LMFDB - Embedded newform 799.2.b.c.424.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [799,2,Mod(424,799)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(799, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("799.424");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 799 = 17 \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	799.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.38004712150$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			424.3
Character	$\chi$	$=$	799.424
Dual form			799.2.b.c.424.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67224 q^{2} -1.20994i q^{3} +5.14087 q^{4} +1.97515i q^{5} +3.23326i q^{6} +5.12847i q^{7} -8.39315 q^{8} +1.53604 q^{9} +O(q^{10})$	\(q-2.67224 q^{2} -1.20994i q^{3} +5.14087 q^{4} +1.97515i q^{5} +3.23326i q^{6} +5.12847i q^{7} -8.39315 q^{8} +1.53604 q^{9} -5.27807i q^{10} -3.26489i q^{11} -6.22015i q^{12} +6.27909 q^{13} -13.7045i q^{14} +2.38982 q^{15} +12.1468 q^{16} +(2.71785 - 3.10053i) q^{17} -4.10466 q^{18} -6.12840 q^{19} +10.1540i q^{20} +6.20516 q^{21} +8.72458i q^{22} +3.97734i q^{23} +10.1552i q^{24} +1.09878 q^{25} -16.7792 q^{26} -5.48835i q^{27} +26.3648i q^{28} +3.75635i q^{29} -6.38617 q^{30} -2.38763i q^{31} -15.6728 q^{32} -3.95034 q^{33} +(-7.26274 + 8.28536i) q^{34} -10.1295 q^{35} +7.89657 q^{36} +6.07466i q^{37} +16.3765 q^{38} -7.59734i q^{39} -16.5777i q^{40} +0.399791i q^{41} -16.5817 q^{42} +9.49861 q^{43} -16.7844i q^{44} +3.03390i q^{45} -10.6284i q^{46} +1.00000 q^{47} -14.6969i q^{48} -19.3012 q^{49} -2.93622 q^{50} +(-3.75147 - 3.28844i) q^{51} +32.2800 q^{52} +2.70871 q^{53} +14.6662i q^{54} +6.44866 q^{55} -43.0440i q^{56} +7.41501i q^{57} -10.0379i q^{58} -2.20822 q^{59} +12.2857 q^{60} +10.7270i q^{61} +6.38032i q^{62} +7.87753i q^{63} +17.5879 q^{64} +12.4021i q^{65} +10.5562 q^{66} -2.26153 q^{67} +(13.9721 - 15.9394i) q^{68} +4.81236 q^{69} +27.0685 q^{70} -5.70228i q^{71} -12.8922 q^{72} +5.66356i q^{73} -16.2329i q^{74} -1.32947i q^{75} -31.5053 q^{76} +16.7439 q^{77} +20.3019i q^{78} -1.26216i q^{79} +23.9917i q^{80} -2.03247 q^{81} -1.06834i q^{82} -12.8421 q^{83} +31.8999 q^{84} +(6.12401 + 5.36816i) q^{85} -25.3826 q^{86} +4.54497 q^{87} +27.4027i q^{88} +15.5223 q^{89} -8.10732i q^{90} +32.2022i q^{91} +20.4470i q^{92} -2.88890 q^{93} -2.67224 q^{94} -12.1045i q^{95} +18.9632i q^{96} +0.0910806i q^{97} +51.5775 q^{98} -5.01500i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 6 q^{2} + 46 q^{4} - 18 q^{8} - 46 q^{9}+O(q^{10}) $ 40 * q - 6 * q^2 + 46 * q^4 - 18 * q^8 - 46 * q^9	$ 40 q - 6 q^{2} + 46 q^{4} - 18 q^{8} - 46 q^{9} + 14 q^{13} - 18 q^{15} + 58 q^{16} + 2 q^{17} - 10 q^{18} - 22 q^{19} + 24 q^{21} - 58 q^{25} - 6 q^{26} + 34 q^{30} - 92 q^{32} + 50 q^{33} + 8 q^{34} - 18 q^{35} - 68 q^{36} + 6 q^{38} + 36 q^{42} - 26 q^{43} + 40 q^{47} - 78 q^{49} + 50 q^{50} + 20 q^{51} - 24 q^{52} - 22 q^{53} + 22 q^{55} + 18 q^{59} - 74 q^{60} + 94 q^{64} - 96 q^{66} + 52 q^{67} + 71 q^{68} - 26 q^{69} + 2 q^{70} + 16 q^{72} - 2 q^{76} - 60 q^{77} + 96 q^{81} + 10 q^{83} + 138 q^{84} + 38 q^{85} - 152 q^{86} - 10 q^{87} - 6 q^{89} + 14 q^{93} - 6 q^{94} + 60 q^{98}+O(q^{100}) $ 40 * q - 6 * q^2 + 46 * q^4 - 18 * q^8 - 46 * q^9 + 14 * q^13 - 18 * q^15 + 58 * q^16 + 2 * q^17 - 10 * q^18 - 22 * q^19 + 24 * q^21 - 58 * q^25 - 6 * q^26 + 34 * q^30 - 92 * q^32 + 50 * q^33 + 8 * q^34 - 18 * q^35 - 68 * q^36 + 6 * q^38 + 36 * q^42 - 26 * q^43 + 40 * q^47 - 78 * q^49 + 50 * q^50 + 20 * q^51 - 24 * q^52 - 22 * q^53 + 22 * q^55 + 18 * q^59 - 74 * q^60 + 94 * q^64 - 96 * q^66 + 52 * q^67 + 71 * q^68 - 26 * q^69 + 2 * q^70 + 16 * q^72 - 2 * q^76 - 60 * q^77 + 96 * q^81 + 10 * q^83 + 138 * q^84 + 38 * q^85 - 152 * q^86 - 10 * q^87 - 6 * q^89 + 14 * q^93 - 6 * q^94 + 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/799\mathbb{Z}\right)^\times$.

$n$	$52$	$377$
$\chi(n)$	$1$	$-1$

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 $

$2$	−2.67224			−1.88956			−0.944779	−	0.327707i	$-0.893724\pi$
$2$	−2.67224			−1.88956			−0.944779	+	0.327707i	$0.893724\pi$
$3$		−	1.20994i		−	0.698561i	−0.937018	−	0.349280i	$-0.886426\pi$
$3$		−	1.20994i		−	0.698561i	0.937018	−	0.349280i	$-0.113574\pi$
$4$	5.14087			2.57043
$5$			1.97515i			0.883314i	0.897184	+	0.441657i	$0.145609\pi$
$5$			1.97515i			0.883314i	−0.897184	+	0.441657i	$0.854391\pi$
$6$			3.23326i			1.31997i
$7$			5.12847i			1.93838i	0.246313	+	0.969190i	$0.420781\pi$
$7$			5.12847i			1.93838i	−0.246313	+	0.969190i	$0.579219\pi$
$8$	−8.39315			−2.96743
$9$	1.53604			0.512013
$10$		−	5.27807i		−	1.66907i
$11$		−	3.26489i		−	0.984403i	−0.870481	−	0.492201i	$-0.836192\pi$
$11$		−	3.26489i		−	0.984403i	0.870481	−	0.492201i	$-0.163808\pi$
$12$		−	6.22015i		−	1.79560i
$13$	6.27909			1.74151			0.870753	−	0.491720i	$-0.163632\pi$
$13$	6.27909			1.74151			0.870753	+	0.491720i	$0.163632\pi$
$14$		−	13.7045i		−	3.66268i
$15$	2.38982			0.617048
$16$	12.1468			3.03669
$17$	2.71785	−	3.10053i	0.659175	−	0.751989i
$17$	2.71785	−	3.10053i	0.659175	−	0.751989i
$18$	−4.10466			−0.967478
$19$	−6.12840			−1.40595			−0.702975	−	0.711214i	$-0.748146\pi$
$19$	−6.12840			−1.40595			−0.702975	+	0.711214i	$0.748146\pi$
$20$			10.1540i			2.27050i
$21$	6.20516			1.35408
$22$			8.72458i			1.86009i
$23$			3.97734i			0.829334i	0.909973	+	0.414667i	$0.136102\pi$
$23$			3.97734i			0.829334i	−0.909973	+	0.414667i	$0.863898\pi$
$24$			10.1552i			2.07293i
$25$	1.09878			0.219757
$26$	−16.7792			−3.29068
$27$		−	5.48835i		−	1.05623i
$28$			26.3648i			4.98248i
$29$			3.75635i			0.697536i	0.937209	+	0.348768i	$0.113400\pi$
$29$			3.75635i			0.697536i	−0.937209	+	0.348768i	$0.886600\pi$
$30$	−6.38617			−1.16595
$31$		−	2.38763i		−	0.428831i	−0.976743	−	0.214416i	$-0.931215\pi$
$31$		−	2.38763i		−	0.428831i	0.976743	−	0.214416i	$-0.0687847\pi$
$32$	−15.6728			−2.77058
$33$	−3.95034			−0.687665
$34$	−7.26274	+	8.28536i	−1.24555	+	1.42093i
$35$	−10.1295			−1.71220
$36$	7.89657			1.31609
$37$			6.07466i			0.998668i	0.866410	+	0.499334i	$0.166422\pi$
$37$			6.07466i			0.998668i	−0.866410	+	0.499334i	$0.833578\pi$
$38$	16.3765			2.65663
$39$		−	7.59734i		−	1.21655i
