	+	8.37494i	0.0182844	+	0.0136845i
$613$	−92.8359			−0.151445			−0.0757226	−	0.997129i	$-0.524126\pi$
$613$	−92.8359			−0.151445			−0.0757226	+	0.997129i	$0.524126\pi$
$614$			383.891i			0.625229i
$615$	−123.647	−	246.983i	−0.201052	−	0.401598i
$616$	−317.929			−0.516118
$617$		−	954.229i		−	1.54656i	−0.634063	−	0.773281i	$-0.718614\pi$
$617$		−	954.229i		−	1.54656i	0.634063	−	0.773281i	$-0.281386\pi$
$618$	190.297	−	95.2686i	0.307925	−	0.154156i
$619$	36.1660			0.0584265			0.0292132	−	0.999573i	$-0.490700\pi$
$619$	36.1660			0.0584265			0.0292132	+	0.999573i	$0.490700\pi$
$620$			152.900i			0.246613i
$621$	−22.9708	+	127.434i	−0.0369900	+	0.205207i
$622$	−280.130			−0.450369
$623$		−	1156.36i		−	1.85611i
$624$	−19.3447	−	38.6407i	−0.0310011	−	0.0619241i
$625$	25.0000			0.0400000
$626$			95.6000i			0.152716i
$627$	1304.02	−	652.833i	2.07978	−	1.04120i
$628$	400.488			0.637720
$629$			26.1947i			0.0416450i
$630$	−145.036	+	193.787i	−0.230215	+	0.307599i
$631$	−503.591			−0.798084			−0.399042	−	0.916933i	$-0.630657\pi$
$631$	−503.591			−0.798084			−0.399042	+	0.916933i	$0.630657\pi$
$632$			205.397i			0.324996i
$633$	11.0400	+	22.0521i	0.0174407	+	0.0348375i
$634$	562.632			0.887432
$635$		−	194.749i		−	0.306692i
$636$	83.9044	−	42.0051i	0.131925	−	0.0660457i
$637$	84.0195			0.131899
$638$		−	475.647i		−	0.745528i
$639$	793.275	+	593.708i	1.24143	+	0.929121i
$640$	25.2982			0.0395285
$641$			589.686i			0.919947i	0.887933	+	0.459974i	$0.152141\pi$
$641$			589.686i			0.919947i	−0.887933	+	0.459974i	$0.847859\pi$
$642$	−296.907	−	593.066i	−0.462472	−	0.923779i
$643$	−53.2769			−0.0828567			−0.0414283	−	0.999141i	$-0.513191\pi$
$643$	−53.2769			−0.0828567			−0.0414283	+	0.999141i	$0.513191\pi$
$644$			81.5754i			0.126670i
$645$	−180.982	+	90.6053i	−0.280593	+	0.140473i
$646$	−40.3893			−0.0625221
$647$		−	110.016i		−	0.170040i	−0.996379	−	0.0850202i	$-0.972905\pi$
$647$		−	110.016i		−	0.170040i	0.996379	−	0.0850202i	$-0.0270955\pi$
$648$	219.809	−	64.5919i	0.339211	−	0.0996788i
$649$	−935.020			−1.44071
$650$			25.4632i			0.0391741i
$651$	390.510	+	780.037i	0.599862	+	1.19821i
$652$	371.006			0.569027
$653$			442.472i			0.677599i	0.940859	+	0.338800i	$0.110021\pi$
$653$			442.472i			0.677599i	−0.940859	+	0.338800i	$0.889979\pi$
$654$	758.078	−	379.517i	1.15914	−	0.580301i
$655$	123.640			0.188763
$656$			164.697i			0.251062i
$657$	−463.860	+	619.780i	−0.706027	+	0.943348i
$658$	−74.9296			−0.113875
$659$		−	561.159i		−	0.851531i	−0.904833	−	0.425766i	$-0.860005\pi$
$659$		−	561.159i		−	0.851531i	0.904833	−	0.425766i	$-0.139995\pi$
$660$	−79.3794	−	158.559i	−0.120272	−	0.240241i
$661$	−801.121			−1.21198			−0.605992	−	0.795471i	$-0.707224\pi$
$661$	−801.121			−1.21198			−0.605992	+	0.795471i	$0.707224\pi$
$662$			603.425i			0.911518i
$663$	7.50113	−	3.75529i	0.0113139	−	0.00566409i
$664$	−425.149			−0.640284
$665$		−	699.454i		−	1.05181i
