LMFDB - Embedded newform 287.2.c.b.204.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(204,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("287.204");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.c (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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 113x^{8} + 290x^{6} + 258x^{4} + 49x^{2} + 1 $ x^12 + 18x^10 + 113x^8 + 290x^6 + 258x^4 + 49*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			204.4
Root			$-2.16363i$ of defining polynomial
Character	$\chi$	$=$	287.204
Dual form			287.2.c.b.204.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.16363 q^{2} +1.16363i q^{3} +2.68131 q^{4} +2.90865 q^{5} -2.51768i q^{6} +1.00000i q^{7} -1.47412 q^{8} +1.64595 q^{9} +O(q^{10})$	\(q-2.16363 q^{2} +1.16363i q^{3} +2.68131 q^{4} +2.90865 q^{5} -2.51768i q^{6} +1.00000i q^{7} -1.47412 q^{8} +1.64595 q^{9} -6.29325 q^{10} -4.29325i q^{11} +3.12007i q^{12} -1.70145i q^{13} -2.16363i q^{14} +3.38460i q^{15} -2.17318 q^{16} +4.15170i q^{17} -3.56124 q^{18} -5.64730i q^{19} +7.79900 q^{20} -1.16363 q^{21} +9.28903i q^{22} +7.57803 q^{23} -1.71533i q^{24} +3.46023 q^{25} +3.68131i q^{26} +5.40619i q^{27} +2.68131i q^{28} +6.78750i q^{29} -7.32305i q^{30} -1.41862 q^{31} +7.65020 q^{32} +4.99578 q^{33} -8.98277i q^{34} +2.90865i q^{35} +4.41332 q^{36} +4.59180 q^{37} +12.2187i q^{38} +1.97987 q^{39} -4.28768 q^{40} +(3.10814 + 5.59817i) q^{41} +2.51768 q^{42} -8.58996 q^{43} -11.5116i q^{44} +4.78750 q^{45} -16.3961 q^{46} -9.95443i q^{47} -2.52879i q^{48} -1.00000 q^{49} -7.48668 q^{50} -4.83107 q^{51} -4.56212i q^{52} +7.83302i q^{53} -11.6970i q^{54} -12.4876i q^{55} -1.47412i q^{56} +6.57139 q^{57} -14.6857i q^{58} -3.09135 q^{59} +9.07519i q^{60} -9.99956 q^{61} +3.06938 q^{62} +1.64595i q^{63} -12.2059 q^{64} -4.94892i q^{65} -10.8090 q^{66} +11.6742i q^{67} +11.1320i q^{68} +8.81806i q^{69} -6.29325i q^{70} -10.0234i q^{71} -2.42633 q^{72} -5.04161 q^{73} -9.93498 q^{74} +4.02645i q^{75} -15.1422i q^{76} +4.29325 q^{77} -4.28371 q^{78} +0.438259i q^{79} -6.32102 q^{80} -1.35297 q^{81} +(-6.72488 - 12.1124i) q^{82} -9.03492 q^{83} -3.12007 q^{84} +12.0758i q^{85} +18.5855 q^{86} -7.89817 q^{87} +6.32875i q^{88} +5.59603i q^{89} -10.3584 q^{90} +1.70145 q^{91} +20.3191 q^{92} -1.65076i q^{93} +21.5378i q^{94} -16.4260i q^{95} +8.90204i q^{96} -9.39533i q^{97} +2.16363 q^{98} -7.06650i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 + 12 * q^4 + 2 * q^5 - 24 * q^8 - 4 * q^9	$ 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9} - 4 q^{10} + 28 q^{16} - 40 q^{18} + 2 q^{20} + 8 q^{21} + 16 q^{23} + 34 q^{25} - 6 q^{31} - 42 q^{32} + 18 q^{33} - 36 q^{36} - 10 q^{37} + 10 q^{39} + 38 q^{40} - 2 q^{41} + 32 q^{42} - 50 q^{43} + 6 q^{45} - 8 q^{46} - 12 q^{49} + 18 q^{50} - 2 q^{51} - 50 q^{57} - 70 q^{59} + 52 q^{61} + 68 q^{62} + 8 q^{64} + 92 q^{66} + 2 q^{72} - 64 q^{73} + 18 q^{74} - 20 q^{77} - 12 q^{78} - 32 q^{80} - 4 q^{81} - 56 q^{82} + 60 q^{83} - 20 q^{84} + 48 q^{86} - 20 q^{87} - 42 q^{90} + 14 q^{91} + 56 q^{92} + 4 q^{98}+O(q^{100}) $ 12 * q - 4 * q^2 + 12 * q^4 + 2 * q^5 - 24 * q^8 - 4 * q^9 - 4 * q^10 + 28 * q^16 - 40 * q^18 + 2 * q^20 + 8 * q^21 + 16 * q^23 + 34 * q^25 - 6 * q^31 - 42 * q^32 + 18 * q^33 - 36 * q^36 - 10 * q^37 + 10 * q^39 + 38 * q^40 - 2 * q^41 + 32 * q^42 - 50 * q^43 + 6 * q^45 - 8 * q^46 - 12 * q^49 + 18 * q^50 - 2 * q^51 - 50 * q^57 - 70 * q^59 + 52 * q^61 + 68 * q^62 + 8 * q^64 + 92 * q^66 + 2 * q^72 - 64 * q^73 + 18 * q^74 - 20 * q^77 - 12 * q^78 - 32 * q^80 - 4 * q^81 - 56 * q^82 + 60 * q^83 - 20 * q^84 + 48 * q^86 - 20 * q^87 - 42 * q^90 + 14 * q^91 + 56 * q^92 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$-1$

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 $

$2$	−2.16363			−1.52992			−0.764960	−	0.644077i	$-0.777241\pi$
$2$	−2.16363			−1.52992			−0.764960	+	0.644077i	$0.777241\pi$
$3$			1.16363i			0.671825i	0.941893	+	0.335912i	$0.109045\pi$
$3$			1.16363i			0.671825i	−0.941893	+	0.335912i	$0.890955\pi$
$4$	2.68131			1.34066
$5$	2.90865			1.30079			0.650393	−	0.759597i	$-0.274604\pi$
$5$	2.90865			1.30079			0.650393	+	0.759597i	$0.274604\pi$
$6$		−	2.51768i		−	1.02784i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−1.47412			−0.521179
$9$	1.64595			0.548651
$10$	−6.29325			−1.99010
$11$		−	4.29325i		−	1.29446i	−0.762293	−	0.647232i	$-0.775926\pi$
$11$		−	4.29325i		−	1.29446i	0.762293	−	0.647232i	$-0.224074\pi$
$12$			3.12007i			0.900687i
$13$		−	1.70145i		−	0.471897i	−0.971766	−	0.235949i	$-0.924180\pi$
$13$		−	1.70145i		−	0.471897i	0.971766	−	0.235949i	$-0.0758197\pi$
$14$		−	2.16363i		−	0.578256i
$15$			3.38460i			0.873901i
$16$	−2.17318			−0.543295
$17$			4.15170i			1.00694i	0.864014	+	0.503468i	$0.167943\pi$
$17$			4.15170i			1.00694i	−0.864014	+	0.503468i	$0.832057\pi$
$18$	−3.56124			−0.839393
$19$		−	5.64730i		−	1.29558i	−0.761819	−	0.647789i	$-0.775694\pi$
$19$		−	5.64730i		−	1.29558i	0.761819	−	0.647789i	$-0.224306\pi$
$20$	7.79900			1.74391
$21$	−1.16363			−0.253926
$22$			9.28903i			1.98043i
$23$	7.57803			1.58013			0.790064	−	0.613024i	$-0.210047\pi$
$23$	7.57803			1.58013			0.790064	+	0.613024i	$0.210047\pi$
$24$		−	1.71533i		−	0.350141i
$25$	3.46023			0.692047
$26$			3.68131i			0.721965i
$27$			5.40619i			1.04042i
$28$			2.68131i			0.506721i
$29$			6.78750i			1.26041i	0.776430	+	0.630204i	$0.217029\pi$
$29$			6.78750i			1.26041i	−0.776430	+	0.630204i	$0.782971\pi$
$30$		−	7.32305i		−	1.33700i
$31$	−1.41862			−0.254792			−0.127396	−	0.991852i	$-0.540662\pi$
$31$	−1.41862			−0.254792			−0.127396	+	0.991852i	$0.540662\pi$
$32$	7.65020			1.35238
$33$	4.99578			0.869653
$34$		−	8.98277i		−	1.54053i
$35$			2.90865i			0.491651i
$36$	4.41332			0.735554
$37$	4.59180			0.754888			0.377444	−	0.926032i	$-0.376803\pi$
$37$	4.59180			0.754888			0.377444	+	0.926032i	$0.376803\pi$
$38$			12.2187i			1.98213i
$39$	1.97987			0.317032
$40$	−4.28768			−0.677943
$41$	3.10814	+	5.59817i	0.485410	+	0.874287i
$41$	3.10814	+	5.59817i	0.485410	+	0.874287i
$42$	2.51768			0.388486
$43$	−8.58996			−1.30996			−0.654979	−	0.755648i	$-0.727322\pi$
$43$	−8.58996			−1.30996			−0.654979	+	0.755648i	$0.727322\pi$
$44$		−	11.5116i		−	1.73543i
$45$	4.78750			0.713679
$46$	−16.3961			−2.41747
$47$		−	9.95443i		−	1.45200i	−0.687693	−	0.726002i	$-0.741377\pi$
$47$		−	9.95443i		−	1.45200i	0.687693	−	0.726002i	$-0.258623\pi$
$48$		−	2.52879i		−	0.364999i
$49$	−1.00000			−0.142857
$50$	−7.48668			−1.05878
$51$	−4.83107			−0.676485
$52$		−	4.56212i		−	0.632652i