$40$		−	16.5777i		−	2.62117i
$41$			0.399791i			0.0624368i	0.999513	+	0.0312184i	$0.00993874\pi$
$41$			0.399791i			0.0624368i	−0.999513	+	0.0312184i	$0.990061\pi$
$42$	−16.5817			−2.55861
$43$	9.49861			1.44852			0.724262	−	0.689524i	$-0.242180\pi$
$43$	9.49861			1.44852			0.724262	+	0.689524i	$0.242180\pi$
$44$		−	16.7844i		−	2.53034i
$45$			3.03390i			0.452268i
$46$		−	10.6284i		−	1.56707i
$47$	1.00000			0.145865
$47$	1.00000			0.145865
$48$		−	14.6969i		−	2.12131i
$49$	−19.3012			−2.75732
$50$	−2.93622			−0.415244
$51$	−3.75147	−	3.28844i	−0.525310	−	0.460474i
$52$	32.2800			4.47643
$53$	2.70871			0.372070			0.186035	−	0.982543i	$-0.440436\pi$
$53$	2.70871			0.372070			0.186035	+	0.982543i	$0.440436\pi$
$54$			14.6662i			1.99581i
$55$	6.44866			0.869536
$56$		−	43.0440i		−	5.75200i
$57$			7.41501i			0.982142i
$58$		−	10.0379i		−	1.31804i
$59$	−2.20822			−0.287486			−0.143743	−	0.989615i	$-0.545914\pi$
$59$	−2.20822			−0.287486			−0.143743	+	0.989615i	$0.545914\pi$
$60$	12.2857			1.58608
$61$			10.7270i			1.37345i	0.726915	+	0.686727i	$0.240953\pi$
$61$			10.7270i			1.37345i	−0.726915	+	0.686727i	$0.759047\pi$
$62$			6.38032i			0.810302i
$63$			7.87753i			0.992476i
$64$	17.5879			2.19849
$65$			12.4021i			1.53830i
$66$	10.5562			1.29938
$67$	−2.26153			−0.276289			−0.138145	−	0.990412i	$-0.544114\pi$
$67$	−2.26153			−0.276289			−0.138145	+	0.990412i	$0.544114\pi$
$68$	13.9721	−	15.9394i	1.69437	−	1.93294i
$69$	4.81236			0.579340
$70$	27.0685			3.23530
$71$		−	5.70228i		−	0.676736i	−0.941014	−	0.338368i	$-0.890125\pi$
$71$		−	5.70228i		−	0.676736i	0.941014	−	0.338368i	$-0.109875\pi$
$72$	−12.8922			−1.51936
$73$			5.66356i			0.662870i	0.943478	+	0.331435i	$0.107533\pi$
$73$			5.66356i			0.662870i	−0.943478	+	0.331435i	$0.892467\pi$
$74$		−	16.2329i		−	1.88704i
$75$		−	1.32947i		−	0.153514i
$76$	−31.5053			−3.61390
$77$	16.7439			1.90815
$78$			20.3019i			2.29874i
$79$		−	1.26216i		−	0.142004i	−0.997476	−	0.0710021i	$-0.977380\pi$
$79$		−	1.26216i		−	0.142004i	0.997476	−	0.0710021i	$-0.0226197\pi$
$80$			23.9917i			2.68235i
$81$	−2.03247			−0.225830
$82$		−	1.06834i		−	0.117978i
$83$	−12.8421			−1.40961			−0.704804	−	0.709402i	$-0.748965\pi$
$83$	−12.8421			−1.40961			−0.704804	+	0.709402i	$0.748965\pi$
$84$	31.8999			3.48056
$85$	6.12401	+	5.36816i	0.664242	+	0.582258i
$86$	−25.3826			−2.73707
$87$	4.54497			0.487271
$88$			27.4027i			2.92114i
$89$	15.5223			1.64536			0.822680	−	0.568505i	$-0.192478\pi$
$89$	15.5223			1.64536			0.822680	+	0.568505i	$0.192478\pi$
$90$		−	8.10732i		−	0.854587i
$91$			32.2022i			3.37570i
$92$			20.4470i			2.13175i
$93$	−2.88890			−0.299565
$94$	−2.67224			−0.275620
$95$		−	12.1045i		−	1.24190i
$96$			18.9632i			1.93542i
$97$			0.0910806i			0.00924783i	0.999989	+	0.00462392i	$0.00147184\pi$
$97$			0.0910806i			0.00924783i	−0.999989	+	0.00462392i	$0.998528\pi$
$98$	51.5775			5.21012
$99$		−	5.01500i		−	0.504027i
$100$	5.64871			0.564871
$101$	−4.43990			−0.441787			−0.220893	−	0.975298i	$-0.570897\pi$
$101$	−4.43990			−0.441787			−0.220893	+	0.975298i	$0.570897\pi$
$102$	10.0248	+	8.78751i	0.992605	+	0.870093i
$103$	7.66409			0.755165			0.377583	−	0.925976i	$-0.376755\pi$
$103$	7.66409			0.755165			0.377583	+	0.925976i	$0.376755\pi$
$104$	−52.7013			−5.16779
$105$			12.2561i			1.19607i
$106$	−7.23831			−0.703047
$107$			14.8311i			1.43378i	0.697189	+	0.716888i	$0.254434\pi$
$107$			14.8311i			1.43378i	−0.697189	+	0.716888i	$0.745566\pi$
$108$		−	28.2149i		−	2.71498i
$109$		−	6.54796i		−	0.627181i	−0.949558	−	0.313590i	$-0.898468\pi$
$109$		−	6.54796i		−	0.627181i	0.949558	−	0.313590i	$-0.101532\pi$
$110$	−17.2324			−1.64304
$111$	7.34999			0.697630
$112$			62.2944i			5.88627i
$113$		−	13.1762i		−	1.23951i	−0.784796	−	0.619754i	$-0.787232\pi$
$113$		−	13.1762i		−	1.23951i	0.784796	−	0.619754i	$-0.212768\pi$
$114$		−	19.8147i		−	1.85581i
$115$	−7.85585			−0.732562
$116$			19.3109i			1.79297i
$117$	9.64493			0.891674
$118$	5.90090			0.543222
$119$	15.9010	+	13.9384i	1.45764	+	1.27773i
$120$	−20.0581			−1.83105
$121$	0.340461			0.0309510
$122$		−	28.6652i		−	2.59522i
$123$	0.483724			0.0436159
$124$		−	12.2745i		−	1.10228i
$125$			12.0460i			1.07743i
$126$		−	21.0507i		−	1.87534i
$127$	0.613704			0.0544574			0.0272287	−	0.999629i	$-0.491332\pi$
$127$	0.613704			0.0544574			0.0272287	+	0.999629i	$0.491332\pi$
$128$	−15.6535			−1.38359
$129$		−	11.4928i		−	1.01188i
$130$		−	33.1415i		−	2.90670i
$131$			10.0019i			0.873874i	0.899492	+	0.436937i	$0.143937\pi$
$131$			10.0019i			0.873874i	−0.899492	+	0.436937i	$0.856063\pi$
$132$	−20.3081			−1.76760
$133$		−	31.4293i		−	2.72527i
$134$	6.04334			0.522065
$135$	10.8403			0.932985
$136$	−22.8113	+	26.0232i	−1.95605	+	2.23147i
$137$	0.764019			0.0652745			0.0326373	−	0.999467i	$-0.489609\pi$
$137$	0.764019			0.0652745			0.0326373	+	0.999467i	$0.489609\pi$
$138$	−12.8598			−1.09470
$139$		−	1.94410i		−	0.164897i	−0.996595	−	0.0824484i	$-0.973726\pi$
$139$		−	1.94410i		−	0.164897i	0.996595	−	0.0824484i	$-0.0262740\pi$
$140$	−52.0744			−4.40109
$141$		−	1.20994i		−	0.101896i
$142$			15.2379i			1.27873i
$143$		−	20.5006i		−	1.71434i
$144$	18.6579			1.55483
$145$	−7.41935			−0.616143
$146$		−	15.1344i		−	1.25253i
$147$			23.3534i			1.92616i
$148$			31.2290i			2.56701i
$149$	−6.66284			−0.545841			−0.272920	−	0.962037i	$-0.587990\pi$
$149$	−6.66284			−0.545841			−0.272920	+	0.962037i	$0.587990\pi$
$150$			3.55265i			0.290073i
$151$	12.4791			1.01553			0.507766	−	0.861495i	$-0.330472\pi$
$151$	12.4791			1.01553			0.507766	+	0.861495i	$0.330472\pi$
$152$	51.4365			4.17205
$153$	4.17472	−	4.76253i	0.337506	−	0.385028i
$154$	−44.7438			−3.60556
$155$	4.71593			0.378792
$156$		−	39.0569i		−	3.12706i
$157$	−5.72238			−0.456695			−0.228348	−	0.973580i	$-0.573332\pi$
$157$	−5.72238			−0.456695			−0.228348	+	0.973580i	$0.573332\pi$
$158$			3.37280i			0.268325i
$159$		−	3.27738i		−	0.259913i
$160$		−	30.9561i		−	2.44729i
$161$	−20.3977			−1.60756
$162$	5.43125			0.426720
$163$			1.47232i			0.115321i	0.998336	+	0.0576606i	$0.0183641\pi$
$163$			1.47232i			0.115321i	−0.998336	+	0.0576606i	$0.981636\pi$
$164$			2.05527i			0.160490i