$666$	343.753	+	257.274i	0.516146	+	0.386297i
$667$	−122.043			−0.182974
$668$		−	317.120i		−	0.474731i
$669$	−180.051	−	359.649i	−0.269135	−	0.537592i
$670$	340.838			0.508713
$671$			941.937i			1.40378i
$672$	129.062	−	64.6121i	0.192056	−	0.0961490i
$673$	−96.4810			−0.143360			−0.0716798	−	0.997428i	$-0.522836\pi$
$673$	−96.4810			−0.143360			−0.0716798	+	0.997428i	$0.522836\pi$
$674$			679.279i			1.00783i
$675$	−132.859	−	23.9487i	−0.196828	−	0.0354796i
$676$	312.065			0.461635
$677$		−	314.499i		−	0.464549i	−0.972650	−	0.232274i	$-0.925383\pi$
$677$		−	314.499i		−	0.464549i	0.972650	−	0.232274i	$-0.0746167\pi$
$678$	−17.9895	−	35.9336i	−0.0265331	−	0.0529995i
$679$	−1597.40			−2.35258
$680$			4.91103i			0.00722210i
$681$	676.409	−	338.631i	0.993258	−	0.497255i
$682$	−639.039			−0.937007
$683$			189.054i			0.276800i	0.990376	+	0.138400i	$0.0441959\pi$
$683$			189.054i			0.276800i	−0.990376	+	0.138400i	$0.955804\pi$
$684$	−396.687	+	530.029i	−0.579952	+	0.774896i
$685$	286.791			0.418673
$686$		−	308.725i		−	0.450037i
$687$	544.768	+	1088.17i	0.792967	+	1.58394i
$688$	120.685			0.175415
$689$		−	56.3152i		−	0.0817347i
$690$	−40.6837	+	20.3675i	−0.0589619	+	0.0295181i
$691$	−491.731			−0.711622			−0.355811	−	0.934558i	$-0.615795\pi$
$691$	−491.731			−0.711622			−0.355811	+	0.934558i	$0.615795\pi$
$692$			110.528i			0.159723i
$693$	−809.925	−	606.170i	−1.16872	−	0.874704i
$694$	−561.955			−0.809734
$695$			318.468i			0.458227i
$696$	96.6649	+	193.087i	0.138886	+	0.277423i
$697$	−31.9718			−0.0458705
$698$		−	712.810i		−	1.02122i
$699$	472.460	−	236.528i	0.675909	−	0.338380i
$700$	−85.0482			−0.121497
$701$		−	873.449i		−	1.24600i	−0.782220	−	0.623002i	$-0.785913\pi$
$701$		−	873.449i		−	1.24600i	0.782220	−	0.623002i	$-0.214087\pi$
$702$	24.3924	−	135.320i	0.0347471	−	0.192764i
$703$	−1240.74			−1.76492
$704$			105.733i			0.150188i
$705$	−18.7082	−	37.3693i	−0.0265364	−	0.0530061i
$706$	−802.045			−1.13604
$707$			375.699i			0.531400i
$708$	379.567	−	190.023i	0.536111	−	0.268393i
$709$	−1127.06			−1.58965			−0.794825	−	0.606839i	$-0.792437\pi$
$709$	−1127.06			−1.58965			−0.794825	+	0.606839i	$0.792437\pi$
$710$			348.148i			0.490349i
$711$	−391.615	+	523.251i	−0.550795	+	0.735937i
$712$	−384.567			−0.540122
$713$			163.967i			0.229968i
$714$	12.5428	+	25.0541i	0.0175670	+	0.0350898i
$715$	−106.422			−0.148842
$716$			206.766i			0.288779i
$717$	−140.808	+	70.4929i	−0.196385	+	0.0983164i
$718$	418.795			0.583279
$719$			826.971i			1.15017i	0.818094	+	0.575084i	$0.195031\pi$
$719$			826.971i			1.15017i	−0.818094	+	0.575084i	$0.804969\pi$
$720$	64.4474	+	48.2341i	0.0895103	+	0.0669919i
$721$	426.606			0.591686
$722$		−	1402.55i		−	1.94259i
$723$	−322.591	−	644.369i	−0.446184	−	0.891244i
$724$	322.885			0.445974
$725$		−	127.239i		−	0.175502i
$726$	203.643	−	101.950i	0.280500	−	0.140427i
$727$	587.838			0.808580			0.404290	−	0.914631i	$-0.367519\pi$