$53$			7.83302i			1.07595i	0.842961	+	0.537974i	$0.180810\pi$
$53$			7.83302i			1.07595i	−0.842961	+	0.537974i	$0.819190\pi$
$54$		−	11.6970i		−	1.59176i
$55$		−	12.4876i		−	1.68382i
$56$		−	1.47412i		−	0.196987i
$57$	6.57139			0.870402
$58$		−	14.6857i		−	1.92832i
$59$	−3.09135			−0.402460			−0.201230	−	0.979544i	$-0.564494\pi$
$59$	−3.09135			−0.402460			−0.201230	+	0.979544i	$0.564494\pi$
$60$			9.07519i			1.17160i
$61$	−9.99956			−1.28031			−0.640156	−	0.768245i	$-0.721130\pi$
$61$	−9.99956			−1.28031			−0.640156	+	0.768245i	$0.721130\pi$
$62$	3.06938			0.389811
$63$			1.64595i			0.207371i
$64$	−12.2059			−1.52573
$65$		−	4.94892i		−	0.613838i
$66$	−10.8090			−1.33050
$67$			11.6742i			1.42623i	0.701048	+	0.713114i	$0.252716\pi$
$67$			11.6742i			1.42623i	−0.701048	+	0.713114i	$0.747284\pi$
$68$			11.1320i			1.34996i
$69$			8.81806i			1.06157i
$70$		−	6.29325i		−	0.752187i
$71$		−	10.0234i		−	1.18956i	−0.803888	−	0.594781i	$-0.797239\pi$
$71$		−	10.0234i		−	1.18956i	0.803888	−	0.594781i	$-0.202761\pi$
$72$	−2.42633			−0.285946
$73$	−5.04161			−0.590076			−0.295038	−	0.955486i	$-0.595332\pi$
$73$	−5.04161			−0.590076			−0.295038	+	0.955486i	$0.595332\pi$
$74$	−9.93498			−1.15492
$75$			4.02645i			0.464934i
$76$		−	15.1422i		−	1.73693i
$77$	4.29325			0.489261
$78$	−4.28371			−0.485034
$79$			0.438259i			0.0493080i	0.999696	+	0.0246540i	$0.00784841\pi$
$79$			0.438259i			0.0493080i	−0.999696	+	0.0246540i	$0.992152\pi$
$80$	−6.32102			−0.706711
$81$	−1.35297			−0.150330
$82$	−6.72488	−	12.1124i	−0.742639	−	1.33759i
$83$	−9.03492			−0.991711			−0.495856	−	0.868405i	$-0.665145\pi$
$83$	−9.03492			−0.991711			−0.495856	+	0.868405i	$0.665145\pi$
$84$	−3.12007			−0.340428
$85$			12.0758i			1.30981i
$86$	18.5855			2.00413
$87$	−7.89817			−0.846773
$88$			6.32875i			0.674647i
$89$			5.59603i			0.593178i	0.955005	+	0.296589i	$0.0958491\pi$
$89$			5.59603i			0.593178i	−0.955005	+	0.296589i	$0.904151\pi$
$90$	−10.3584			−1.09187
$91$	1.70145			0.178360
$92$	20.3191			2.11841
$93$		−	1.65076i		−	0.171176i
$94$			21.5378i			2.22145i
$95$		−	16.4260i		−	1.68527i
$96$			8.90204i			0.908561i
$97$		−	9.39533i		−	0.953951i	−0.878917	−	0.476975i	$-0.841733\pi$
$97$		−	9.39533i		−	0.953951i	0.878917	−	0.476975i	$-0.158267\pi$
$98$	2.16363			0.218560
$99$		−	7.06650i		−	0.710210i
$100$	9.27797			0.927797
$101$		−	4.29169i		−	0.427039i	−0.976939	−	0.213520i	$-0.931507\pi$
$101$		−	4.29169i		−	0.427039i	0.976939	−	0.213520i	$-0.0684927\pi$
$102$	10.4527			1.03497
$103$	8.47740			0.835303			0.417652	−	0.908607i	$-0.362853\pi$
$103$	8.47740			0.835303			0.417652	+	0.908607i	$0.362853\pi$
$104$			2.50813i			0.245943i
$105$	−3.38460			−0.330303
$106$		−	16.9478i		−	1.64611i
$107$	14.0774			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$107$	14.0774			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$108$			14.4957i			1.39485i
$109$		−	9.88901i		−	0.947195i	−0.880741	−	0.473598i	$-0.842955\pi$
$109$		−	9.88901i		−	0.947195i	0.880741	−	0.473598i	$-0.157045\pi$
$110$			27.0185i			2.57611i
$111$			5.34318i			0.507152i
$112$		−	2.17318i		−	0.205346i
$113$	1.07094			0.100746			0.0503728	−	0.998730i	$-0.483959\pi$
$113$	1.07094			0.100746			0.0503728	+	0.998730i	$0.483959\pi$
$114$	−14.2181			−1.33165
$115$	22.0418			2.05541
$116$			18.1994i			1.68977i
$117$		−	2.80051i		−	0.258907i
$118$	6.68856			0.615732
$119$	−4.15170			−0.380586
$120$		−	4.98930i		−	0.455459i
$121$	−7.43201			−0.675637
$122$	21.6354			1.95878
$123$	−6.51422	+	3.61674i	−0.587367	+	0.326110i
$124$	−3.80377			−0.341589
$125$	−4.47864			−0.400582
$126$		−	3.56124i		−	0.317261i
$127$	−4.94918			−0.439169			−0.219585	−	0.975593i	$-0.570470\pi$
$127$	−4.94918			−0.439169			−0.219585	+	0.975593i	$0.570470\pi$
$128$	11.1087			0.981876
$129$		−	9.99558i		−	0.880062i
$130$			10.7076i			0.939123i
$131$	1.20234			0.105049			0.0525245	−	0.998620i	$-0.483273\pi$
$131$	1.20234			0.105049			0.0525245	+	0.998620i	$0.483273\pi$
$132$	13.3952			1.16591
$133$	5.64730			0.489683
$134$		−	25.2587i		−	2.18202i
$135$			15.7247i			1.35337i
$136$		−	6.12009i		−	0.524794i
$137$		−	2.95160i		−	0.252172i	−0.992019	−	0.126086i	$-0.959758\pi$
$137$		−	2.95160i		−	0.252172i	0.992019	−	0.126086i	$-0.0402416\pi$
$138$		−	19.0791i		−	1.62412i
$139$	−13.7403			−1.16544			−0.582720	−	0.812673i	$-0.698011\pi$
$139$	−13.7403			−1.16544			−0.582720	+	0.812673i	$0.698011\pi$
$140$			7.79900i			0.659136i
$141$	11.5833			0.975492
$142$			21.6870i			1.81993i
$143$	−7.30475			−0.610854
$144$	−3.57696			−0.298080
$145$			19.7425i			1.63952i
$146$	10.9082			0.902770
$147$		−	1.16363i		−	0.0959750i
$148$	12.3121			1.01205
$149$		−	11.8046i		−	0.967068i	−0.875326	−	0.483534i	$-0.839353\pi$
$149$		−	11.8046i		−	0.967068i	0.875326	−	0.483534i	$-0.160647\pi$
$150$		−	8.71176i		−	0.711312i
$151$			9.04552i			0.736114i	0.929803	+	0.368057i	$0.119977\pi$
$151$			9.04552i			0.736114i	−0.929803	+	0.368057i	$0.880023\pi$
$152$			8.32477i			0.675228i
$153$			6.83352i			0.552457i
$154$	−9.28903			−0.748531
$155$	−4.12627			−0.331430
$156$	5.30864			0.425032
$157$			5.04951i			0.402995i	0.979489	+	0.201497i	$0.0645808\pi$
$157$			5.04951i			0.402995i	−0.979489	+	0.201497i	$0.935419\pi$
$158$		−	0.948232i		−	0.0754373i
$159$	−9.11477			−0.722848
$160$	22.2517			1.75915
$161$			7.57803i			0.597233i
$162$	2.92733			0.229993
$163$	−19.9976			−1.56633			−0.783165	−	0.621814i	$-0.786396\pi$
$163$	−19.9976			−1.56633			−0.783165	+	0.621814i	$0.786396\pi$
$164$	8.33390	+	15.0104i	0.650768	+	1.17212i
$165$	14.5310			1.13123
$166$	19.5483			1.51724
$167$			18.9535i			1.46667i	0.679870	+	0.733333i	$0.262036\pi$
$167$			18.9535i			1.46667i	−0.679870	+	0.733333i	$0.737964\pi$
$168$	1.71533			0.132341
$169$	10.1051			0.777313
$170$		−	26.1277i		−	2.00390i
$171$		−	9.29519i		−	0.710821i
$172$	−23.0324			−1.75620
$173$	−17.4604			−1.32749			−0.663747	−	0.747957i	$-0.731035\pi$
$173$	−17.4604			−1.32749			−0.663747	+	0.747957i	$0.731035\pi$
$174$	17.0888			1.29550
$175$			3.46023i			0.261569i
$176$			9.33001i			0.703276i
$177$		−	3.59720i		−	0.270382i
$178$		−	12.1078i		−	0.907515i
$179$		−	16.3152i		−	1.21946i	−0.792610	−	0.609729i	$-0.791278\pi$
$179$		−	16.3152i		−	1.21946i	0.792610	−	0.609729i	$-0.208722\pi$
$180$	12.8368			0.956799
$181$			3.01306i			0.223959i	0.993711	+	0.111980i	$0.0357191\pi$
$181$			3.01306i			0.223959i	−0.993711	+	0.111980i	$0.964281\pi$
$182$	−3.68131			−0.272877
$183$		−	11.6358i		−	0.860145i
$184$	−11.1709			−0.823530
$185$	13.3559			0.981948
$186$			3.57163i			0.261885i
$187$	17.8243			1.30344
$188$		−	26.6910i		−	1.94664i