$165$		−	7.80250i		−	0.607424i
$166$	34.3173			2.66354
$167$			22.8037i			1.76461i	0.470682	+	0.882303i	$0.344008\pi$
$167$			22.8037i			1.76461i	−0.470682	+	0.882303i	$0.655992\pi$
$168$	−52.0808			−4.01812
$169$	26.4270			2.03285
$170$	−16.3648	−	14.3450i	−1.25513	−	1.10021i
$171$	−9.41345			−0.719864
$172$	48.8311			3.72334
$173$			3.22034i			0.244838i	0.992479	+	0.122419i	$0.0390651\pi$
$173$			3.22034i			0.244838i	−0.992479	+	0.122419i	$0.960935\pi$
$174$	−12.1452			−0.920728
$175$			5.63509i			0.425973i
$176$		−	39.6579i		−	2.98933i
$177$			2.67182i			0.200826i
$178$	−41.4793			−3.10900
$179$	−12.1786			−0.910273			−0.455136	−	0.890422i	$-0.650410\pi$
$179$	−12.1786			−0.910273			−0.455136	+	0.890422i	$0.650410\pi$
$180$			15.5969i			1.16252i
$181$		−	10.2172i		−	0.759442i	−0.925101	−	0.379721i	$-0.876020\pi$
$181$		−	10.2172i		−	0.759442i	0.925101	−	0.379721i	$-0.123980\pi$
$182$		−	86.0519i		−	6.37859i
$183$	12.9791			0.959442
$184$		−	33.3824i		−	2.46099i
$185$	−11.9984			−0.882137
$186$	7.71983			0.566045
$187$	−10.1229	−	8.87349i	−0.740260	−	0.648894i
$188$	5.14087			0.374936
$189$	28.1468			2.04738
$190$			32.3461i			2.34663i
$191$	−5.99023			−0.433438			−0.216719	−	0.976234i	$-0.569535\pi$
$191$	−5.99023			−0.433438			−0.216719	+	0.976234i	$0.569535\pi$
$192$		−	21.2804i		−	1.53578i
$193$		−	4.91620i		−	0.353876i	−0.984222	−	0.176938i	$-0.943381\pi$
$193$		−	4.91620i		−	0.353876i	0.984222	−	0.176938i	$-0.0566192\pi$
$194$		−	0.243389i		−	0.0174743i
$195$	15.0059			1.07459
$196$	−99.2251			−7.08751
$197$			14.8444i			1.05762i	0.848740	+	0.528811i	$0.177362\pi$
$197$			14.8444i			1.05762i	−0.848740	+	0.528811i	$0.822638\pi$
$198$			13.4013i			0.952388i
$199$		−	19.7936i		−	1.40313i	−0.712605	−	0.701566i	$-0.752485\pi$
$199$		−	19.7936i		−	1.40313i	0.712605	−	0.701566i	$-0.247515\pi$
$200$	−9.22226			−0.652113
$201$			2.73632i			0.193005i
$202$	11.8645			0.834782
$203$	−19.2643			−1.35209
$204$	−19.2858	−	16.9054i	−1.35028	−	1.18362i
$205$	−0.789646			−0.0551513
$206$	−20.4803			−1.42693
$207$			6.10935i			0.424629i
$208$	76.2707			5.28842
$209$			20.0086i			1.38402i
$210$		−	32.7513i		−	2.26005i
$211$			0.313934i			0.0216121i	0.999942	+	0.0108061i	$0.00343975\pi$
$211$			0.313934i			0.0216121i	−0.999942	+	0.0108061i	$0.996560\pi$
$212$	13.9251			0.956380
$213$	−6.89943			−0.472741
$214$		−	39.6322i		−	2.70920i
$215$			18.7612i			1.27950i
$216$			46.0645i			3.13429i
$217$	12.2449			0.831238
$218$			17.4977i			1.18509i
$219$	6.85259			0.463055
$220$	33.1517			2.23509
$221$	17.0656	−	19.4685i	1.14796	−	1.30959i
$222$	−19.6409			−1.31821
$223$	−9.75286			−0.653100			−0.326550	−	0.945180i	$-0.605886\pi$
$223$	−9.75286			−0.653100			−0.326550	+	0.945180i	$0.605886\pi$
$224$		−	80.3775i		−	5.37045i
$225$	1.68778			0.112518
$226$			35.2099i			2.34212i
$227$		−	6.10137i		−	0.404962i	−0.979286	−	0.202481i	$-0.935100\pi$
$227$		−	6.10137i		−	0.404962i	0.979286	−	0.202481i	$-0.0649004\pi$
$228$			38.1196i			2.52453i
$229$	−20.7242			−1.36949			−0.684745	−	0.728783i	$-0.740087\pi$
$229$	−20.7242			−1.36949			−0.684745	+	0.728783i	$0.740087\pi$
$230$	20.9927			1.38422
$231$		−	20.2592i		−	1.33296i
$232$		−	31.5276i		−	2.06989i
$233$			14.6825i			0.961882i	0.876753	+	0.480941i	$0.159705\pi$
$233$			14.6825i			0.961882i	−0.876753	+	0.480941i	$0.840295\pi$
$234$	−25.7736			−1.68487
$235$			1.97515i			0.128845i
$236$	−11.3522			−0.738964
$237$	−1.52714			−0.0991986
$238$	−42.4913	−	37.2468i	−2.75430	−	2.41435i
$239$	−0.0412265			−0.00266672			−0.00133336	−	0.999999i	$-0.500424\pi$
$239$	−0.0412265			−0.00266672			−0.00133336	+	0.999999i	$0.500424\pi$
$240$	29.0286			1.87379
$241$			6.08032i			0.391668i	0.980637	+	0.195834i	$0.0627413\pi$
$241$			6.08032i			0.391668i	−0.980637	+	0.195834i	$0.937259\pi$
$242$	−0.909795			−0.0584838
$243$		−	14.0059i		−	0.898477i
$244$			55.1462i			3.53037i
$245$		−	38.1228i		−	2.43558i
$246$	−1.29263			−0.0824148
$247$	−38.4808			−2.44847
$248$			20.0397i			1.27252i
$249$			15.5383i			0.984697i
$250$		−	32.1898i		−	2.03586i
$251$	−13.1407			−0.829432			−0.414716	−	0.909951i	$-0.636119\pi$
$251$	−13.1407			−0.829432			−0.414716	+	0.909951i	$0.636119\pi$
$252$			40.4973i			2.55109i
$253$	12.9856			0.816398
$254$	−1.63996			−0.102901
$255$	6.49516	−	7.40971i	0.406743	−	0.464014i
$256$	6.65420			0.415887
$257$	9.92956			0.619389			0.309694	−	0.950836i	$-0.399773\pi$
$257$	9.92956			0.619389			0.309694	+	0.950836i	$0.399773\pi$
$258$			30.7115i			1.91201i
$259$	−31.1537			−1.93580
$260$			63.7578i			3.95409i
$261$			5.76989i			0.357147i
$262$		−	26.7276i		−	1.65124i
$263$	7.30515			0.450455			0.225227	−	0.974306i	$-0.427688\pi$
$263$	7.30515			0.450455			0.225227	+	0.974306i	$0.427688\pi$
$264$	33.1558			2.04060
$265$			5.35010i			0.328654i
$266$			83.9867i			5.14955i
$267$		−	18.7811i		−	1.14938i
$268$	−11.6262			−0.710183
$269$		−	6.32692i		−	0.385759i	−0.981222	−	0.192880i	$-0.938217\pi$
$269$		−	6.32692i		−	0.385759i	0.981222	−	0.192880i	$-0.0617827\pi$
$270$	−28.9679			−1.76293
$271$	8.33620			0.506388			0.253194	−	0.967415i	$-0.418519\pi$
$271$	8.33620			0.506388			0.253194	+	0.967415i	$0.418519\pi$
$272$	33.0131	−	37.6614i	2.00171	−	2.28356i
$273$	38.9628			2.35813
$274$	−2.04164			−0.123340
$275$		−	3.58742i		−	0.216329i
$276$	24.7397			1.48915
$277$			9.37063i			0.563026i	0.959557	+	0.281513i	$0.0908363\pi$
$277$			9.37063i			0.563026i	−0.959557	+	0.281513i	$0.909164\pi$
$278$			5.19511i			0.311582i
$279$		−	3.66749i		−	0.219567i
$280$	85.0184			5.08082
$281$	1.12145			0.0669000			0.0334500	−	0.999440i	$-0.489351\pi$
$281$	1.12145			0.0669000			0.0334500	+	0.999440i	$0.489351\pi$
$282$			3.23326i			0.192538i
$283$		−	18.2488i		−	1.08478i	−0.840127	−	0.542389i	$-0.817520\pi$
$283$		−	18.2488i		−	1.08478i	0.840127	−	0.542389i	$-0.182480\pi$
$284$		−	29.3146i		−	1.73950i
$285$	−14.6457			−0.867539
$286$			54.7825i			3.23935i
$287$	−2.05032			−0.121026
$288$	−24.0740			−1.41857
$289$	−2.22659	−	16.8536i	−0.130976	−	0.991386i
$290$	19.8263			1.16424
$291$	0.110202			0.00646018
$292$			29.1156i			1.70386i
$293$	−10.9752			−0.641179			−0.320589	−	0.947218i	$-0.603881\pi$