$727$	587.838			0.808580			0.404290	+	0.914631i	$0.367519\pi$
$728$		−	86.6240i		−	0.118989i
$729$	683.117	+	254.544i	0.937060	+	0.349169i
$730$	−272.005			−0.372610
$731$			23.4281i			0.0320494i
$732$	−191.428	−	382.375i	−0.261514	−	0.522370i
$733$	240.718			0.328401			0.164200	−	0.986427i	$-0.447496\pi$
$733$	240.718			0.328401			0.164200	+	0.986427i	$0.447496\pi$
$734$			40.7187i			0.0554750i
$735$	−139.957	+	70.0666i	−0.190417	+	0.0953287i
$736$	27.1293			0.0368605
$737$			1424.51i			1.93286i
$738$	−314.014	+	419.566i	−0.425493	+	0.568517i
$739$	430.770			0.582909			0.291455	−	0.956585i	$-0.405861\pi$
$739$	430.770			0.582909			0.291455	+	0.956585i	$0.405861\pi$
$740$			150.864i			0.203870i
$741$	177.873	+	355.299i	0.240045	+	0.479485i
$742$	188.096			0.253498
$743$			1255.07i			1.68919i	0.535408	+	0.844594i	$0.320158\pi$
$743$			1255.07i			1.68919i	−0.535408	+	0.844594i	$0.679842\pi$
$744$	259.415	−	129.871i	0.348676	−	0.174558i
$745$	320.445			0.430127
$746$			304.382i			0.408019i
$747$	−1083.07	−	810.598i	−1.44989	−	1.08514i
$748$	−20.5254			−0.0274404
$749$		−	1329.53i		−	1.77507i
$750$	−21.2346	−	42.4157i	−0.0283128	−	0.0565543i
$751$	−447.953			−0.596476			−0.298238	−	0.954492i	$-0.596399\pi$
$751$	−447.953			−0.596476			−0.298238	+	0.954492i	$0.596399\pi$
$752$			24.9191i			0.0331372i
$753$	−556.520	+	278.611i	−0.739070	+	0.370001i
$754$	129.596			0.171879
$755$			328.340i			0.434888i
$756$	451.976	+	81.4719i	0.597852	+	0.107767i
$757$	439.559			0.580660			0.290330	−	0.956927i	$-0.406235\pi$
$757$	439.559			0.580660			0.290330	+	0.956927i	$0.406235\pi$
$758$			788.184i			1.03982i
$759$	−85.1250	−	170.036i	−0.112154	−	0.224026i
$760$	−232.616			−0.306073
$761$			74.4722i			0.0978609i	0.998802	+	0.0489305i	$0.0155813\pi$
$761$			74.4722i			0.0978609i	−0.998802	+	0.0489305i	$0.984419\pi$
$762$	−330.417	+	165.417i	−0.433618	+	0.217082i
$763$	1699.45			2.22732
$764$		−	114.165i		−	0.149431i
$765$	−9.36347	+	12.5109i	−0.0122398	+	0.0163541i
$766$	−39.2492			−0.0512392
$767$		−	254.759i		−	0.332150i
$768$	−21.4879	−	42.9217i	−0.0279790	−	0.0558876i
$769$	−496.554			−0.645714			−0.322857	−	0.946448i	$-0.604643\pi$
$769$	−496.554			−0.645714			−0.322857	+	0.946448i	$0.604643\pi$
$770$		−	355.455i		−	0.461630i
$771$	−262.161	+	131.246i	−0.340027	+	0.170228i
$772$	212.299			0.274999
$773$			1431.40i			1.85175i	0.377829	+	0.925876i	$0.376671\pi$
$773$			1431.40i			1.85175i	−0.377829	+	0.925876i	$0.623329\pi$
$774$	307.447	+	230.101i	0.397218	+	0.297289i
$775$	−170.948			−0.220578
$776$			531.244i			0.684593i
$777$	385.310	+	769.650i	0.495894	+	0.990540i
$778$	498.589			0.640860
$779$		−	1514.37i		−	1.94400i
$780$	43.2016	−	21.6280i	0.0553866	−	0.0277282i
$781$	−1455.07			−1.86308
$782$			5.26649i			0.00673464i
$783$	−121.889	+	676.193i	−0.155669	+	0.863593i
$784$	93.3281			0.119041
$785$			447.759i			0.570394i
$786$	−105.018	−	209.771i	−0.133610	−	0.266884i