$189$	−5.40619			−0.393243
$190$			35.5399i			2.57833i
$191$		−	21.5236i		−	1.55739i	−0.627401	−	0.778697i	$-0.715881\pi$
$191$		−	21.5236i		−	1.55739i	0.627401	−	0.778697i	$-0.284119\pi$
$192$		−	14.2032i		−	1.02503i
$193$		−	21.1906i		−	1.52533i	−0.646791	−	0.762667i	$-0.723890\pi$
$193$		−	21.1906i		−	1.52533i	0.646791	−	0.762667i	$-0.276110\pi$
$194$			20.3281i			1.45947i
$195$	5.75873			0.412391
$196$	−2.68131			−0.191522
$197$	−16.8272			−1.19889			−0.599445	−	0.800416i	$-0.704612\pi$
$197$	−16.8272			−1.19889			−0.599445	+	0.800416i	$0.704612\pi$
$198$			15.2893i			1.08656i
$199$			10.2162i			0.724210i	0.932137	+	0.362105i	$0.117942\pi$
$199$			10.2162i			0.724210i	−0.932137	+	0.362105i	$0.882058\pi$
$200$	−5.10079			−0.360680
$201$	−13.5845			−0.958175
$202$			9.28565i			0.653336i
$203$	−6.78750			−0.476389
$204$	−12.9536			−0.906934
$205$	9.04048	+	16.2831i	0.631415	+	1.13726i
$206$	−18.3420			−1.27795
$207$	12.4731			0.866940
$208$			3.69756i			0.256379i
$209$	−24.2453			−1.67708
$210$	7.32305			0.505338
$211$		−	16.4509i		−	1.13252i	−0.824225	−	0.566262i	$-0.808389\pi$
$211$		−	16.4509i		−	1.13252i	0.824225	−	0.566262i	$-0.191611\pi$
$212$			21.0028i			1.44248i
$213$	11.6636			0.799177
$214$	−30.4584			−2.08209
$215$	−24.9852			−1.70397
$216$		−	7.96936i		−	0.542246i
$217$		−	1.41862i		−	0.0963023i
$218$			21.3962i			1.44913i
$219$		−	5.86659i		−	0.396428i
$220$		−	33.4831i		−	2.25743i
$221$	7.06391			0.475170
$222$		−	11.5607i		−	0.775903i
$223$	−7.91647			−0.530126			−0.265063	−	0.964231i	$-0.585393\pi$
$223$	−7.91647			−0.530126			−0.265063	+	0.964231i	$0.585393\pi$
$224$			7.65020i			0.511151i
$225$	5.69539			0.379692
$226$	−2.31712			−0.154133
$227$			10.2225i			0.678493i	0.940697	+	0.339247i	$0.110172\pi$
$227$			10.2225i			0.678493i	−0.940697	+	0.339247i	$0.889828\pi$
$228$	17.6200			1.16691
$229$		−	10.2922i		−	0.680130i	−0.940402	−	0.340065i	$-0.889551\pi$
$229$		−	10.2922i		−	0.680130i	0.940402	−	0.340065i	$-0.110449\pi$
$230$	−47.6905			−3.14462
$231$			4.99578i			0.328698i
$232$		−	10.0056i		−	0.656898i
$233$		−	5.91268i		−	0.387352i	−0.981066	−	0.193676i	$-0.937959\pi$
$233$		−	5.91268i		−	0.387352i	0.981066	−	0.193676i	$-0.0620411\pi$
$234$			6.05928i			0.396107i
$235$		−	28.9539i		−	1.88875i
$236$	−8.28889			−0.539561
$237$	−0.509973			−0.0331263
$238$	8.98277			0.582266
$239$			2.83068i			0.183102i	0.995800	+	0.0915508i	$0.0291824\pi$
$239$			2.83068i			0.183102i	−0.995800	+	0.0915508i	$0.970818\pi$
$240$		−	7.35536i		−	0.474786i
$241$	9.05177			0.583076			0.291538	−	0.956559i	$-0.405833\pi$
$241$	9.05177			0.583076			0.291538	+	0.956559i	$0.405833\pi$
$242$	16.0801			1.03367
$243$			14.6442i			0.939427i
$244$	−26.8120			−1.71646
$245$	−2.90865			−0.185827
$246$	14.0944	−	7.82530i	0.898626	−	0.498923i
$247$	−9.60859			−0.611380
$248$	2.09121			0.132792
$249$		−	10.5133i		−	0.666256i
$250$	9.69014			0.612858
$251$	15.8376			0.999660			0.499830	−	0.866124i	$-0.333396\pi$
$251$	15.8376			0.999660			0.499830	+	0.866124i	$0.333396\pi$
$252$			4.41332i			0.278013i
$253$		−	32.5344i		−	2.04542i
$254$	10.7082			0.671894
$255$	−14.0519			−0.879962
$256$	0.376678			0.0235424
$257$			10.2210i			0.637567i	0.947828	+	0.318783i	$0.103274\pi$
$257$			10.2210i			0.637567i	−0.947828	+	0.318783i	$0.896726\pi$
$258$			21.6268i			1.34642i
$259$			4.59180i			0.285321i
$260$		−	13.2696i		−	0.822946i
$261$			11.1719i			0.691524i
$262$	−2.60143			−0.160717
$263$			14.7762i			0.911141i	0.890200	+	0.455570i	$0.150565\pi$
$263$			14.7762i			0.911141i	−0.890200	+	0.455570i	$0.849435\pi$
$264$	−7.36435			−0.453245
$265$			22.7835i			1.39958i
$266$	−12.2187			−0.749176
$267$	−6.51173			−0.398511
$268$			31.3021i			1.91208i
$269$	−26.5539			−1.61902			−0.809511	−	0.587105i	$-0.800268\pi$
$269$	−26.5539			−1.61902			−0.809511	+	0.587105i	$0.800268\pi$
$270$		−	34.0225i		−	2.07055i
$271$	−10.3060			−0.626044			−0.313022	−	0.949746i	$-0.601341\pi$
$271$	−10.3060			−0.626044			−0.313022	+	0.949746i	$0.601341\pi$
$272$		−	9.02240i		−	0.547064i
$273$			1.97987i			0.119827i
$274$			6.38619i			0.385804i
$275$		−	14.8556i		−	0.895829i
$276$			23.6440i			1.42320i
$277$	23.3739			1.40440			0.702200	−	0.711979i	$-0.252201\pi$
$277$	23.3739			1.40440			0.702200	+	0.711979i	$0.252201\pi$
$278$	29.7290			1.78303
$279$	−2.33499			−0.139792
$280$		−	4.28768i		−	0.256238i
$281$		−	15.6447i		−	0.933287i	−0.884445	−	0.466644i	$-0.845463\pi$
$281$		−	15.6447i		−	0.933287i	0.884445	−	0.466644i	$-0.154537\pi$
$282$	−25.0621			−1.49242
$283$	−30.0964			−1.78904			−0.894522	−	0.447024i	$-0.852484\pi$
$283$	−30.0964			−1.78904			−0.894522	+	0.447024i	$0.852484\pi$
$284$		−	26.8759i		−	1.59479i
$285$	19.1139			1.13221
$286$	15.8048			0.934558
$287$	−5.59817	+	3.10814i	−0.330449	+	0.183468i
$288$	12.5919			0.741984
$289$	−0.236644			−0.0139202
$290$		−	42.7155i		−	2.50834i
$291$	10.9327			0.640888
$292$	−13.5181			−0.791090
$293$		−	23.4530i		−	1.37014i	−0.728478	−	0.685069i	$-0.759772\pi$
$293$		−	23.4530i		−	1.37014i	0.728478	−	0.685069i	$-0.240228\pi$
$294$			2.51768i			0.146834i
$295$	−8.99165			−0.523514
$296$	−6.76885			−0.393431
$297$	23.2101			1.34679
$298$			25.5408i			1.47954i
$299$		−	12.8936i		−	0.745658i
$300$			10.7962i			0.623317i
$301$		−	8.58996i		−	0.495117i
$302$		−	19.5712i		−	1.12620i
$303$	4.99396			0.286895
$304$			12.2726i			0.703882i
$305$	−29.0852			−1.66541
$306$		−	14.7852i		−	0.845215i
$307$	16.9770			0.968931			0.484465	−	0.874810i	$-0.339014\pi$
$307$	16.9770			0.968931			0.484465	+	0.874810i	$0.339014\pi$
$308$	11.5116			0.655932
$309$			9.86460i			0.561177i
$310$	8.92774			0.507062
$311$			19.7861i			1.12197i	0.827826	+	0.560985i	$0.189577\pi$
$311$			19.7861i			1.12197i	−0.827826	+	0.560985i	$0.810423\pi$
$312$	−2.91855			−0.165230
$313$			2.20526i			0.124648i	0.998056	+	0.0623242i	$0.0198513\pi$
$313$			2.20526i			0.124648i	−0.998056	+	0.0623242i	$0.980149\pi$
$314$		−	10.9253i		−	0.616550i
$315$			4.78750i			0.269745i
$316$			1.17511i			0.0661051i
$317$			24.0464i			1.35058i	0.737552	+	0.675291i	$0.235982\pi$
$317$			24.0464i			1.35058i	−0.737552	+	0.675291i	$0.764018\pi$
$318$	19.7210			1.10590
$319$	29.1405			1.63155
$320$	−35.5026			−1.98466
$321$			16.3810i			0.914297i
$322$		−	16.3961i		−	0.913718i
$323$	23.4459			1.30456
$324$	−3.62774			−0.201541
$325$		−	5.88741i		−	0.326575i
$326$	43.2674			2.39636
$327$	11.5072			0.636349
$328$	−4.58176	−	8.25235i	−0.252985	−	0.455660i
$329$	9.95443			0.548806
$330$	−31.4397			−1.73070
$331$			25.6682i			1.41085i	0.708785	+	0.705425i	$0.249244\pi$