$293$	−10.9752			−0.641179			−0.320589	+	0.947218i	$0.603881\pi$
$294$		−	62.4059i		−	3.63958i
$295$		−	4.36157i		−	0.253940i
$296$		−	50.9855i		−	2.96347i
$297$	−17.9189			−1.03976
$298$	17.8047			1.03140
$299$			24.9741i			1.44429i
$300$		−	6.83461i		−	0.394597i
$301$			48.7134i			2.80779i
$302$	−33.3470			−1.91891
$303$			5.37203i			0.308615i
$304$	−74.4402			−4.26944
$305$	−21.1875			−1.21319
$306$	−11.1559	+	12.7266i	−0.637738	+	0.727533i
$307$	10.6748			0.609245			0.304623	−	0.952473i	$-0.401470\pi$
$307$	10.6748			0.609245			0.304623	+	0.952473i	$0.401470\pi$
$308$	86.0783			4.90477
$309$		−	9.27311i		−	0.527529i
$310$	−12.6021			−0.715751
$311$		−	7.84119i		−	0.444633i	−0.974975	−	0.222317i	$-0.928638\pi$
$311$		−	7.84119i		−	0.444633i	0.974975	−	0.222317i	$-0.0713619\pi$
$312$			63.7656i			3.61002i
$313$		−	25.1753i		−	1.42299i	−0.702689	−	0.711497i	$-0.748017\pi$
$313$		−	25.1753i		−	1.42299i	0.702689	−	0.711497i	$-0.251983\pi$
$314$	15.2916			0.862953
$315$	−15.5593			−0.876667
$316$		−	6.48860i		−	0.365012i
$317$		−	13.5802i		−	0.762742i	−0.924422	−	0.381371i	$-0.875452\pi$
$317$		−	13.5802i		−	0.762742i	0.924422	−	0.381371i	$-0.124548\pi$
$318$			8.75795i			0.491121i
$319$	12.2641			0.686656
$320$			34.7388i			1.94196i
$321$	17.9448			1.00158
$322$	54.5076			3.03759
$323$	−16.6561	+	19.0013i	−0.926768	+	1.05726i
$324$	−10.4487			−0.580482
$325$	6.89937			0.382708
$326$		−	3.93440i		−	0.217906i
$327$	−7.92266			−0.438124
$328$		−	3.35550i		−	0.185277i
$329$			5.12847i			0.282742i
$330$			20.8502i			1.14776i
$331$	12.9312			0.710764			0.355382	−	0.934721i	$-0.384351\pi$
$331$	12.9312			0.710764			0.355382	+	0.934721i	$0.384351\pi$
$332$	−66.0197			−3.62330
$333$			9.33091i			0.511331i
$334$		−	60.9370i		−	3.33433i
$335$		−	4.46685i		−	0.244050i
$336$	75.3727			4.11192
$337$		−	16.7789i		−	0.914005i	−0.889466	−	0.457002i	$-0.848923\pi$
$337$		−	16.7789i		−	0.914005i	0.889466	−	0.457002i	$-0.151077\pi$
$338$	−70.6193			−3.84118
$339$	−15.9424			−0.865872
$340$	31.4827	+	27.5970i	1.70739	+	1.49666i
$341$	−7.79536			−0.422143
$342$	25.1550			1.36023
$343$		−	63.0866i		−	3.40635i
$344$	−79.7233			−4.29839
$345$			9.50513i			0.511739i
$346$		−	8.60551i		−	0.462635i
$347$			24.9331i			1.33848i	0.743046	+	0.669240i	$0.233380\pi$
$347$			24.9331i			1.33848i	−0.743046	+	0.669240i	$0.766620\pi$
$348$	23.3651			1.25250
$349$	1.73186			0.0927044			0.0463522	−	0.998925i	$-0.485240\pi$
$349$	1.73186			0.0927044			0.0463522	+	0.998925i	$0.485240\pi$
$350$		−	15.0583i		−	0.804901i
$351$		−	34.4618i		−	1.83944i
$352$			51.1700i			2.72737i
$353$	19.2408			1.02409			0.512043	−	0.858960i	$-0.328889\pi$
$353$	19.2408			1.02409			0.512043	+	0.858960i	$0.328889\pi$
$354$		−	7.13975i		−	0.379473i
$355$	11.2629			0.597770
$356$	79.7980			4.22929
$357$	16.8647	−	19.2393i	0.892574	−	1.01825i
$358$	32.5442			1.72001
$359$	4.92836			0.260109			0.130055	−	0.991507i	$-0.458485\pi$
$359$	4.92836			0.260109			0.130055	+	0.991507i	$0.458485\pi$
$360$		−	25.4640i		−	1.34207i
$361$	18.5572			0.976696
$362$			27.3029i			1.43501i
$363$		−	0.411939i		−	0.0216212i
$364$			165.547i			8.67702i
$365$	−11.1864			−0.585522
$366$	−34.6832			−1.81292
$367$			23.8430i			1.24460i	0.782780	+	0.622298i	$0.213801\pi$
$367$			23.8430i			1.24460i	−0.782780	+	0.622298i	$0.786199\pi$
$368$			48.3119i			2.51843i
$369$			0.614094i			0.0319684i
$370$	32.0625			1.66685
$371$			13.8915i			0.721212i
$372$	−14.8514			−0.770011
$373$	25.3346			1.31177			0.655887	−	0.754859i	$-0.272295\pi$
$373$	25.3346			1.31177			0.655887	+	0.754859i	$0.272295\pi$
$374$	27.0508	+	23.7121i	1.39877	+	1.22612i
$375$	14.5750			0.752649
$376$	−8.39315			−0.432844
$377$			23.5864i			1.21476i
$378$	−75.2151			−3.86865
$379$			7.07338i			0.363335i	0.983360	+	0.181668i	$0.0581495\pi$
$379$			7.07338i			0.363335i	−0.983360	+	0.181668i	$0.941851\pi$
$380$		−	62.2276i		−	3.19221i
$381$		−	0.742547i		−	0.0380418i
$382$	16.0073			0.819006
$383$	27.1072			1.38511			0.692556	−	0.721364i	$-0.256484\pi$
$383$	27.1072			1.38511			0.692556	+	0.721364i	$0.256484\pi$
$384$			18.9399i			0.966522i
$385$			33.0718i			1.68549i
$386$			13.1373i			0.668670i
$387$	14.5902			0.741663
$388$			0.468233i			0.0237709i
$389$	−26.7523			−1.35639			−0.678196	−	0.734881i	$-0.737238\pi$
$389$	−26.7523			−1.35639			−0.678196	+	0.734881i	$0.737238\pi$
$390$	−40.0993			−2.03051
$391$	12.3319	+	10.8098i	0.623650	+	0.546676i
$392$	161.998			8.18214
$393$	12.1018			0.610454
$394$		−	39.6679i		−	1.99844i
$395$	2.49296			0.125434
$396$		−	25.7815i		−	1.29557i
$397$			35.4864i			1.78101i	0.454972	+	0.890506i	$0.349649\pi$
$397$			35.4864i			1.78101i	−0.454972	+	0.890506i	$0.650351\pi$
$398$			52.8932i			2.65130i
$399$	−38.0277			−1.90376
$400$	13.3467			0.667334
$401$		−	28.1664i		−	1.40656i	−0.710911	−	0.703282i	$-0.751717\pi$
$401$		−	28.1664i		−	1.40656i	0.710911	−	0.703282i	$-0.248283\pi$
$402$		−	7.31210i		−	0.364694i
$403$		−	14.9922i		−	0.746812i
$404$	−22.8249			−1.13558
$405$		−	4.01444i		−	0.199479i
$406$	51.4789			2.55485
$407$	19.8331			0.983091
$408$	31.4866	+	27.6004i	1.55882	+	1.36642i
$409$	2.61194			0.129152			0.0645760	−	0.997913i	$-0.479431\pi$
$409$	2.61194			0.129152			0.0645760	+	0.997913i	$0.479431\pi$
$410$	2.11012			0.104212
$411$		−	0.924419i		−	0.0455982i
$412$	39.4000			1.94110
$413$		−	11.3248i		−	0.557257i
$414$		−	16.3257i		−	0.802362i
$415$		−	25.3652i		−	1.24513i
$416$	−98.4109			−4.82499
$417$	−2.35225			−0.115190
$418$		−	53.4677i		−	2.61519i
$419$		−	22.0982i		−	1.07957i	−0.841804	−	0.539783i	$-0.818506\pi$
$419$		−	22.0982i		−	1.07957i	0.841804	−	0.539783i	$-0.181494\pi$
$420$			63.0071i			3.07443i
$421$	−15.0160			−0.731836			−0.365918	−	0.930647i	$-0.619245\pi$
$421$	−15.0160			−0.731836			−0.365918	+	0.930647i	$0.619245\pi$
$422$		−	0.838908i		−	0.0408374i
$423$	1.53604			0.0746847
$424$	−22.7346			−1.10409
$425$	2.98633	−	3.40682i	0.144858	−	0.165255i
$426$	18.4369			0.893272
$427$	−55.0133			−2.66228
$428$			76.2446i			3.68542i
$429$	−24.8045			−1.19757
$430$		−	50.1344i		−	2.41769i
$431$			23.8626i			1.14942i	0.818357	+	0.574710i	$0.194885\pi$
$431$			23.8626i			1.14942i	−0.818357	+	0.574710i	$0.805115\pi$