$787$	212.110			0.269517			0.134758	−	0.990878i	$-0.456974\pi$
$787$	212.110			0.269517			0.134758	+	0.990878i	$0.456974\pi$
$788$		−	376.241i		−	0.477463i
$789$	−250.952	+	125.634i	−0.318064	+	0.159232i
$790$	−229.641			−0.290685
$791$		−	80.5554i		−	0.101840i
$792$	−201.592	+	269.355i	−0.254536	+	0.340094i
$793$	−256.643			−0.323636
$794$		−	0.317964i		−	0.000400459i
$795$	46.9631	+	93.8080i	0.0590731	+	0.117997i
$796$	516.695			0.649115
$797$		−	638.216i		−	0.800773i	−0.916346	−	0.400387i	$-0.868876\pi$
$797$		−	638.216i		−	0.800773i	0.916346	−	0.400387i	$-0.131124\pi$
$798$	−1186.71	+	594.104i	−1.48711	+	0.744492i
$799$	−4.83744			−0.00605436
$800$			28.2843i			0.0353553i
$801$	−979.688	−	733.224i	−1.22308	−	0.915386i
$802$	−626.396			−0.781043
$803$		−	1136.83i		−	1.41573i
$804$	−289.502	−	578.275i	−0.360077	−	0.719247i
$805$	−91.2041			−0.113297
$806$		−	174.115i		−	0.216023i
$807$	574.043	−	287.383i	0.711330	−	0.356113i
$808$	124.945			0.154635
$809$		−	1260.54i		−	1.55814i	−0.626936	−	0.779071i	$-0.715691\pi$
$809$		−	1260.54i		−	1.55814i	0.626936	−	0.779071i	$-0.284309\pi$
$810$	72.2159	+	245.754i	0.0891554	+	0.303400i
$811$	−679.934			−0.838389			−0.419195	−	0.907896i	$-0.637688\pi$
$811$	−679.934			−0.838389			−0.419195	+	0.907896i	$0.637688\pi$
$812$			432.858i			0.533077i
$813$	−386.494	−	772.015i	−0.475392	−	0.949588i
$814$	−630.529			−0.774606
$815$			414.797i			0.508953i
$816$	8.33219	−	4.17134i	0.0102110	−	0.00511194i
$817$	−1109.70			−1.35826
$818$		−	97.9559i		−	0.119751i
$819$	165.159	−	220.675i	0.201660	−	0.269445i
$820$	−184.136			−0.224556
$821$		−	395.989i		−	0.482325i	−0.970485	−	0.241163i	$-0.922471\pi$
$821$		−	395.989i		−	0.482325i	0.970485	−	0.241163i	$-0.0775287\pi$
$822$	−243.595	−	486.578i	−0.296345	−	0.591943i
$823$	−992.123			−1.20550			−0.602748	−	0.797931i	$-0.705928\pi$
$823$	−992.123			−1.20550			−0.602748	+	0.797931i	$0.705928\pi$
$824$		−	141.875i		−	0.172179i
$825$	177.274	−	88.7489i	0.214878	−	0.107574i
$826$	850.907			1.03015
$827$			258.849i			0.312998i	0.987678	+	0.156499i	$0.0500207\pi$
$827$			258.849i			0.312998i	−0.987678	+	0.156499i	$0.949979\pi$
$828$	69.1121	+	51.7254i	0.0834688	+	0.0624702i
$829$	195.288			0.235571			0.117786	−	0.993039i	$-0.462420\pi$
$829$	195.288			0.235571			0.117786	+	0.993039i	$0.462420\pi$
$830$		−	475.331i		−	0.572687i
$831$	−164.450	−	328.487i	−0.197895	−	0.395291i
$832$	−28.8083			−0.0346254
$833$			18.1173i			0.0217495i
$834$	540.321	−	270.501i	0.647867	−	0.324342i
$835$	354.551			0.424612
$836$		−	972.206i		−	1.16293i
$837$	908.476	+	163.759i	1.08540	+	0.195650i
$838$	−1097.90			−1.31014
$839$		−	737.892i		−	0.879490i	−0.898123	−	0.439745i	$-0.855069\pi$
$839$		−	737.892i		−	0.879490i	0.898123	−	0.439745i	$-0.144931\pi$
$840$	72.2385	+	144.295i	0.0859983	+	0.171780i
$841$	193.409			0.229975
$842$			990.389i			1.17623i
$843$	−485.243	+	242.927i	−0.575614	+	0.288170i
$844$	16.4408			0.0194797