$331$			25.6682i			1.41085i	−0.708785	+	0.705425i	$0.750756\pi$
$332$	−24.2255			−1.32954
$333$	7.55790			0.414170
$334$		−	41.0084i		−	2.24388i
$335$			33.9561i			1.85522i
$336$	2.52879			0.137957
$337$	21.5841			1.17576			0.587882	−	0.808947i	$-0.299962\pi$
$337$	21.5841			1.17576			0.587882	+	0.808947i	$0.299962\pi$
$338$	−21.8637			−1.18923
$339$			1.24618i			0.0676834i
$340$			32.3791i			1.75601i
$341$			6.09050i			0.329819i
$342$			20.1114i			1.08750i
$343$		−	1.00000i		−	0.0539949i
$344$	12.6626			0.682722
$345$			25.6486i			1.38088i
$346$	37.7780			2.03096
$347$		−	0.720820i		−	0.0386956i	−0.999813	−	0.0193478i	$-0.993841\pi$
$347$		−	0.720820i		−	0.0386956i	0.999813	−	0.0193478i	$-0.00615899\pi$
$348$	−21.1775			−1.13523
$349$	5.09905			0.272946			0.136473	−	0.990644i	$-0.456423\pi$
$349$	5.09905			0.272946			0.136473	+	0.990644i	$0.456423\pi$
$350$		−	7.48668i		−	0.400180i
$351$	9.19836			0.490972
$352$		−	32.8442i		−	1.75060i
$353$	35.4010			1.88421			0.942103	−	0.335323i	$-0.108846\pi$
$353$	35.4010			1.88421			0.942103	+	0.335323i	$0.108846\pi$
$354$			7.78304i			0.413664i
$355$		−	29.1546i		−	1.54737i
$356$			15.0047i			0.795248i
$357$		−	4.83107i		−	0.255687i
$358$			35.3002i			1.86567i
$359$	3.74660			0.197738			0.0988690	−	0.995100i	$-0.468478\pi$
$359$	3.74660			0.197738			0.0988690	+	0.995100i	$0.468478\pi$
$360$	−7.05733			−0.371954
$361$	−12.8920			−0.678524
$362$		−	6.51916i		−	0.342640i
$363$		−	8.64814i		−	0.453910i
$364$	4.56212			0.239120
$365$	−14.6643			−0.767563
$366$			25.1757i			1.31595i
$367$	−30.6358			−1.59917			−0.799587	−	0.600550i	$-0.794948\pi$
$367$	−30.6358			−1.59917			−0.799587	+	0.600550i	$0.794948\pi$
$368$	−16.4684			−0.858476
$369$	5.11586	+	9.21433i	0.266321	+	0.479679i
$370$	−28.8974			−1.50230
$371$	−7.83302			−0.406670
$372$		−	4.42620i		−	0.229488i
$373$	6.52113			0.337651			0.168826	−	0.985646i	$-0.446003\pi$
$373$	6.52113			0.337651			0.168826	+	0.985646i	$0.446003\pi$
$374$	−38.5653			−1.99416
$375$		−	5.21150i		−	0.269121i
$376$			14.6740i			0.756753i
$377$	11.5486			0.594783
$378$	11.6970			0.601630
$379$	−7.13618			−0.366561			−0.183280	−	0.983061i	$-0.558672\pi$
$379$	−7.13618			−0.366561			−0.183280	+	0.983061i	$0.558672\pi$
$380$		−	44.0433i		−	2.25937i
$381$		−	5.75904i		−	0.295045i
$382$			46.5692i			2.38269i
$383$		−	8.92538i		−	0.456066i	−0.973653	−	0.228033i	$-0.926771\pi$
$383$		−	8.92538i		−	0.456066i	0.973653	−	0.228033i	$-0.0732294\pi$
$384$			12.9264i			0.659649i
$385$	12.4876			0.636425
$386$			45.8488i			2.33364i
$387$	−14.1387			−0.718710
$388$		−	25.1918i		−	1.27892i
$389$	−4.94005			−0.250471			−0.125235	−	0.992127i	$-0.539969\pi$
$389$	−4.94005			−0.250471			−0.125235	+	0.992127i	$0.539969\pi$
$390$	−12.4598			−0.630926
$391$			31.4617i			1.59109i
$392$	1.47412			0.0744541
$393$			1.39909i			0.0705746i
$394$	36.4080			1.83421
$395$			1.27474i			0.0641392i
$396$		−	18.9475i		−	0.952148i
$397$			3.84071i			0.192760i	0.995345	+	0.0963798i	$0.0307263\pi$
$397$			3.84071i			0.192760i	−0.995345	+	0.0963798i	$0.969274\pi$
$398$		−	22.1042i		−	1.10798i
$399$			6.57139i			0.328981i
$400$	−7.51971			−0.375986
$401$	0.159243			0.00795222			0.00397611	−	0.999992i	$-0.498734\pi$
$401$	0.159243			0.00795222			0.00397611	+	0.999992i	$0.498734\pi$
$402$	29.3918			1.46593
$403$			2.41371i			0.120236i
$404$		−	11.5074i		−	0.572513i
$405$	−3.93531			−0.195547
$406$	14.6857			0.728838
$407$		−	19.7138i		−	0.977175i
$408$	7.12155			0.352569
$409$	−23.4483			−1.15944			−0.579722	−	0.814814i	$-0.696839\pi$
$409$	−23.4483			−1.15944			−0.579722	+	0.814814i	$0.696839\pi$
$410$	−19.5603	−	35.2307i	−0.966015	−	1.73992i
$411$	3.43459			0.169416
$412$	22.7306			1.11986
$413$		−	3.09135i		−	0.152115i
$414$	−26.9872			−1.32635
$415$	−26.2794			−1.29000
$416$		−	13.0164i		−	0.638183i
$417$		−	15.9887i		−	0.782971i
$418$	52.4579			2.56580
$419$	11.9088			0.581782			0.290891	−	0.956756i	$-0.406048\pi$
$419$	11.9088			0.581782			0.290891	+	0.956756i	$0.406048\pi$
$420$	−9.07519			−0.442824
$421$			1.20166i			0.0585652i	0.999571	+	0.0292826i	$0.00932227\pi$
$421$			1.20166i			0.0585652i	−0.999571	+	0.0292826i	$0.990678\pi$
$422$			35.5936i			1.73267i
$423$		−	16.3845i		−	0.796644i
$424$		−	11.5468i		−	0.560761i
$425$			14.3659i			0.696847i
$426$	−25.2358			−1.22268
$427$		−	9.99956i		−	0.483913i
$428$	37.7460			1.82452
$429$		−	8.50006i		−	0.410387i
$430$	54.0588			2.60695
$431$	−22.0097			−1.06017			−0.530085	−	0.847945i	$-0.677840\pi$
$431$	−22.0097			−1.06017			−0.530085	+	0.847945i	$0.677840\pi$
$432$		−	11.7486i		−	0.565256i
$433$	−19.9839			−0.960367			−0.480184	−	0.877168i	$-0.659430\pi$
$433$	−19.9839			−0.960367			−0.480184	+	0.877168i	$0.659430\pi$
$434$			3.06938i			0.147335i
$435$	−22.9730			−1.10147
$436$		−	26.5155i		−	1.26986i
$437$		−	42.7954i		−	2.04718i
$438$			12.6932i			0.606503i
$439$		−	6.17043i		−	0.294499i	−0.989099	−	0.147249i	$-0.952958\pi$
$439$		−	6.17043i		−	0.294499i	0.989099	−	0.147249i	$-0.0470420\pi$
$440$			18.4081i			0.877572i
$441$	−1.64595			−0.0783788
$442$	−15.2837			−0.726973
$443$	−26.6708			−1.26717			−0.633583	−	0.773674i	$-0.718417\pi$
$443$	−26.6708			−1.26717			−0.633583	+	0.773674i	$0.718417\pi$
$444$			14.3267i			0.679917i
$445$			16.2769i			0.771598i
$446$	17.1283			0.811051
$447$	13.7362			0.649700
$448$		−	12.2059i		−	0.576674i
$449$	26.3172			1.24199			0.620994	−	0.783816i	$-0.286729\pi$
$449$	26.3172			1.24199			0.620994	+	0.783816i	$0.286729\pi$
$450$	−12.3227			−0.580899
$451$	24.0343	−	13.3440i	1.13173	−	0.628346i
$452$	2.87153			0.135065
$453$	−10.5257			−0.494539
$454$		−	22.1178i		−	1.03804i
$455$	4.94892			0.232009
$456$	−9.68699			−0.453635
$457$			30.8713i			1.44410i	0.691842	+	0.722049i	$0.256800\pi$
$457$			30.8713i			1.44410i	−0.691842	+	0.722049i	$0.743200\pi$
$458$			22.2686i			1.04055i
$459$	−22.4449			−1.04764
$460$	59.1011			2.75560
$461$	17.8208			0.829995			0.414998	−	0.909822i	$-0.363782\pi$
$461$	17.8208			0.829995			0.414998	+	0.909822i	$0.363782\pi$
$462$		−	10.8090i		−	0.502882i
$463$			15.1200i			0.702688i	0.936246	+	0.351344i	$0.114275\pi$
$463$			15.1200i			0.702688i	−0.936246	+	0.351344i	$0.885725\pi$
$464$		−	14.7505i		−	0.684773i
$465$		−	4.80147i		−	0.222663i
$466$			12.7929i			0.592618i
$467$	12.1778			0.563522			0.281761	−	0.959485i	$-0.409081\pi$
$467$	12.1778			0.563522			0.281761	+	0.959485i	$0.409081\pi$
$468$		−	7.50904i		−	0.347106i
$469$	−11.6742			−0.539063
$470$			62.6457i			2.88963i
$471$	−5.87579			−0.270742
$472$	4.55701			0.209753
$473$			36.8789i			1.69569i