$432$		−	66.6657i		−	3.20745i
$433$	−26.6770			−1.28202			−0.641008	−	0.767534i	$-0.721484\pi$
$433$	−26.6770			−1.28202			−0.641008	+	0.767534i	$0.721484\pi$
$434$	−32.7213			−1.57067
$435$			8.97698i			0.430413i
$436$		−	33.6622i		−	1.61213i
$437$		−	24.3747i		−	1.16600i
$438$	−18.3118			−0.874970
$439$		−	32.2134i		−	1.53746i	−0.639572	−	0.768731i	$-0.720888\pi$
$439$		−	32.2134i		−	1.53746i	0.639572	−	0.768731i	$-0.279112\pi$
$440$	−54.1245			−2.58028
$441$	−29.6474			−1.41178
$442$	−45.6034	+	52.0246i	−2.16913	+	2.47456i
$443$	−7.35408			−0.349403			−0.174701	−	0.984621i	$-0.555896\pi$
$443$	−7.35408			−0.349403			−0.174701	+	0.984621i	$0.555896\pi$
$444$	37.7853			1.79321
$445$			30.6588i			1.45337i
$446$	26.0620			1.23407
$447$			8.06165i			0.381303i
$448$			90.1991i			4.26151i
$449$		−	30.3509i		−	1.43235i	−0.697922	−	0.716173i	$-0.745892\pi$
$449$		−	30.3509i		−	1.43235i	0.697922	−	0.716173i	$-0.254108\pi$
$450$	−4.51014			−0.212610
$451$	1.30527			0.0614630
$452$		−	67.7369i		−	3.18607i
$453$		−	15.0989i		−	0.709410i
$454$			16.3043i			0.765200i
$455$	−63.6041			−2.98180
$456$		−	62.2353i		−	2.91443i
$457$	−34.9781			−1.63620			−0.818102	−	0.575073i	$-0.804974\pi$
$457$	−34.9781			−1.63620			−0.818102	+	0.575073i	$0.804974\pi$
$458$	55.3799			2.58773
$459$	−17.0168	−	14.9165i	−0.794276	−	0.696243i
$460$	−40.3859			−1.88300
$461$	−3.41481			−0.159044			−0.0795219	−	0.996833i	$-0.525339\pi$
$461$	−3.41481			−0.159044			−0.0795219	+	0.996833i	$0.525339\pi$
$462$			54.1374i			2.51870i
$463$	−27.0968			−1.25929			−0.629647	−	0.776881i	$-0.716801\pi$
$463$	−27.0968			−1.25929			−0.629647	+	0.776881i	$0.716801\pi$
$464$			45.6275i			2.11820i
$465$		−	5.70600i		−	0.264610i
$466$		−	39.2352i		−	1.81753i
$467$	−16.2651			−0.752658			−0.376329	−	0.926486i	$-0.622814\pi$
$467$	−16.2651			−0.752658			−0.376329	+	0.926486i	$0.622814\pi$
$468$	49.5833			2.29199
$469$		−	11.5982i		−	0.535554i
$470$		−	5.27807i		−	0.243459i
$471$			6.92375i			0.319030i
$472$	18.5339			0.853093
$473$		−	31.0120i		−	1.42593i
$474$	4.08089			0.187442
$475$	−6.73379			−0.308967
$476$	81.7449	+	71.6555i	3.74677	+	3.28433i
$477$	4.16068			0.190504
$478$	0.110167			0.00503893
$479$		−	33.9459i		−	1.55103i	−0.631330	−	0.775514i	$-0.717491\pi$
$479$		−	33.9459i		−	1.55103i	0.631330	−	0.775514i	$-0.282509\pi$
$480$	−37.4551			−1.70958
$481$			38.1433i			1.73919i
$482$		−	16.2481i		−	0.740079i
$483$			24.6801i			1.12298i
$484$	1.75027			0.0795576
$485$	−0.179898			−0.00816874
$486$			37.4270i			1.69772i
$487$		−	12.3380i		−	0.559087i	−0.960133	−	0.279543i	$-0.909817\pi$
$487$		−	12.3380i		−	0.559087i	0.960133	−	0.279543i	$-0.0901830\pi$
$488$		−	90.0335i		−	4.07562i
$489$	1.78143			0.0805589
$490$			101.873i			4.60217i
$491$	27.7653			1.25303			0.626516	−	0.779409i	$-0.284480\pi$
$491$	27.7653			1.25303			0.626516	+	0.779409i	$0.284480\pi$
$492$	2.48676			0.112112
$493$	11.6467	+	10.2092i	0.524540	+	0.459798i
$494$	102.830			4.62653
$495$	9.90538			0.445214
$496$		−	29.0020i		−	1.30223i
$497$	29.2440			1.31177
$498$		−	41.5220i		−	1.86064i
$499$		−	40.0626i		−	1.79345i	−0.442589	−	0.896725i	$-0.645940\pi$
$499$		−	40.0626i		−	1.79345i	0.442589	−	0.896725i	$-0.354060\pi$
$500$			61.9269i			2.76946i
$501$	27.5912			1.23268
$502$	35.1150			1.56726
$503$		−	9.13789i		−	0.407438i	−0.979029	−	0.203719i	$-0.934697\pi$
$503$		−	9.13789i		−	0.407438i	0.979029	−	0.203719i	$-0.0653030\pi$
$504$		−	66.1173i		−	2.94510i
$505$		−	8.76947i		−	0.390236i
$506$	−34.7007			−1.54263
$507$		−	31.9752i		−	1.42007i
$508$	3.15497			0.139979
$509$	25.6218			1.13566			0.567832	−	0.823144i	$-0.307782\pi$
$509$	25.6218			1.13566			0.567832	+	0.823144i	$0.307782\pi$
$510$	−17.3566	+	19.8005i	−0.768565	+	0.876781i
$511$	−29.0454			−1.28489
$512$	13.5255			0.597747
$513$			33.6348i			1.48501i
$514$	−26.5342			−1.17037
$515$			15.1377i			0.667048i
$516$		−	59.0828i		−	2.60098i
$517$		−	3.26489i		−	0.143590i
$518$	83.2502			3.65780
$519$	3.89642			0.171034
$520$		−	104.093i		−	4.56478i
$521$			33.0408i			1.44754i	0.690040	+	0.723771i	$0.257593\pi$
$521$			33.0408i			1.44754i	−0.690040	+	0.723771i	$0.742407\pi$
$522$		−	15.4185i		−	0.674851i
$523$	−35.0385			−1.53213			−0.766064	−	0.642764i	$-0.777787\pi$
$523$	−35.0385			−1.53213			−0.766064	+	0.642764i	$0.777787\pi$
$524$			51.4187i			2.24624i
$525$	6.81814			0.297568
$526$	−19.5211			−0.851161
$527$	−7.40293	−	6.48922i	−0.322477	−	0.282675i
$528$	−47.9838			−2.08823
$529$	7.18073			0.312206
$530$		−	14.2968i		−	0.621011i
$531$	−3.39191			−0.147196
$532$		−	161.574i		−	7.00512i
$533$			2.51032i			0.108734i
$534$			50.1876i			2.17183i
$535$	−29.2936			−1.26647
$536$	18.9813			0.819868
$537$			14.7354i			0.635881i
$538$			16.9071i			0.728915i
$539$			63.0165i			2.71431i
$540$	55.7286			2.39818
$541$		−	10.6435i		−	0.457598i	−0.973474	−	0.228799i	$-0.926520\pi$
$541$		−	10.6435i		−	0.457598i	0.973474	−	0.228799i	$-0.0734799\pi$
$542$	−22.2763			−0.956850
$543$	−12.3623			−0.530516
$544$	−42.5963	+	48.5940i	−1.82630	+	2.08345i
$545$	12.9332			0.553997
$546$	−104.118			−4.45583
$547$		−	4.51612i		−	0.193095i	−0.995328	−	0.0965476i	$-0.969220\pi$
$547$		−	4.51612i		−	0.193095i	0.995328	−	0.0965476i	$-0.0307800\pi$
$548$	3.92772			0.167784
$549$			16.4771i			0.703226i
$550$			9.58644i			0.408767i
$551$		−	23.0204i		−	0.980701i
$552$	−40.3908			−1.71915
$553$	6.47296			0.275258
$554$		−	25.0406i		−	1.06387i
$555$			14.5173i			0.616226i
$556$		−	9.99438i		−	0.423856i
$557$	−24.6347			−1.04381			−0.521903	−	0.853005i	$-0.674778\pi$
$557$	−24.6347			−1.04381			−0.521903	+	0.853005i	$0.674778\pi$
$558$			9.80042i			0.414885i
$559$	59.6427			2.52262
$560$	−123.041			−5.19942
$561$	−10.7364	+	12.2481i	−0.453292	+	0.517117i
$562$	−2.99678			−0.126412
$563$	−12.3988			−0.522548			−0.261274	−	0.965265i	$-0.584143\pi$
$563$	−12.3988			−0.522548			−0.261274	+	0.965265i	$0.584143\pi$
$564$		−	6.22015i		−	0.261916i
$565$	26.0249			1.09488
$566$			48.7651i			2.04975i
$567$		−	10.4235i		−	0.437745i
$568$			47.8601i			2.00816i
$569$	17.5051			0.733852			0.366926	−	0.930250i	$-0.380410\pi$