$845$			348.899i			0.412899i
$846$	−47.5114	+	63.4817i	−0.0561600	+	0.0750375i
$847$	456.523			0.538989
$848$		−	62.5544i		−	0.0737670i
$849$	−210.127	−	419.726i	−0.247500	−	0.494377i
$850$	−5.49069			−0.00645964
$851$			161.784i			0.190110i
$852$	590.677	−	295.711i	0.693283	−	0.347078i
$853$	273.990			0.321207			0.160604	−	0.987019i	$-0.448656\pi$
$853$	273.990			0.321207			0.160604	+	0.987019i	$0.448656\pi$
$854$		−	857.201i		−	1.00375i
$855$	−592.590	−	443.510i	−0.693088	−	0.518725i
$856$	−442.157			−0.516538
$857$			953.725i			1.11287i	0.830893	+	0.556433i	$0.187830\pi$
$857$			953.725i			1.11287i	−0.830893	+	0.556433i	$0.812170\pi$
$858$	90.3932	+	180.559i	0.105353	+	0.210442i
$859$	702.096			0.817341			0.408671	−	0.912682i	$-0.365993\pi$
$859$	702.096			0.817341			0.408671	+	0.912682i	$0.365993\pi$
$860$			134.930i			0.156896i
$861$	−939.391	+	470.287i	−1.09105	+	0.546211i
$862$	783.942			0.909446
$863$			635.320i			0.736176i	0.929791	+	0.368088i	$0.119988\pi$
$863$			635.320i			0.736176i	−0.929791	+	0.368088i	$0.880012\pi$
$864$	27.0949	−	150.313i	0.0313598	−	0.173973i
$865$	−123.574			−0.142861
$866$		−	598.239i		−	0.690808i
$867$	−387.315	−	773.655i	−0.446730	−	0.892336i
$868$	581.552			0.669990
$869$		−	959.775i		−	1.10446i
$870$	−215.877	+	108.075i	−0.248135	+	0.124224i
$871$	−388.128			−0.445612
$872$		−	565.181i		−	0.648143i
$873$	−1012.88	+	1353.35i	−1.16023	+	1.55023i
$874$	−249.452			−0.285415
$875$		−	95.0868i		−	0.108671i
$876$	231.037	+	461.492i	0.263740	+	0.526817i
$877$	45.3899			0.0517559			0.0258780	−	0.999665i	$-0.491762\pi$
$877$	45.3899			0.0517559			0.0258780	+	0.999665i	$0.491762\pi$
$878$		−	616.721i		−	0.702416i
$879$	−7.74403	+	3.87689i	−0.00881004	+	0.00441057i
$880$	−118.213			−0.134333
$881$		−	644.412i		−	0.731455i	−0.930722	−	0.365727i	$-0.880820\pi$
$881$		−	644.412i		−	0.731455i	0.930722	−	0.365727i	$-0.119180\pi$
$882$	237.754	+	177.941i	0.269562	+	0.201748i
$883$	−1586.87			−1.79713			−0.898565	−	0.438840i	$-0.855390\pi$
$883$	−1586.87			−1.79713			−0.898565	+	0.438840i	$0.855390\pi$
$884$		−	5.59242i		−	0.00632627i
$885$	212.452	+	424.369i	0.240058	+	0.479513i
$886$	−601.843			−0.679281
$887$		−	1561.91i		−	1.76089i	−0.474148	−	0.880445i	$-0.657244\pi$
$887$		−	1561.91i		−	1.76089i	0.474148	−	0.880445i	$-0.342756\pi$
$888$	255.960	−	128.141i	0.288244	−	0.144303i
$889$	−740.724			−0.833210
$890$		−	429.959i		−	0.483100i
$891$	−1027.12	+	301.823i	−1.15277	+	0.338746i
$892$	−268.134			−0.300599
$893$		−	229.130i		−	0.256585i
$894$	−272.180	−	543.675i	−0.304452	−	0.608138i
$895$	−231.171			−0.258292
$896$		−	96.2211i		−	0.107390i
$897$	46.3285	−	23.1934i	0.0516483	−	0.0258567i
$898$	502.231			0.559277
$899$			870.048i			0.967796i
$900$	−53.9274	+	72.0544i	−0.0599194	+	0.0800604i
$901$	12.1434			0.0134777
$902$		−	769.589i		−	0.853203i
$903$	344.615	+	688.362i	0.381633	+	0.762306i
$904$	−26.7901			−0.0296351