$474$	1.10340			0.0506807
$475$		−	19.5410i		−	0.896601i
$476$	−11.1320			−0.510235
$477$			12.8928i			0.590320i
$478$		−	6.12456i		−	0.280131i
$479$			33.9244i			1.55005i	0.631934	+	0.775023i	$0.282262\pi$
$479$			33.9244i			1.55005i	−0.631934	+	0.775023i	$0.717738\pi$
$480$			25.8929i			1.18184i
$481$		−	7.81272i		−	0.356229i
$482$	−19.5847			−0.892059
$483$	−8.81806			−0.401236
$484$	−19.9276			−0.905798
$485$		−	27.3277i		−	1.24089i
$486$		−	31.6847i		−	1.43725i
$487$	−32.8823			−1.49004			−0.745020	−	0.667042i	$-0.767560\pi$
$487$	−32.8823			−1.49004			−0.745020	+	0.667042i	$0.767560\pi$
$488$	14.7405			0.667271
$489$		−	23.2698i		−	1.05230i
$490$	6.29325			0.284300
$491$	21.1915			0.956359			0.478179	−	0.878262i	$-0.341297\pi$
$491$	21.1915			0.956359			0.478179	+	0.878262i	$0.341297\pi$
$492$	−17.4667	+	9.69762i	−0.787459	+	0.437202i
$493$	−28.1797			−1.26915
$494$	20.7895			0.935363
$495$		−	20.5540i		−	0.923831i
$496$	3.08292			0.138427
$497$	10.0234			0.449612
$498$			22.7470i			1.01932i
$499$		−	16.7642i		−	0.750469i	−0.926930	−	0.375234i	$-0.877562\pi$
$499$		−	16.7642i		−	0.750469i	0.926930	−	0.375234i	$-0.122438\pi$
$500$	−12.0086			−0.537043
$501$	−22.0549			−0.985342
$502$	−34.2668			−1.52940
$503$		−	27.9230i		−	1.24502i	−0.782611	−	0.622512i	$-0.786112\pi$
$503$		−	27.9230i		−	1.24502i	0.782611	−	0.622512i	$-0.213888\pi$
$504$		−	2.42633i		−	0.108077i
$505$		−	12.4830i		−	0.555487i
$506$			70.3925i			3.12933i
$507$			11.7586i			0.522218i
$508$	−13.2703			−0.588775
$509$			20.7134i			0.918105i	0.888409	+	0.459053i	$0.151811\pi$
$509$			20.7134i			0.918105i	−0.888409	+	0.459053i	$0.848189\pi$
$510$	30.4031			1.34627
$511$		−	5.04161i		−	0.223028i
$512$	−23.0323			−1.01789
$513$	30.5304			1.34795
$514$		−	22.1144i		−	0.975426i
$515$	24.6578			1.08655
$516$		−	26.8013i		−	1.17986i
$517$	−42.7369			−1.87957
$518$		−	9.93498i		−	0.436518i
$519$		−	20.3176i		−	0.891843i
$520$			7.29528i			0.319919i
$521$			39.7393i			1.74101i	0.492161	+	0.870504i	$0.336207\pi$
$521$			39.7393i			1.74101i	−0.492161	+	0.870504i	$0.663793\pi$
$522$		−	24.1720i		−	1.05798i
$523$	−23.9247			−1.04615			−0.523077	−	0.852285i	$-0.675216\pi$
$523$	−23.9247			−1.04615			−0.523077	+	0.852285i	$0.675216\pi$
$524$	3.22386			0.140835
$525$	−4.02645			−0.175729
$526$		−	31.9703i		−	1.39397i
$527$		−	5.88970i		−	0.256559i
$528$	−10.8567			−0.472478
$529$	34.4266			1.49681
$530$		−	49.2952i		−	2.14124i
$531$	−5.08822			−0.220810
$532$	15.1422			0.656497
$533$	9.52500	−	5.28834i	0.412573	−	0.229064i
$534$	14.0890			0.609691
$535$	40.9462			1.77026
$536$		−	17.2091i		−	0.743320i
$537$	18.9850			0.819262
$538$	57.4530			2.47697
$539$			4.29325i			0.184923i
$540$			42.1629i			1.81440i
$541$	−2.85132			−0.122588			−0.0612939	−	0.998120i	$-0.519523\pi$
$541$	−2.85132			−0.122588			−0.0612939	+	0.998120i	$0.519523\pi$
$542$	22.2984			0.957797
$543$	−3.50610			−0.150461
$544$			31.7614i			1.36176i
$545$		−	28.7636i		−	1.23210i
$546$		−	4.28371i		−	0.183326i
$547$			18.2680i			0.781084i	0.920585	+	0.390542i	$0.127712\pi$
$547$			18.2680i			0.781084i	−0.920585	+	0.390542i	$0.872288\pi$
$548$		−	7.91417i		−	0.338077i
$549$	−16.4588			−0.702445
$550$			32.1422i			1.37055i
$551$	38.3310			1.63296
$552$		−	12.9988i		−	0.553268i
$553$	−0.438259			−0.0186367
$554$	−50.5726			−2.14862
$555$			15.5414i			0.659697i
$556$	−36.8421			−1.56245
$557$			31.7596i			1.34570i	0.739779	+	0.672850i	$0.234930\pi$
$557$			31.7596i			1.34570i	−0.739779	+	0.672850i	$0.765070\pi$
$558$	5.05206			0.213871
$559$			14.6154i			0.618165i
$560$		−	6.32102i		−	0.267112i
$561$			20.7410i			0.875685i
$562$			33.8495i			1.42786i
$563$			23.3559i			0.984334i	0.870501	+	0.492167i	$0.163795\pi$
$563$			23.3559i			0.984334i	−0.870501	+	0.492167i	$0.836205\pi$
$564$	31.0585			1.30780
$565$	3.11499			0.131049
$566$	65.1176			2.73710
$567$		−	1.35297i		−	0.0568194i
$568$			14.7757i			0.619974i
$569$	29.1746			1.22306			0.611531	−	0.791221i	$-0.290554\pi$
$569$	29.1746			1.22306			0.611531	+	0.791221i	$0.290554\pi$
$570$	−41.3554			−1.73219
$571$		−	13.4241i		−	0.561782i	−0.959740	−	0.280891i	$-0.909370\pi$
$571$		−	13.4241i		−	0.561782i	0.959740	−	0.280891i	$-0.0906299\pi$
$572$	−19.5863			−0.818946
$573$	25.0456			1.04630
$574$	12.1124	−	6.72488i	0.505561	−	0.280691i
$575$	26.2218			1.09352
$576$	−20.0903			−0.837097
$577$		−	24.2268i		−	1.00857i	−0.863536	−	0.504287i	$-0.831755\pi$
$577$		−	24.2268i		−	1.00857i	0.863536	−	0.504287i	$-0.168245\pi$
$578$	0.512011			0.0212968
$579$	24.6581			1.02476
$580$			52.9357i			2.19804i
$581$		−	9.03492i		−	0.374832i
$582$	−23.6544			−0.980508
$583$	33.6291			1.39278
$584$	7.43192			0.307535
$585$		−	8.14569i		−	0.336783i
$586$			50.7437i			2.09620i
$587$		−	35.1063i		−	1.44899i	−0.689279	−	0.724496i	$-0.742073\pi$
$587$		−	35.1063i		−	1.44899i	0.689279	−	0.724496i	$-0.257927\pi$
$588$		−	3.12007i		−	0.128670i
$589$			8.01138i			0.330103i
$590$	19.4547			0.800935
$591$		−	19.5807i		−	0.805444i
$592$	−9.97882			−0.410127
$593$		−	2.98320i		−	0.122505i	−0.998122	−	0.0612527i	$-0.980490\pi$
$593$		−	2.98320i		−	0.122505i	0.998122	−	0.0612527i	$-0.0195096\pi$
$594$	−50.2183			−2.06048
$595$	−12.0758			−0.495061
$596$		−	31.6518i		−	1.29651i
$597$	−11.8880			−0.486542
$598$			27.8971i			1.14080i
$599$	−3.28952			−0.134406			−0.0672031	−	0.997739i	$-0.521408\pi$
$599$	−3.28952			−0.134406			−0.0672031	+	0.997739i	$0.521408\pi$
$600$		−	5.93545i		−	0.242314i
$601$		−	39.4451i		−	1.60900i	−0.593954	−	0.804499i	$-0.702434\pi$
$601$		−	39.4451i		−	1.60900i	0.593954	−	0.804499i	$-0.297566\pi$
$602$			18.5855i			0.757490i
$603$			19.2152i			0.782502i
$604$			24.2539i			0.986876i
$605$	−21.6171			−0.878860
$606$	−10.8051			−0.438927
$607$	−27.5019			−1.11627			−0.558135	−	0.829750i	$-0.688483\pi$
$607$	−27.5019			−1.11627			−0.558135	+	0.829750i	$0.688483\pi$
$608$		−	43.2030i		−	1.75211i
$609$		−	7.89817i		−	0.320050i
$610$	62.9297			2.54795
$611$	−16.9370			−0.685196
$612$			18.3228i			0.740656i
$613$	−1.19432			−0.0482381			−0.0241191	−	0.999709i	$-0.507678\pi$
$613$	−1.19432			−0.0482381			−0.0241191	+	0.999709i	$0.507678\pi$
$614$	−36.7321			−1.48239
$615$	−18.9476	+	10.5198i	−0.764040	+	0.424200i
$616$	−6.32875			−0.254993
$617$	−31.9618			−1.28674			−0.643368	−	0.765557i	$-0.722463\pi$
$617$	−31.9618			−1.28674			−0.643368	+	0.765557i	$0.722463\pi$
$618$		−	21.3434i		−	0.858557i
$619$	−0.728517			−0.0292816			−0.0146408	−	0.999893i	$-0.504660\pi$
$619$	−0.728517			−0.0292816			−0.0146408	+	0.999893i	$0.504660\pi$
$620$	−11.0638			−0.444334