$569$	17.5051			0.733852			0.366926	+	0.930250i	$0.380410\pi$
$570$	39.1370			1.63927
$571$			14.9256i			0.624618i	0.949981	+	0.312309i	$0.101102\pi$
$571$			14.9256i			0.624618i	−0.949981	+	0.312309i	$0.898898\pi$
$572$		−	105.391i		−	4.40661i
$573$			7.24783i			0.302783i
$574$	5.47894			0.228686
$575$			4.37025i			0.182252i
$576$	27.0157			1.12565
$577$	−9.00000			−0.374675			−0.187337	−	0.982296i	$-0.559986\pi$
$577$	−9.00000			−0.374675			−0.187337	+	0.982296i	$0.559986\pi$
$578$	5.94999	+	45.0367i	0.247487	+	1.87328i
$579$	−5.94833			−0.247204
$580$	−38.1419			−1.58375
$581$		−	65.8606i		−	2.73236i
$582$	−0.294487			−0.0122069
$583$		−	8.84364i		−	0.366266i
$584$		−	47.5351i		−	1.96702i
$585$			19.0502i			0.787628i
$586$	29.3284			1.21154
$587$	26.0901			1.07685			0.538427	−	0.842672i	$-0.319019\pi$
$587$	26.0901			1.07685			0.538427	+	0.842672i	$0.319019\pi$
$588$			120.057i			4.95105i
$589$			14.6323i			0.602915i
$590$			11.6552i			0.479835i
$591$	17.9609			0.738813
$592$			73.7875i			3.03265i
$593$	34.9290			1.43436			0.717181	−	0.696887i	$-0.245432\pi$
$593$	34.9290			1.43436			0.717181	+	0.696887i	$0.245432\pi$
$594$	47.8835			1.96469
$595$	−27.5305	+	31.4068i	−1.12864	+	1.28755i
$596$	−34.2527			−1.40305
$597$	−23.9491			−0.980172
$598$		−	66.7368i		−	2.72907i
$599$	18.6105			0.760405			0.380202	−	0.924903i	$-0.375854\pi$
$599$	18.6105			0.760405			0.380202	+	0.924903i	$0.375854\pi$
$600$			11.1584i			0.455540i
$601$		−	40.4901i		−	1.65163i	−0.563944	−	0.825813i	$-0.690716\pi$
$601$		−	40.4901i		−	1.65163i	0.563944	−	0.825813i	$-0.309284\pi$
$602$		−	130.174i		−	5.30549i
$603$	−3.47379			−0.141464
$604$	64.1531			2.61035
$605$			0.672462i			0.0273395i
$606$		−	14.3553i		−	0.583146i
$607$		−	21.6464i		−	0.878600i	−0.898340	−	0.439300i	$-0.855226\pi$
$607$		−	21.6464i		−	0.878600i	0.898340	−	0.439300i	$-0.144774\pi$
$608$	96.0491			3.89530
$609$			23.3087i			0.944517i
$610$	56.6180			2.29240
$611$	6.27909			0.254025
$612$	21.4617	−	24.4836i	0.867537	−	0.989689i
$613$	17.2349			0.696111			0.348056	−	0.937474i	$-0.386842\pi$
$613$	17.2349			0.696111			0.348056	+	0.937474i	$0.386842\pi$
$614$	−28.5257			−1.15120
$615$			0.955427i			0.0385265i
$616$	−140.534			−5.66229
$617$		−	7.28913i		−	0.293449i	−0.989177	−	0.146725i	$-0.953127\pi$
$617$		−	7.28913i		−	0.293449i	0.989177	−	0.146725i	$-0.0468731\pi$
$618$			24.7800i			0.996797i
$619$			14.5888i			0.586374i	0.956055	+	0.293187i	$0.0947158\pi$
$619$			14.5888i			0.586374i	−0.956055	+	0.293187i	$0.905284\pi$
$620$	24.2440			0.973661
$621$	21.8290			0.875969
$622$			20.9535i			0.840161i
$623$			79.6056i			3.18933i
$624$		−	92.2832i		−	3.69428i
$625$	−18.2987			−0.731950
$626$			67.2746i			2.68883i
$627$	24.2092			0.966823
$628$	−29.4180			−1.17391
$629$	18.8347	+	16.5100i	0.750988	+	0.658297i
$630$	41.5782			1.65651
$631$	7.34643			0.292457			0.146228	−	0.989251i	$-0.453287\pi$
$631$	7.34643			0.292457			0.146228	+	0.989251i	$0.453287\pi$
$632$			10.5935i			0.421387i
$633$	0.379843			0.0150974
$634$			36.2896i			1.44125i
$635$			1.21216i			0.0481030i
$636$		−	16.8486i		−	0.668089i
$637$	−121.194			−4.80189
$638$	−32.7726			−1.29748
$639$		−	8.75892i		−	0.346497i
$640$		−	30.9181i		−	1.22214i
$641$		−	4.52508i		−	0.178730i	−0.995999	−	0.0893649i	$-0.971516\pi$
$641$		−	4.52508i		−	0.178730i	0.995999	−	0.0893649i	$-0.0284837\pi$
$642$	−47.9527			−1.89254
$643$		−	41.0975i		−	1.62073i	−0.585928	−	0.810363i	$-0.699270\pi$
$643$		−	41.0975i		−	1.62073i	0.585928	−	0.810363i	$-0.300730\pi$
$644$	−104.862			−4.13214
$645$	22.7000			0.893810
$646$	44.5090	−	50.7760i	1.75118	−	1.99775i
$647$	−26.3482			−1.03586			−0.517928	−	0.855424i	$-0.673296\pi$
$647$	−26.3482			−1.03586			−0.517928	+	0.855424i	$0.673296\pi$
$648$	17.0588			0.670134
$649$			7.20961i			0.283002i
$650$	−18.4368			−0.723150
$651$		−	14.8156i		−	0.580670i
$652$			7.56901i			0.296425i
$653$		−	26.3173i		−	1.02987i	−0.857228	−	0.514937i	$-0.827815\pi$
$653$		−	26.3173i		−	1.02987i	0.857228	−	0.514937i	$-0.172185\pi$
$654$	21.1712			0.827861
$655$	−19.7553			−0.771905
$656$			4.85617i			0.189601i
$657$			8.69945i			0.339398i
$658$		−	13.7045i		−	0.534257i
$659$	−5.73091			−0.223245			−0.111622	−	0.993751i	$-0.535605\pi$
$659$	−5.73091			−0.223245			−0.111622	+	0.993751i	$0.535605\pi$
$660$		−	40.1116i		−	1.56134i
$661$	31.7948			1.23667			0.618337	−	0.785913i	$-0.287807\pi$
$661$	31.7948			1.23667			0.618337	+	0.785913i	$0.287807\pi$
$662$	−34.5553			−1.34303
$663$	−23.5558	−	20.6484i	−0.914832	−	0.801919i
$664$	107.786			4.18291
$665$	62.0776			2.40727
$666$		−	24.9344i		−	0.966189i
$667$	−14.9403			−0.578490
$668$			117.231i			4.53580i
$669$			11.8004i			0.456230i
$670$			11.9365i			0.461147i
$671$	35.0226			1.35203
$672$	−97.2522			−3.75158
$673$		−	10.9772i		−	0.423141i	−0.977363	−	0.211570i	$-0.932142\pi$
$673$		−	10.9772i		−	0.423141i	0.977363	−	0.211570i	$-0.0678577\pi$
$674$			44.8372i			1.72707i
$675$		−	6.03051i		−	0.232115i
$676$	135.858			5.22529
$677$		−	36.5951i		−	1.40646i	−0.710961	−	0.703232i	$-0.751740\pi$
$677$		−	36.5951i		−	1.40646i	0.710961	−	0.703232i	$-0.248260\pi$
$678$	42.6019			1.63612
$679$	−0.467104			−0.0179258
$680$	−51.3997	−	45.0557i	−1.97109	−	1.72781i
$681$	−7.38231			−0.282891
$682$	20.8311			0.797663
$683$			4.64423i			0.177707i	0.996045	+	0.0888533i	$0.0283202\pi$
$683$			4.64423i			0.177707i	−0.996045	+	0.0888533i	$0.971680\pi$
$684$	−48.3933			−1.85036
$685$			1.50905i			0.0576579i
$686$			168.582i			6.43651i
$687$			25.0750i			0.956672i
$688$	115.377			4.39872
$689$	17.0082			0.647962
$690$		−	25.4000i		−	0.966961i
$691$		−	16.1964i		−	0.616140i	−0.951364	−	0.308070i	$-0.900317\pi$
$691$		−	16.1964i		−	0.616140i	0.951364	−	0.308070i	$-0.0996831\pi$
$692$			16.5553i			0.629339i
$693$	25.7193			0.976996
$694$		−	66.6273i		−	2.52914i
$695$	3.83990			0.145656
$696$	−38.1466			−1.44594
$697$	1.23956	+	1.08657i	0.0469518	+	0.0411568i
$698$	−4.62795			−0.175171
$699$	17.7650			0.671933
$700$			28.9692i			1.09493i
$701$	−28.8059			−1.08799			−0.543993	−	0.839090i	$-0.683088\pi$
$701$	−28.8059			−1.08799			−0.543993	+	0.839090i	$0.683088\pi$
$702$			92.0903i			3.47572i