$905$			360.997i			0.398892i
$906$	557.071	−	278.887i	0.614869	−	0.307822i
$907$	1128.40			1.24410			0.622049	−	0.782979i	$-0.286301\pi$
$907$	1128.40			1.24410			0.622049	+	0.782979i	$0.286301\pi$
$908$		−	504.293i		−	0.555388i
$909$	318.299	+	238.224i	0.350164	+	0.262072i
$910$	96.8485			0.106427
$911$		−	953.339i		−	1.04648i	−0.852187	−	0.523238i	$-0.824724\pi$
$911$		−	953.339i		−	1.04648i	0.852187	−	0.523238i	$-0.175276\pi$
$912$	197.580	+	394.662i	0.216644	+	0.432744i
$913$	1986.62			2.17593
$914$			563.734i			0.616777i
$915$	427.508	−	214.023i	0.467222	−	0.233905i
$916$	811.275			0.885672
$917$		−	470.261i		−	0.512826i
$918$	29.1795	+	5.25981i	0.0317859	+	0.00572964i
$919$	−449.412			−0.489023			−0.244512	−	0.969646i	$-0.578628\pi$
$919$	−449.412			−0.489023			−0.244512	+	0.969646i	$0.578628\pi$
$920$			30.3315i			0.0329690i
$921$	364.558	+	728.198i	0.395828	+	0.790660i
$922$	811.164			0.879788
$923$		−	396.453i		−	0.429526i
$924$	−603.075	+	301.917i	−0.652679	+	0.326751i
$925$	−168.671			−0.182347
$926$			379.945i			0.410308i
$927$	270.502	−	361.428i	0.291804	−	0.389890i
$928$	143.955			0.155123
$929$			434.163i			0.467345i	0.972315	+	0.233672i	$0.0750743\pi$
$929$			434.163i			0.467345i	−0.972315	+	0.233672i	$0.924926\pi$
$930$	145.200	+	290.035i	0.156129	+	0.311865i
$931$	−858.146			−0.921747
$932$		−	352.240i		−	0.377940i
$933$	−531.375	+	266.022i	−0.569534	+	0.285126i
$934$	795.345			0.851548
$935$		−	22.9481i		−	0.0245434i
$936$	−73.3894	−	54.9266i	−0.0784074	−	0.0586822i
$937$	411.423			0.439085			0.219543	−	0.975603i	$-0.429544\pi$
$937$	411.423			0.439085			0.219543	+	0.975603i	$0.429544\pi$
$938$		−	1296.37i		−	1.38205i
$939$	90.7855	+	181.343i	0.0966832	+	0.193123i
$940$	−27.8604			−0.0296388
$941$		−	593.790i		−	0.631020i	−0.948922	−	0.315510i	$-0.897824\pi$
$941$		−	593.790i		−	0.631020i	0.948922	−	0.315510i	$-0.102176\pi$
$942$	759.681	−	380.319i	0.806455	−	0.403736i
$943$	−197.464			−0.209400
$944$		−	282.984i		−	0.299771i
$945$	−91.0883	+	505.325i	−0.0963898	+	0.534735i
$946$	−563.935			−0.596126
$947$			1059.68i			1.11899i	0.828834	+	0.559495i	$0.189005\pi$
$947$			1059.68i			1.11899i	−0.828834	+	0.559495i	$0.810995\pi$
$948$	195.053	+	389.616i	0.205753	+	0.410987i
$949$	309.745			0.326391
$950$		−	260.072i		−	0.273760i
$951$	1067.25	−	534.297i	1.12224	−	0.561827i
$952$	18.6790			0.0196207
$953$		−	166.354i		−	0.174558i	−0.996184	−	0.0872790i	$-0.972183\pi$
$953$		−	166.354i		−	0.174558i	0.996184	−	0.0872790i	$-0.0278172\pi$
$954$	119.268	−	159.358i	0.125019	−	0.167042i
$955$	127.641			0.133655
$956$			104.979i			0.109810i
$957$	−451.693	−	902.249i	−0.471988	−	0.942789i
$958$	−710.684			−0.741841
$959$		−	1090.80i		−	1.13744i
$960$	47.9879	−	24.0242i	0.0499874	−	0.0250252i
$961$	207.924			0.216362
$962$		−	171.796i		−	0.178582i
$963$	−1126.40	−	843.026i	−1.16968	−	0.875416i
$964$	−480.406			−0.498346
$965$			237.358i			0.245967i