$621$			40.9683i			1.64400i
$622$		−	42.8100i		−	1.71652i
$623$	−5.59603			−0.224200
$624$	−4.30261			−0.172242
$625$	−30.3280			−1.21312
$626$		−	4.77137i		−	0.190702i
$627$		−	28.2126i		−	1.12670i
$628$			13.5393i			0.540278i
$629$			19.0638i			0.760124i
$630$		−	10.3584i		−	0.412689i
$631$	23.0402			0.917217			0.458608	−	0.888639i	$-0.348348\pi$
$631$	23.0402			0.917217			0.458608	+	0.888639i	$0.348348\pi$
$632$		−	0.646045i		−	0.0256983i
$633$	19.1428			0.760857
$634$		−	52.0277i		−	2.06628i
$635$	−14.3954			−0.571265
$636$	−24.4396			−0.969092
$637$			1.70145i			0.0674139i
$638$	−63.0493			−2.49615
$639$		−	16.4981i		−	0.652654i
$640$	32.3112			1.27721
$641$		−	27.4319i		−	1.08350i	−0.840541	−	0.541748i	$-0.817763\pi$
$641$		−	27.4319i		−	1.08350i	0.840541	−	0.541748i	$-0.182237\pi$
$642$		−	35.4424i		−	1.39880i
$643$			4.00945i			0.158117i	0.996870	+	0.0790586i	$0.0251914\pi$
$643$			4.00945i			0.158117i	−0.996870	+	0.0790586i	$0.974809\pi$
$644$			20.3191i			0.800684i
$645$		−	29.0736i		−	1.14477i
$646$	−50.7284			−1.99588
$647$	22.7745			0.895357			0.447678	−	0.894195i	$-0.352251\pi$
$647$	22.7745			0.895357			0.447678	+	0.894195i	$0.352251\pi$
$648$	1.99444			0.0783488
$649$			13.2720i			0.520970i
$650$			12.7382i			0.499634i
$651$	1.65076			0.0646983
$652$	−53.6197			−2.09991
$653$		−	42.0071i		−	1.64387i	−0.569584	−	0.821933i	$-0.692896\pi$
$653$		−	42.0071i		−	1.64387i	0.569584	−	0.821933i	$-0.307104\pi$
$654$	−24.8974			−0.973564
$655$	3.49719			0.136646
$656$	−6.75455	−	12.1658i	−0.263721	−	0.474996i
$657$	−8.29826			−0.323746
$658$	−21.5378			−0.839629
$659$			26.1306i			1.01790i	0.860795	+	0.508952i	$0.169967\pi$
$659$			26.1306i			1.01790i	−0.860795	+	0.508952i	$0.830033\pi$
$660$	38.9621			1.51660
$661$	12.1558			0.472807			0.236403	−	0.971655i	$-0.424031\pi$
$661$	12.1558			0.472807			0.236403	+	0.971655i	$0.424031\pi$
$662$		−	55.5365i		−	2.15849i
$663$			8.21981i			0.319231i
$664$	13.3185			0.516859
$665$	16.4260			0.636973
$666$	−16.3525			−0.633648
$667$			51.4359i			1.99161i
$668$			50.8203i			1.96630i
$669$		−	9.21188i		−	0.356152i
$670$		−	73.4685i		−	2.83834i
$671$			42.9306i			1.65732i
$672$	−8.90204			−0.343404
$673$		−	8.01953i		−	0.309130i	−0.987983	−	0.154565i	$-0.950602\pi$
$673$		−	8.01953i		−	0.309130i	0.987983	−	0.154565i	$-0.0493977\pi$
$674$	−46.7002			−1.79883
$675$			18.7067i			0.720021i
$676$	27.0949			1.04211
$677$	−1.84922			−0.0710713			−0.0355356	−	0.999368i	$-0.511314\pi$
$677$	−1.84922			−0.0710713			−0.0355356	+	0.999368i	$0.511314\pi$
$678$		−	2.69628i		−	0.103550i
$679$	9.39533			0.360560
$680$		−	17.8012i		−	0.682645i
$681$	−11.8953			−0.455829
$682$		−	13.1776i		−	0.504597i
$683$			17.6789i			0.676463i	0.941063	+	0.338232i	$0.109829\pi$
$683$			17.6789i			0.676463i	−0.941063	+	0.338232i	$0.890171\pi$
$684$		−	24.9233i		−	0.952968i
$685$		−	8.58517i		−	0.328023i
$686$			2.16363i			0.0826080i
$687$	11.9764			0.456928
$688$	18.6675			0.711693
$689$	13.3275			0.507737
$690$		−	55.4943i		−	2.11263i
$691$			12.3366i			0.469306i	0.972079	+	0.234653i	$0.0753954\pi$
$691$			12.3366i			0.469306i	−0.972079	+	0.234653i	$0.924605\pi$
$692$	−46.8170			−1.77971
$693$	7.06650			0.268434
$694$			1.55959i			0.0592013i
$695$	−39.9658			−1.51599
$696$	11.6428			0.441320
$697$	−23.2419	+	12.9041i	−0.880351	+	0.488777i
$698$	−11.0325			−0.417585
$699$	6.88019			0.260233
$700$			9.27797i			0.350674i
$701$	−16.4749			−0.622248			−0.311124	−	0.950369i	$-0.600706\pi$
$701$	−16.4749			−0.622248			−0.311124	+	0.950369i	$0.600706\pi$
$702$	−19.9019			−0.751149
$703$		−	25.9313i		−	0.978016i
$704$			52.4029i			1.97501i
$705$	33.6918			1.26891
$706$	−76.5949			−2.88269
$707$	4.29169			0.161406
$708$		−	9.64524i		−	0.362490i
$709$		−	8.35947i		−	0.313947i	−0.987603	−	0.156973i	$-0.949826\pi$
$709$		−	8.35947i		−	0.313947i	0.987603	−	0.156973i	$-0.0501737\pi$
$710$			63.0799i			2.36735i
$711$			0.721354i			0.0270529i
$712$		−	8.24919i		−	0.309152i
$713$	−10.7504			−0.402604
$714$			10.4527i			0.391181i
$715$	−21.2469			−0.794591
$716$		−	43.7463i		−	1.63487i
$717$	−3.29388			−0.123012
$718$	−8.10627			−0.302523
$719$		−	28.7363i		−	1.07168i	−0.844318	−	0.535842i	$-0.819994\pi$
$719$		−	28.7363i		−	1.07168i	0.844318	−	0.535842i	$-0.180006\pi$
$720$	−10.4041			−0.387738
$721$			8.47740i			0.315715i
$722$	27.8935			1.03809
$723$			10.5330i			0.391725i
$724$			8.07896i			0.300252i
$725$			23.4863i			0.872261i
$726$			18.7114i			0.694446i
$727$			31.3355i			1.16217i	0.813843	+	0.581085i	$0.197372\pi$
$727$			31.3355i			1.16217i	−0.813843	+	0.581085i	$0.802628\pi$
$728$	−2.50813			−0.0929576
$729$	−21.0994			−0.781460
$730$	31.7281			1.17431
$731$		−	35.6630i		−	1.31904i
$732$		−	31.1993i		−	1.15316i
$733$	−35.4817			−1.31055			−0.655273	−	0.755392i	$-0.727446\pi$
$733$	−35.4817			−1.31055			−0.655273	+	0.755392i	$0.727446\pi$
$734$	66.2846			2.44661
$735$		−	3.38460i		−	0.124843i
$736$	57.9735			2.13693
$737$	50.1202			1.84620
$738$	−11.0688	−	19.9364i	−0.407450	−	0.733870i
$739$	52.6462			1.93662			0.968311	−	0.249746i	$-0.0803470\pi$
$739$	52.6462			1.93662			0.968311	+	0.249746i	$0.0803470\pi$
$740$	35.8115			1.31646
$741$		−	11.1809i		−	0.410740i
$742$	16.9478			0.622173
$743$	−10.5631			−0.387523			−0.193761	−	0.981049i	$-0.562069\pi$
$743$	−10.5631			−0.387523			−0.193761	+	0.981049i	$0.562069\pi$
$744$			2.43341i			0.0892130i
$745$		−	34.3353i		−	1.25795i
$746$	−14.1093			−0.516580
$747$	−14.8711			−0.544104
$748$	47.7926			1.74747
$749$			14.0774i			0.514378i
$750$			11.2758i			0.411733i
$751$		−	2.79252i		−	0.101900i	−0.998701	−	0.0509502i	$-0.983775\pi$
$751$		−	2.79252i		−	0.101900i	0.998701	−	0.0509502i	$-0.0162250\pi$
$752$			21.6328i			0.788866i
$753$			18.4292i			0.671596i
$754$	−24.9869			−0.909970
$755$			26.3102i			0.957527i
$756$	−14.4957			−0.527204
$757$		−	29.7727i		−	1.08211i	−0.840988	−	0.541054i	$-0.818026\pi$
$757$		−	29.7727i		−	1.08211i	0.840988	−	0.541054i	$-0.181974\pi$
$758$	15.4401			0.560809
$759$	37.8581			1.37416
$760$			24.2138i			0.878328i
$761$	12.8254			0.464921			0.232461	−	0.972606i	$-0.425322\pi$
$761$	12.8254			0.464921			0.232461	+	0.972606i	$0.425322\pi$
$762$			12.4605i			0.451395i
$763$	9.88901			0.358006
$764$		−	57.7116i		−	2.08793i
$765$			19.8763i			0.718629i
$766$			19.3113i			0.697744i
$767$			5.25978i			0.189920i
$768$			0.438315i			0.0158163i
$769$	49.3635			1.78009			0.890047	−	0.455869i	$-0.150672\pi$
$769$	49.3635			1.78009			0.890047	+	0.455869i	$0.150672\pi$
$770$	−27.0185			−0.973680
$771$	−11.8935			−0.428333