$703$		−	37.2279i		−	1.40408i
$704$		−	57.4227i		−	2.16420i
$705$	2.38982			0.0900058
$706$	−51.4161			−1.93507
$707$		−	22.7699i		−	0.856351i
$708$			13.7355i			0.516211i
$709$		−	17.4811i		−	0.656517i	−0.944588	−	0.328258i	$-0.893538\pi$
$709$		−	17.4811i		−	0.656517i	0.944588	−	0.328258i	$-0.106462\pi$
$710$	−30.0970			−1.12952
$711$		−	1.93873i		−	0.0727080i
$712$	−130.281			−4.88248
$713$	9.49643			0.355644
$714$	−45.0665	+	51.4120i	−1.68657	+	1.92405i
$715$	40.4917			1.51430
$716$	−62.6087			−2.33980
$717$			0.0498818i			0.00186287i
$718$	−13.1698			−0.491491
$719$		−	5.56858i		−	0.207673i	−0.994594	−	0.103837i	$-0.966888\pi$
$719$		−	5.56858i		−	0.207673i	0.994594	−	0.103837i	$-0.0331119\pi$
$720$			36.8521i			1.37340i
$721$			39.3051i			1.46380i
$722$	−49.5894			−1.84553
$723$	7.35684			0.273604
$724$		−	52.5255i		−	1.95209i
$725$			4.12742i			0.153288i
$726$			1.10080i			0.0408545i
$727$	−21.8916			−0.811914			−0.405957	−	0.913892i	$-0.633062\pi$
$727$	−21.8916			−0.811914			−0.405957	+	0.913892i	$0.633062\pi$
$728$		−	270.277i		−	10.0171i
$729$	−23.0437			−0.853471
$730$	29.8927			1.10638
$731$	25.8158	−	29.4508i	0.954832	−	1.08928i
$732$	66.7237			2.46618
$733$	−40.8550			−1.50901			−0.754507	−	0.656292i	$-0.772124\pi$
$733$	−40.8550			−1.50901			−0.754507	+	0.656292i	$0.772124\pi$
$734$		−	63.7143i		−	2.35174i
$735$	−46.1264			−1.70140
$736$		−	62.3361i		−	2.29774i
$737$			7.38365i			0.271980i
$738$		−	1.64101i		−	0.0604063i
$739$	48.8921			1.79852			0.899262	−	0.437410i	$-0.144104\pi$
$739$	48.8921			1.79852			0.899262	+	0.437410i	$0.144104\pi$
$740$	−61.6820			−2.26747
$741$			46.5595i			1.71041i
$742$		−	37.1215i		−	1.36277i
$743$			13.6623i			0.501222i	0.968088	+	0.250611i	$0.0806315\pi$
$743$			13.6623i			0.501222i	−0.968088	+	0.250611i	$0.919368\pi$
$744$	24.2469			0.888936
$745$		−	13.1601i		−	0.482149i
$746$	−67.7001			−2.47868
$747$	−19.7260			−0.721737
$748$	−52.0405	−	45.6174i	−1.90279	−	1.66794i
$749$	−76.0608			−2.77920
$750$	−38.9479			−1.42217
$751$		−	16.1098i		−	0.587854i	−0.955828	−	0.293927i	$-0.905038\pi$
$751$		−	16.1098i		−	0.587854i	0.955828	−	0.293927i	$-0.0949622\pi$
$752$	12.1468			0.442947
$753$			15.8995i			0.579409i
$754$		−	63.0286i		−	2.29537i
$755$			24.6480i			0.897032i
$756$	144.699			5.26266
$757$	36.7273			1.33488			0.667439	−	0.744665i	$-0.267391\pi$
$757$	36.7273			1.33488			0.667439	+	0.744665i	$0.267391\pi$
$758$		−	18.9018i		−	0.686543i
$759$		−	15.7118i		−	0.570304i
$760$			101.595i			3.68523i
$761$	10.2455			0.371401			0.185700	−	0.982606i	$-0.440545\pi$
$761$	10.2455			0.371401			0.185700	+	0.982606i	$0.440545\pi$
$762$			1.98426i			0.0718823i
$763$	33.5810			1.21571
$764$	−30.7950			−1.11412
$765$	9.40672	+	8.24570i	0.340101	+	0.298124i
$766$	−72.4369			−2.61725
$767$	−13.8656			−0.500659
$768$		−	8.05120i		−	0.290523i
$769$	−49.5597			−1.78717			−0.893584	−	0.448897i	$-0.851817\pi$
$769$	−49.5597			−1.78717			−0.893584	+	0.448897i	$0.851817\pi$
$770$		−	88.3757i		−	3.18484i
$771$		−	12.0142i		−	0.432681i
$772$		−	25.2735i		−	0.909615i
$773$	25.3202			0.910705			0.455353	−	0.890311i	$-0.349513\pi$
$773$	25.3202			0.910705			0.455353	+	0.890311i	$0.349513\pi$
$774$	−38.9886			−1.40142
$775$		−	2.62349i		−	0.0942387i
$776$		−	0.764453i		−	0.0274423i
$777$			37.6942i			1.35227i
$778$	71.4884			2.56298
$779$		−	2.45008i		−	0.0877831i
$780$	77.1433			2.76217
$781$	−18.6173			−0.666181
$782$	−32.9537	−	28.8864i	−1.17842	−	1.03298i
$783$	20.6161			0.736761
$784$	−234.448			−8.37313
$785$		−	11.3026i		−	0.403405i
$786$	−32.3389			−1.15349
$787$			14.9795i			0.533961i	0.963702	+	0.266980i	$0.0860259\pi$
$787$			14.9795i			0.533961i	−0.963702	+	0.266980i	$0.913974\pi$
$788$			76.3132i			2.71855i
$789$		−	8.83881i		−	0.314670i
$790$	−6.66178			−0.237016
$791$	67.5736			2.40264
$792$			42.0917i			1.49566i
$793$			67.3560i			2.39188i
$794$		−	94.8282i		−	3.36533i
$795$	6.47332			0.229585
$796$		−	101.756i		−	3.60665i
$797$	51.0930			1.80981			0.904904	−	0.425616i	$-0.139943\pi$
$797$	51.0930			1.80981			0.904904	+	0.425616i	$0.139943\pi$
$798$	101.619			3.59728
$799$	2.71785	−	3.10053i	0.0961506	−	0.109689i
$800$	−17.2210			−0.608855
$801$	23.8428			0.842445
$802$			75.2675i			2.65779i
$803$	18.4909			0.652531
$804$			14.0670i			0.496106i
$805$		−	40.2885i		−	1.41998i
$806$			40.0626i			1.41115i
$807$	−7.65521			−0.269476
$808$	37.2648			1.31097
$809$			18.3350i			0.644626i	0.946633	+	0.322313i	$0.104460\pi$
$809$			18.3350i			0.644626i	−0.946633	+	0.322313i	$0.895540\pi$
$810$			10.7275i			0.376927i
$811$		−	27.9964i		−	0.983087i	−0.870853	−	0.491543i	$-0.836433\pi$
$811$		−	27.9964i		−	0.983087i	0.870853	−	0.491543i	$-0.163567\pi$
$812$	−99.0353			−3.47546
$813$		−	10.0863i		−	0.353743i
$814$	−52.9989			−1.85761
$815$	−2.90806			−0.101865
$816$	−45.5682	−	39.9440i	−1.59521	−	1.39832i
$817$	−58.2113			−2.03655
$818$	−6.97972			−0.244040
$819$			49.4637i			1.72840i
$820$	−4.05947			−0.141763
$821$		−	8.52877i		−	0.297656i	−0.988863	−	0.148828i	$-0.952450\pi$
$821$		−	8.52877i		−	0.297656i	0.988863	−	0.148828i	$-0.0475501\pi$
$822$			2.47027i			0.0861605i
$823$			40.1596i			1.39988i	0.714204	+	0.699938i	$0.246789\pi$
$823$			40.1596i			1.39988i	−0.714204	+	0.699938i	$0.753211\pi$
$824$	−64.3258			−2.24090
$825$	−4.34057			−0.151119
$826$			30.2626i			1.05297i
$827$		−	46.8441i		−	1.62893i	−0.580214	−	0.814464i	$-0.697031\pi$
$827$		−	46.8441i		−	1.62893i	0.580214	−	0.814464i	$-0.302969\pi$
$828$			31.4074i			1.09148i
$829$	9.26201			0.321683			0.160841	−	0.986980i	$-0.448579\pi$
$829$	9.26201			0.321683			0.160841	+	0.986980i	$0.448579\pi$
$830$			67.7818i			2.35274i
$831$	11.3379			0.393308
$832$	110.436			3.82868
$833$	−52.4579	+	59.8441i	−1.81756	+	2.07348i
$834$	6.28579			0.217659
$835$	−45.0408			−1.55870
$836$			102.861i			3.55753i
$837$	−13.1041			−0.452946
$838$			59.0516i			2.03990i
$839$			13.6712i			0.471983i	0.971755	+	0.235991i	$0.0758337\pi$
$839$			13.6712i			0.471983i	−0.971755	+	0.235991i	$0.924166\pi$
$840$		−	102.867i		−	3.54926i
$841$	14.8899			0.513443
$842$	40.1264			1.38285
$843$		−	1.35689i		−	0.0467337i