$966$	77.4672	+	154.739i	0.0801938	+	0.160186i
$967$	−1600.34			−1.65495			−0.827474	−	0.561503i	$-0.810223\pi$
$967$	−1600.34			−1.65495			−0.827474	+	0.561503i	$0.810223\pi$
$968$		−	151.825i		−	0.156844i
$969$	−76.6139	+	38.3552i	−0.0790650	+	0.0395823i
$970$	−593.949			−0.612318
$971$			1574.23i			1.62125i	0.585568	+	0.810623i	$0.300872\pi$
$971$			1574.23i			1.62125i	−0.585568	+	0.810623i	$0.699128\pi$
$972$	355.614	−	331.263i	0.365858	−	0.340805i
$973$	1211.28			1.24489
$974$		−	376.460i		−	0.386509i
$975$	24.1808	+	48.3008i	0.0248009	+	0.0495393i
$976$	−285.077			−0.292087
$977$		−	1060.94i		−	1.08592i	−0.839759	−	0.542960i	$-0.817304\pi$
$977$		−	1060.94i		−	1.08592i	0.839759	−	0.542960i	$-0.182696\pi$
$978$	703.756	−	352.321i	0.719587	−	0.360247i
$979$	1796.99			1.83554
$980$			104.344i			0.106473i
$981$	1077.59	−	1439.80i	1.09846	−	1.46769i
$982$	19.4165			0.0197724
$983$			1315.50i			1.33825i	0.743148	+	0.669127i	$0.233332\pi$
$983$			1315.50i			1.33825i	−0.743148	+	0.669127i	$0.766668\pi$
$984$	156.402	+	312.411i	0.158945	+	0.317491i
$985$	420.650			0.427056
$986$			27.9452i			0.0283420i
$987$	−142.133	+	71.1561i	−0.144005	+	0.0720933i
$988$	264.891			0.268108
$989$			144.697i			0.146306i
$990$	−301.148	−	225.387i	−0.304190	−	0.227664i
$991$	−994.920			−1.00396			−0.501978	−	0.864881i	$-0.667394\pi$
$991$	−994.920			−1.00396			−0.501978	+	0.864881i	$0.667394\pi$
$992$		−	193.405i		−	0.194965i
$993$	573.036	+	1144.63i	0.577075	+	1.15270i
$994$	1324.17			1.33216
$995$			577.683i			0.580586i
$996$	−806.459	+	403.738i	−0.809698	+	0.405359i
$997$	602.837			0.604651			0.302325	−	0.953205i	$-0.402237\pi$
$997$	602.837			0.604651			0.302325	+	0.953205i	$0.402237\pi$
$998$		−	432.591i		−	0.433458i
$999$	896.378	+	161.578i	0.897275	+	0.161740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.g.a.461.13	✓	56
3.2	odd	2	inner	690.3.g.a.461.14	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.g.a.461.13	✓	56	1.1	even	1	trivial
690.3.g.a.461.14	yes	56	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-1.34299 - 2.68261i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-3.79378 + 1.89928i) q^{6} -8.50482 q^{7} +2.82843i q^{8} +(-5.39274 + 7.20544i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(-1.34299 - 2.68261i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-3.79378 + 1.89928i) q^{6} -8.50482 q^{7} +2.82843i q^{8} +(-5.39274 + 7.20544i) q^{9} -3.16228 q^{10} -13.2166i q^{11} +(2.68599 + 5.36521i) q^{12} +3.60104 q^{13} +12.0276i q^{14} +(-5.99849 + 3.00302i) q^{15} +4.00000 q^{16} +0.776501i q^{17} +(10.1900 + 7.62649i) q^{18} -36.7798 q^{19} +4.47214i q^{20} +(11.4219 + 22.8151i) q^{21} -18.6911 q^{22} +4.79583i q^{23} +(7.58755 - 3.79856i) q^{24} -5.00000 q^{25} -5.09264i q^{26} +(26.5718 + 4.78975i) q^{27} +17.0096 q^{28} +25.4478i q^{29} +(4.24692 + 8.48314i) q^{30} +34.1895 q^{31} -5.65685i q^{32} +(-35.4549 + 17.7498i) q^{33} +1.09814 