$772$		−	56.8187i		−	2.04495i
$773$		−	43.7832i		−	1.57477i	−0.616461	−	0.787385i	$-0.711434\pi$
$773$		−	43.7832i		−	1.57477i	0.616461	−	0.787385i	$-0.288566\pi$
$774$	30.5910			1.09957
$775$	−4.90876			−0.176328
$776$			13.8498i			0.497179i
$777$	−5.34318			−0.191686
$778$	10.6885			0.383200
$779$	31.6145	−	17.5526i	1.13271	−	0.628887i
$780$	15.4410			0.552875
$781$	−43.0331			−1.53984
$782$		−	68.0717i		−	2.43424i
$783$	−36.6945			−1.31136
$784$	2.17318			0.0776136
$785$			14.6872i			0.524210i
$786$		−	3.02711i		−	0.107974i
$787$	38.8181			1.38371			0.691857	−	0.722034i	$-0.256793\pi$
$787$	38.8181			1.38371			0.691857	+	0.722034i	$0.256793\pi$
$788$	−45.1191			−1.60730
$789$	−17.1941			−0.612127
$790$		−	2.75807i		−	0.0981279i
$791$			1.07094i			0.0380782i
$792$			10.4168i			0.370146i
$793$			17.0137i			0.604176i
$794$		−	8.30988i		−	0.294907i
$795$	−26.5117			−0.940272
$796$			27.3929i			0.970917i
$797$	−43.1918			−1.52993			−0.764965	−	0.644072i	$-0.777244\pi$
$797$	−43.1918			−1.52993			−0.764965	+	0.644072i	$0.777244\pi$
$798$		−	14.2181i		−	0.503315i
$799$	41.3279			1.46207
$800$	26.4715			0.935908
$801$			9.21080i			0.325448i
$802$	−0.344544			−0.0121663
$803$			21.6449i			0.763832i
$804$	−36.4243			−1.28458
$805$			22.0418i			0.776872i
$806$		−	5.22239i		−	0.183951i
$807$		−	30.8991i		−	1.08770i
$808$			6.32645i			0.222564i
$809$			54.2891i			1.90870i	0.298685	+	0.954352i	$0.403452\pi$
$809$			54.2891i			1.90870i	−0.298685	+	0.954352i	$0.596548\pi$
$810$	8.51458			0.299172
$811$	2.77969			0.0976082			0.0488041	−	0.998808i	$-0.484459\pi$
$811$	2.77969			0.0976082			0.0488041	+	0.998808i	$0.484459\pi$
$812$	−18.1994			−0.638675
$813$		−	11.9924i		−	0.420592i
$814$			42.6534i			1.49500i
$815$	−58.1658			−2.03746
$816$	10.4988			0.367531
$817$			48.5101i			1.69715i
$818$	50.7336			1.77386
$819$	2.80051			0.0978577
$820$	24.2404	+	43.6601i	0.846511	+	1.52468i
$821$	21.4820			0.749728			0.374864	−	0.927080i	$-0.377689\pi$
$821$	21.4820			0.749728			0.374864	+	0.927080i	$0.377689\pi$
$822$	−7.43119			−0.259193
$823$		−	21.9922i		−	0.766599i	−0.923624	−	0.383300i	$-0.874788\pi$
$823$		−	21.9922i		−	0.766599i	0.923624	−	0.383300i	$-0.125212\pi$
$824$	−12.4967			−0.435342
$825$	17.2865			0.601840
$826$			6.68856i			0.232725i
$827$			39.3801i			1.36938i	0.728834	+	0.684691i	$0.240063\pi$
$827$			39.3801i			1.36938i	−0.728834	+	0.684691i	$0.759937\pi$
$828$	33.4443			1.16227
$829$	−22.6430			−0.786423			−0.393211	−	0.919448i	$-0.628636\pi$
$829$	−22.6430			−0.786423			−0.393211	+	0.919448i	$0.628636\pi$
$830$	56.8590			1.97361
$831$			27.1987i			0.943511i
$832$			20.7677i			0.719990i
$833$		−	4.15170i		−	0.143848i
$834$			34.5937i			1.19788i
$835$			55.1290i			1.90782i
$836$	−65.0092			−2.24839
$837$		−	7.66934i		−	0.265091i
$838$	−25.7662			−0.890080
$839$			24.1764i			0.834660i	0.908755	+	0.417330i	$0.137034\pi$
$839$			24.1764i			0.834660i	−0.908755	+	0.417330i	$0.862966\pi$
$840$	4.98930			0.172147
$841$	−17.0702			−0.588627
$842$		−	2.59995i		−	0.0896001i
$843$	18.2048			0.627006
$844$		−	44.1099i		−	1.51833i
$845$	29.3921			1.01112
$846$			35.4502i			1.21880i
$847$		−	7.43201i		−	0.255367i
$848$		−	17.0226i		−	0.584557i
$849$		−	35.0212i		−	1.20192i
$850$		−	31.0825i		−	1.06612i
$851$	34.7968			1.19282
$852$	31.2738			1.07142
$853$	13.9967			0.479237			0.239619	−	0.970867i	$-0.422978\pi$
$853$	13.9967			0.479237			0.239619	+	0.970867i	$0.422978\pi$
$854$			21.6354i			0.740348i
$855$		−	27.0364i		−	0.924627i
$856$	−20.7517			−0.709280
$857$	30.3896			1.03809			0.519045	−	0.854747i	$-0.326288\pi$
$857$	30.3896			1.03809			0.519045	+	0.854747i	$0.326288\pi$
$858$			18.3910i			0.627859i
$859$	22.1368			0.755298			0.377649	−	0.925949i	$-0.376733\pi$
$859$	22.1368			0.755298			0.377649	+	0.925949i	$0.376733\pi$
$860$	−66.9931			−2.28445
$861$	−3.61674	−	6.51422i	−0.123258	−	0.222004i
$862$	47.6209			1.62198
$863$	47.2813			1.60947			0.804737	−	0.593631i	$-0.202306\pi$
$863$	47.2813			1.60947			0.804737	+	0.593631i	$0.202306\pi$
$864$			41.3585i			1.40704i
$865$	−50.7863			−1.72679
$866$	43.2380			1.46929
$867$		−	0.275367i		−	0.00935195i
$868$		−	3.80377i		−	0.129108i
$869$	1.88156			0.0638274
$870$	49.7052			1.68516
$871$	19.8630			0.673033
$872$			14.5775i			0.493658i
$873$		−	15.4643i		−	0.523387i
$874$			92.5936i			3.13203i
$875$		−	4.47864i		−	0.151406i
$876$		−	15.7302i		−	0.531474i
$877$	−14.3889			−0.485877			−0.242939	−	0.970042i	$-0.578111\pi$
$877$	−14.3889			−0.485877			−0.242939	+	0.970042i	$0.578111\pi$
$878$			13.3506i			0.450560i
$879$	27.2907			0.920493
$880$			27.1377i			0.914812i
$881$	35.6170			1.19997			0.599984	−	0.800012i	$-0.295174\pi$
$881$	35.6170			1.19997			0.599984	+	0.800012i	$0.295174\pi$
$882$	3.56124			0.119913
$883$		−	21.1974i		−	0.713351i	−0.934228	−	0.356675i	$-0.883910\pi$
$883$		−	21.1974i		−	0.713351i	0.934228	−	0.356675i	$-0.116090\pi$
$884$	18.9406			0.637041
$885$		−	10.4630i		−	0.351710i
$886$	57.7058			1.93866
$887$			46.4641i			1.56011i	0.625709	+	0.780056i	$0.284810\pi$
$887$			46.4641i			1.56011i	−0.625709	+	0.780056i	$0.715190\pi$
$888$		−	7.87647i		−	0.264317i
$889$		−	4.94918i		−	0.165990i
$890$		−	35.2172i		−	1.18048i
$891$			5.80864i			0.194597i
$892$	−21.2265			−0.710717
$893$	−56.2156			−1.88118
$894$	−29.7201			−0.993990
$895$		−	47.4552i		−	1.58625i
$896$			11.1087i			0.371114i
$897$	15.0035			0.500952
$898$	−56.9409			−1.90014
$899$		−	9.62889i		−	0.321142i
$900$	15.2711			0.509037
$901$	−32.5204			−1.08341
$902$	−52.0015	+	28.8716i	−1.73146	+	0.961319i
$903$	9.99558			0.332632
$904$	−1.57869			−0.0525065
$905$			8.76393i			0.291323i
$906$	22.7737			0.756606
$907$	4.87109			0.161742			0.0808709	−	0.996725i	$-0.474230\pi$
$907$	4.87109			0.161742			0.0808709	+	0.996725i	$0.474230\pi$
$908$			27.4098i			0.909627i
$909$		−	7.06393i		−	0.234296i
$910$	−10.7076			−0.354955
$911$	−4.24495			−0.140642			−0.0703208	−	0.997524i	$-0.522402\pi$
$911$	−4.24495			−0.140642			−0.0703208	+	0.997524i	$0.522402\pi$
$912$	−14.2808			−0.472885
$913$			38.7892i			1.28373i
$914$		−	66.7942i		−	2.20936i
$915$		−	33.8445i		−	1.11887i
$916$		−	27.5967i		−	0.911822i
$917$			1.20234i			0.0397048i
$918$	48.5626			1.60280
$919$		−	40.9644i		−	1.35129i	−0.737226	−	0.675646i	$-0.763865\pi$
$919$		−	40.9644i		−	1.35129i	0.737226	−	0.675646i	$-0.236135\pi$
$920$	−32.4922			−1.07124
$921$			19.7551i			0.650952i
$922$	−38.5576			−1.26983
$923$	−17.0543			−0.561350
$924$			13.3952i			0.440671i
$925$	15.8887			0.522417
$926$		−	32.7143i		−	1.07506i
$927$	13.9534			0.458290
$928$			51.9258i			1.70455i
$929$		−	11.3379i		−	0.371984i	−0.982551	−	0.185992i	$-0.940450\pi$
$929$		−	11.3379i		−	0.371984i	0.982551	−	0.185992i	$-0.0595498\pi$
$930$			10.3886i			0.340657i
$931$			5.64730i			0.185083i
$932$		−	15.8537i		−	0.519307i
$933$	−23.0238			−0.753767
$934$	−26.3484			−0.862145
$935$	51.8446			1.69550
$936$			4.12827i			0.134937i
$937$			14.7634i			0.482298i	0.970488	+	0.241149i	$0.0775242\pi$
$937$			14.7634i			0.482298i	−0.970488	+	0.241149i	$0.922476\pi$
$938$	25.2587			0.824724
$939$	−2.56611			−0.0837419
$940$		−	77.6346i		−	2.53216i
$941$	−41.6299			−1.35710			−0.678548	−	0.734556i	$-0.737390\pi$
$941$	−41.6299			−1.35710			−0.678548	+	0.734556i	$0.737390\pi$
$942$	12.7131			0.414214
$943$	23.5536	+	42.4231i	0.767010	+	1.38149i
$944$	6.71807			0.218654
$945$	−15.7247			−0.511525
$946$		−	79.7924i		−	2.59427i
$947$	40.7949			1.32566			0.662828	−	0.748772i	$-0.269356\pi$
$947$	40.7949			1.32566			0.662828	+	0.748772i	$0.269356\pi$
$948$	−1.36740			−0.0444111
$949$			8.57805i			0.278455i
$950$			42.2795i			1.37173i
$951$	−27.9812			−0.907354
$952$	6.12009			0.198353
$953$	31.7024			1.02694			0.513471	−	0.858107i	$-0.328359\pi$
$953$	31.7024			1.02694			0.513471	+	0.858107i	$0.328359\pi$
$954$		−	27.8953i		−	0.903143i
$955$		−	62.6046i		−	2.02584i
$956$			7.58995i			0.245477i
$957$			33.9088i			1.09612i
$958$		−	73.4000i		−	2.37145i
$959$	2.95160			0.0953122
$960$		−	41.3121i		−	1.33334i
$961$	−28.9875			−0.935081
$962$			16.9039i			0.545003i
$963$	23.1708			0.746668
$964$	24.2706			0.781705
$965$		−	61.6360i		−	1.98413i
$966$	19.0791			0.613859
$967$		−	42.7634i		−	1.37518i	−0.726100	−	0.687589i	$-0.758669\pi$
$967$		−	42.7634i		−	1.37518i	0.726100	−	0.687589i	$-0.241331\pi$
$968$	10.9556			0.352128
$969$			27.2825i			0.876439i
$970$			59.1272i			1.89846i
$971$		−	22.7815i		−	0.731093i	−0.930793	−	0.365546i	$-0.880882\pi$
$971$		−	22.7815i		−	0.731093i	0.930793	−	0.365546i	$-0.119118\pi$
$972$			39.2658i			1.25945i
$973$		−	13.7403i		−	0.440495i
$974$	71.1453			2.27964
$975$	6.85080			0.219401
$976$	21.7308			0.695587
$977$			61.2927i			1.96093i	0.196699	+	0.980464i	$0.436978\pi$
$977$			61.2927i			1.96093i	−0.196699	+	0.980464i	$0.563022\pi$
$978$			50.3474i			1.60993i
$979$	24.0251			0.767847
$980$	−7.79900			−0.249130
$981$		−	16.2769i		−	0.519680i
$982$	−45.8506			−1.46315
$983$	−44.4653			−1.41822			−0.709111	−	0.705097i	$-0.750903\pi$
$983$	−44.4653			−1.41822			−0.709111	+	0.705097i	$0.750903\pi$
$984$	9.60272	−	5.33149i	0.306123	−	0.169962i
$985$	−48.9445			−1.55950
$986$	60.9706			1.94170
$987$			11.5833i			0.368701i
$988$	−25.7637			−0.819651
$989$	−65.0950			−2.06990
$990$			44.4712i			1.41339i
$991$			16.0464i			0.509731i	0.966976	+	0.254866i	$0.0820312\pi$
$991$			16.0464i			0.509731i	−0.966976	+	0.254866i	$0.917969\pi$
$992$	−10.8527			−0.344575
$993$	−29.8684			−0.947844
$994$	−21.6870			−0.687870
$995$			29.7154i			0.942043i
$996$		−	28.1896i		−	0.893221i
$997$		−	33.2101i		−	1.05177i	−0.850555	−	0.525886i	$-0.823734\pi$
$997$		−	33.2101i		−	1.05177i	0.850555	−	0.525886i	$-0.176266\pi$
$998$			36.2716i			1.14816i
$999$			24.8242i			0.785402i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.c.b.204.4	yes	12
41.40	even	2	inner	287.2.c.b.204.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.c.b.204.3	✓	12	41.40	even	2	inner
287.2.c.b.204.4	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.16363 q^{2} +1.16363i q^{3} +2.68131 q^{4} +2.90865 q^{5} -2.51768i q^{6} +1.00000i q^{7} -1.47412 q^{8} +1.64595 q^{9} +O(q^{10})\)	\(q-2.16363 q^{2} +1.16363i q^{3} +2.68131 q^{4} +2.90865 q^{5} -2.51768i q^{6} +1.00000i q^{7} -1.47412 q^{8} +1.64595 q^{9} -6.29325 q^{10} -4.29325i q^{11} +3.12007i q^{12} -1.70145i q^{13} -2.16363i q^{14} +3.38460i q^{15} -2.17318 q^{16} +4.15170i q^{17} -3.56124 q^{18} -5.64730i q^{19} +7.79900 q^{20} -1.16363 q^{21} +9.28903i q^{22} +7.57803 q^{23} -1.71533i q^{24} +3.46023 q^{25} +3.68131i q^{26} +5.40619i q^{27} +2.68131i q^{28} +6.78750i q^{29} -7.32305i q^{30} -1.41862 q^{31} +7.65020 q^{32} +4.99578 q^{33} -8.98277i q^{34} +2.90865i q^{35} +4.41332 q^{36} +4.59180 q^{37} +12.2187i q^{38} +1.97987 q^{39} -4.28768 q^{40} +(3.10814 + 5.59817i) q^{41} +2.51768 q^{42} -8.58996 q^{43} -11.5116i q^{44} +4.78750 q^{45} -16.3961 q^{46} -9.95443i q^{47} -2.52879i q^{48} -1.00000 q^{49} -7.48668 q^{50} -4.83107 q^{51} -4.56212i q^{52} +7.83302i q^{53} -11.6970i q^{54} -12.4876i q^{55} -1.47412i q^{56} +6.57139 q^{57} -14.6857i q^{58} -3.09135 q^{59} +9.07519i q^{60} -9.99956 q^{61} +3.06938 q^{62} +1.64595i q^{63} -12.2059 q^{64} -4.94892i q^{65} -10.8090 q^{66} +11.6742i q^{67} +11.1320i q^{68} +8.81806i q^{69} -6.29325i q^{70} -10.0234i q^{71} -2.42633 q^{72} -5.04161 q^{73} -9.93498 q^{74} +4.02645i q^{75} -15.1422i q^{76} +4.29325 q^{77} -4.28371 q^{78} +0.438259i q^{79} -6.32102 q^{80} -1.35297 q^{81} +(-6.72488 - 12.1124i) q^{82} -9.03492 q^{83} -3.12007 q^{84} +12.0758i q^{85} +18.5855 q^{86} -7.89817 q^{87} +6.32875i q^{88} +5.59603i q^{89} -10.3584 q^{90} +1.70145 q^{91} +20.3191 q^{92} -1.65076i q^{93} +21.5378i q^{94} -16.4260i q^{95} +8.90204i q^{96} -9.39533i q^{97} +2.16363 q^{98} -7.06650i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 + 12 * q^4 + 2 * q^5 - 24 * q^8 - 4 * q^9	\( 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9} - 4 q^{10} + 28 q^{16} - 40 q^{18} + 2 q^{20} + 8 q^{21} + 16 q^{23} + 34 q^{25} - 6 q^{31} - 42 q^{32} + 18 q^{33} - 36 q^{36} - 10 q^{37} + 10 q^{39} + 38 q^{40} - 2 q^{41} + 32 q^{42} - 50 q^{43} + 6 q^{45} - 8 q^{46} - 12 q^{49} + 18 q^{50} - 2 q^{51} - 50 q^{57} - 70 q^{59} + 52 q^{61} + 68 q^{62} + 8 q^{64} + 92 q^{66} + 2 q^{72} - 64 q^{73} + 18 q^{74} - 20 q^{77} - 12 q^{78} - 32 q^{80} - 4 q^{81} - 56 q^{82} + 60 q^{83} - 20 q^{84} + 48 q^{86} - 20 q^{87} - 42 q^{90} + 14 q^{91} + 56 q^{92} + 4 q^{98}+O(q^{100}) \) 12 * q - 4 * q^2 + 12 * q^4 + 2 * q^5 - 24 * q^8 - 4 * q^9 - 4 * q^10 + 28 * q^16 - 40 * q^18 + 2 * q^20 + 8 * q^21 + 16 * q^23 + 34 * q^25 - 6 * q^31 - 42 * q^32 + 18 * q^33 - 36 * q^36 - 10 * q^37 + 10 * q^39 + 38 * q^40 - 2 * q^41 + 32 * q^42 - 50 * q^43 + 6 * q^45 - 8 * q^46 - 12 * q^49 + 18 * q^50 - 2 * q^51 - 50 * q^57 - 70 * q^59 + 52 * q^61 + 68 * q^62 + 8 * q^64 + 92 * q^66 + 2 * q^72 - 64 * q^73 + 18 * q^74 - 20 * q^77 - 12 * q^78 - 32 * q^80 - 4 * q^81 - 56 * q^82 + 60 * q^83 - 20 * q^84 + 48 * q^86 - 20 * q^87 - 42 * q^90 + 14 * q^91 + 56 * q^92 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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