q^{34} +19.0174i q^{35} +(10.7855 - 14.4109i) q^{36} +33.7342 q^{37} +52.0144i q^{38} +(-4.83617 - 9.66016i) q^{39} +6.32456 q^{40} +41.1741i q^{41} +(32.2654 - 16.1530i) q^{42} +30.1714 q^{43} +26.4332i q^{44} +(16.1118 + 12.0585i) q^{45} +6.78233 q^{46} +6.22979i q^{47} +(-5.37197 - 10.7304i) q^{48} +23.3320 q^{49} +7.07107i q^{50} +(2.08305 - 1.04284i) q^{51} -7.20208 q^{52} -15.6386i q^{53} +(6.77372 - 37.5781i) q^{54} -29.5532 q^{55} -24.0553i q^{56} +(49.3949 + 98.6656i) q^{57} +35.9886 q^{58} -70.7460i q^{59} +(11.9970 - 6.00605i) q^{60} -71.2693 q^{61} -48.3513i q^{62} +(45.8643 - 61.2810i) q^{63} -8.00000 q^{64} -8.05217i q^{65} +(25.1020 + 50.1408i) q^{66} -107.782 q^{67} -1.55300i q^{68} +(12.8653 - 6.44077i) q^{69} +26.8946 q^{70} -110.094i q^{71} +(-20.3801 - 15.2530i) q^{72} +86.0156 q^{73} -47.7074i q^{74} +(6.71496 + 13.4130i) q^{75} +73.5595 q^{76} +112.405i q^{77} +(-13.6615 + 6.83937i) q^{78} +72.6189 q^{79} -8.94427i q^{80} +(-22.8367 - 77.7141i) q^{81} +58.2290 q^{82} +150.313i q^{83} +(-22.8438 - 45.6302i) q^{84} +1.73631 q^{85} -42.6687i q^{86} +(68.2664 - 34.1762i) q^{87} +37.3822 q^{88} +135.965i q^{89} +(17.0533 - 22.7856i) q^{90} -30.6262 q^{91} -9.59166i q^{92} +(-45.9163 - 91.7170i) q^{93} +8.81025 q^{94} +82.2420i q^{95} +(-15.1751 + 7.59711i) q^{96} +187.823 q^{97} -32.9965i q^{98} +(95.2313 + 71.2736i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7}+O(q^{10}) \) 56 * q - 8 * q^3 - 112 * q^4 + 16 * q^6 - 16 * q^7	\( 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7} + 16 q^{12} + 80 q^{13} - 40 q^{15} + 224 q^{16} - 32 q^{18} - 64 q^{19} + 56 q^{21} - 96 q^{22} - 32 q^{24} - 280 q^{25} + 40 q^{27} + 32 q^{28} - 80 q^{31} + 32 q^{33} + 192 q^{34} + 240 q^{37} - 56 q^{39} - 144 q^{43} - 32 q^{48} + 72 q^{49} - 24 q^{51} - 160 q^{52} + 16 q^{54} - 16 q^{57} + 80 q^{60} + 112 q^{61} - 64 q^{63} - 448 q^{64} + 160 q^{66} + 832 q^{67} + 64 q^{72} - 608 q^{73} + 40 q^{75} + 128 q^{76} - 320 q^{78} + 48 q^{79} - 32 q^{81} - 448 q^{82} - 112 q^{84} + 240 q^{85} + 200 q^{87} + 192 q^{88} + 80 q^{91} - 232 q^{93} + 160 q^{94} + 64 q^{96} - 448 q^{97} + 464 q^{99}+O(q^{100}) \) 56 * q - 8 * q^3 - 112 * q^4 + 16 * q^6 - 16 * q^7 + 16 * q^12 + 80 * q^13 - 40 * q^15 + 224 * q^16 - 32 * q^18 - 64 * q^19 + 56 * q^21 - 96 * q^22 - 32 * q^24 - 280 * q^25 + 40 * q^27 + 32 * q^28 - 80 * q^31 + 32 * q^33 + 192 * q^34 + 240 * q^37 - 56 * q^39 - 144 * q^43 - 32 * q^48 + 72 * q^49 - 24 * q^51 - 160 * q^52 + 16 * q^54 - 16 * q^57 + 80 * q^60 + 112 * q^61 - 64 * q^63 - 448 * q^64 + 160 * q^66 + 832 * q^67 + 64 * q^72 - 608 * q^73 + 40 * q^75 + 128 * q^76 - 320 * q^78 + 48 * q^79 - 32 * q^81 - 448 * q^82 - 112 * q^84 + 240 * q^85 + 200 * q^87 + 192 * q^88 + 80 * q^91 - 232 * q^93 + 160 * q^94 + 64 * q^96 - 448 * q^97 + 464 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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