$844$			1.61389i			0.0555526i
$845$			52.1973i			1.79564i
$846$	−4.10466			−0.141121
$847$			1.74605i			0.0599949i
$848$	32.9020			1.12986
$849$	−22.0800			−0.757784
$850$	−7.98019	+	9.10383i	−0.273718	+	0.312259i
$851$	−24.1610			−0.828229
$852$	−35.4690			−1.21515
$853$		−	15.7811i		−	0.540335i	−0.962813	−	0.270168i	$-0.912921\pi$
$853$		−	15.7811i		−	0.540335i	0.962813	−	0.270168i	$-0.0870791\pi$
$854$	147.009			5.03053
$855$		−	18.5930i		−	0.635866i
$856$		−	124.479i		−	4.25462i
$857$		−	41.7075i		−	1.42470i	−0.701825	−	0.712350i	$-0.747631\pi$
$857$		−	41.7075i		−	1.42470i	0.701825	−	0.712350i	$-0.252369\pi$
$858$	66.2836			2.26289
$859$	44.0615			1.50336			0.751679	−	0.659530i	$-0.229244\pi$
$859$	44.0615			1.50336			0.751679	+	0.659530i	$0.229244\pi$
$860$			96.4487i			3.28887i
$861$			2.48076i			0.0845442i
$862$		−	63.7666i		−	2.17190i
$863$	−50.6217			−1.72318			−0.861591	−	0.507604i	$-0.830531\pi$
$863$	−50.6217			−1.72318			−0.861591	+	0.507604i	$0.830531\pi$
$864$			86.0177i			2.92638i
$865$	−6.36065			−0.216268
$866$	71.2875			2.42245
$867$	−20.3918	+	2.69405i	−0.692543	+	0.0914948i
$868$	62.9494			2.13664
$869$	−4.12082			−0.139789
$870$		−	23.9887i		−	0.813292i
$871$	−14.2003			−0.481160
$872$			54.9580i			1.86111i
$873$			0.139903i			0.00473501i
$874$			65.1351i			2.20323i
$875$	−61.7776			−2.08847
$876$	35.2282			1.19025
$877$		−	18.8479i		−	0.636448i	−0.948016	−	0.318224i	$-0.896914\pi$
$877$		−	18.8479i		−	0.636448i	0.948016	−	0.318224i	$-0.103086\pi$
$878$			86.0820i			2.90513i
$879$			13.2794i			0.447902i
$880$	78.3303			2.64051
$881$			58.7939i			1.98082i	0.138171	+	0.990408i	$0.455878\pi$
$881$			58.7939i			1.98082i	−0.138171	+	0.990408i	$0.544122\pi$
$882$	79.2251			2.66765
$883$	−12.8482			−0.432376			−0.216188	−	0.976352i	$-0.569362\pi$
$883$	−12.8482			−0.432376			−0.216188	+	0.976352i	$0.569362\pi$
$884$	87.7321	−	100.085i	2.95075	−	3.36623i
$885$	−5.27725			−0.177393
$886$	19.6519			0.660217
$887$			0.748411i			0.0251292i	0.999921	+	0.0125646i	$0.00399954\pi$
$887$			0.748411i			0.0251292i	−0.999921	+	0.0125646i	$0.996000\pi$
$888$	−61.6895			−2.07017
$889$			3.14736i			0.105559i
$890$		−	81.9278i		−	2.74623i
$891$			6.63581i			0.222308i
$892$	−50.1382			−1.67875
$893$	−6.12840			−0.205079
$894$		−	21.5427i		−	0.720494i
$895$		−	24.0546i		−	0.804056i
$896$		−	80.2788i		−	2.68193i
$897$	30.2172			1.00892
$898$			81.1048i			2.70650i
$899$	8.96877			0.299125
$900$	8.67663			0.289221
$901$	7.36186	−	8.39843i	0.245259	−	0.279792i
$902$	−3.48801			−0.116138
$903$	58.9404			1.96141
$904$			110.589i			3.67815i
$905$	20.1806			0.670825
$906$			40.3480i			1.34047i
$907$		−	31.1343i		−	1.03380i	−0.856046	−	0.516899i	$-0.827086\pi$
$907$		−	31.1343i		−	1.03380i	0.856046	−	0.516899i	$-0.172914\pi$
$908$		−	31.3663i		−	1.04093i
$909$	−6.81986			−0.226200
$910$	169.965			5.63430
$911$			49.0390i			1.62474i	0.583145	+	0.812368i	$0.301822\pi$
$911$			49.0390i			1.62474i	−0.583145	+	0.812368i	$0.698178\pi$
$912$			90.0684i			2.98246i
$913$			41.9283i			1.38762i
$914$	93.4697			3.09170
$915$			25.6356i			0.847488i
$916$	−106.540			−3.52018
$917$	−51.2947			−1.69390
$918$	45.4730	+	39.8605i	1.50083	+	1.31559i
$919$	19.7655			0.652004			0.326002	−	0.945369i	$-0.394298\pi$
$919$	19.7655			0.652004			0.326002	+	0.945369i	$0.394298\pi$
$920$	65.9353			2.17382
$921$		−	12.9159i		−	0.425595i
$922$	9.12520			0.300523
$923$		−	35.8051i		−	1.17854i
$924$		−	104.150i		−	3.42628i
$925$			6.67474i			0.219464i
$926$	72.4091			2.37951
$927$	11.7723			0.386654
$928$		−	58.8724i		−	1.93258i
$929$		−	32.6178i		−	1.07015i	−0.844803	−	0.535077i	$-0.820283\pi$
$929$		−	32.6178i		−	1.07015i	0.844803	−	0.535077i	$-0.179717\pi$
$930$			15.2478i			0.499995i
$931$	118.286			3.87665
$932$			75.4808i			2.47245i
$933$	−9.48740			−0.310603
$934$	43.4642			1.42219
$935$	17.5265	−	19.9943i	0.573177	−	0.653882i
$936$	−80.9513			−2.64598
$937$	5.24292			0.171279			0.0856394	−	0.996326i	$-0.472707\pi$
$937$	5.24292			0.171279			0.0856394	+	0.996326i	$0.472707\pi$
$938$			30.9931i			1.01196i
$939$	−30.4607			−0.994049
$940$			10.1540i			0.331186i
$941$		−	49.7131i		−	1.62060i	−0.586015	−	0.810300i	$-0.699304\pi$
$941$		−	49.7131i		−	1.62060i	0.586015	−	0.810300i	$-0.300696\pi$
$942$		−	18.5019i		−	0.602825i
$943$	−1.59011			−0.0517809
$944$	−26.8228			−0.873007
$945$			55.5942i			1.80848i
$946$			82.8714i			2.69438i
$947$			15.6584i			0.508830i	0.967095	+	0.254415i	$0.0818829\pi$
$947$			15.6584i			0.508830i	−0.967095	+	0.254415i	$0.918117\pi$
$948$	−7.85084			−0.254983
$949$			35.5620i			1.15439i
$950$	17.9943			0.583812
$951$	−16.4313			−0.532822
$952$	−133.459	−	116.987i	−4.32544	−	3.79158i
$953$	2.97863			0.0964873			0.0482437	−	0.998836i	$-0.484638\pi$
$953$	2.97863			0.0964873			0.0482437	+	0.998836i	$0.484638\pi$
$954$	−11.1183			−0.359969
$955$		−	11.8316i		−	0.382861i
$956$	−0.211940			−0.00685463
$957$		−	14.8388i		−	0.479671i
$958$			90.7116i			2.93076i
$959$			3.91825i			0.126527i
$960$	42.0319			1.35657
$961$	25.2992			0.816104
$962$		−	101.928i		−	3.28630i
$963$			22.7811i			0.734111i
$964$			31.2581i			1.00676i
$965$	9.71024			0.312584
$966$		−	65.9510i		−	2.12194i
$967$	−28.8120			−0.926531			−0.463266	−	0.886220i	$-0.653322\pi$
$967$	−28.8120			−0.926531			−0.463266	+	0.886220i	$0.653322\pi$
$968$	−2.85754			−0.0918449
$969$	22.9905	+	20.1529i	0.738560	+	0.647404i
$970$	0.480730			0.0154353
$971$	4.49678			0.144308			0.0721542	−	0.997393i	$-0.477013\pi$
$971$	4.49678			0.144308			0.0721542	+	0.997393i	$0.477013\pi$
$972$		−	72.0023i		−	2.30947i
$973$	9.97029			0.319633
$974$			32.9700i			1.05643i
$975$		−	8.34785i		−	0.267345i
$976$			130.299i			4.17076i
$977$	8.58126			0.274539			0.137269	−	0.990534i	$-0.456167\pi$
$977$	8.58126			0.274539			0.137269	+	0.990534i	$0.456167\pi$
$978$	−4.76040			−0.152221
$979$		−	50.6786i		−	1.61970i
$980$		−	195.984i		−	6.26049i
$981$		−	10.0579i		−	0.321124i
$982$	−74.1956			−2.36768
$983$		−	13.6495i		−	0.435351i	−0.976021	−	0.217676i	$-0.930152\pi$
$983$		−	13.6495i		−	0.435351i	0.976021	−	0.217676i	$-0.0698475\pi$
$984$	−4.05997			−0.129427
$985$	−29.3200			−0.934212
$986$	−31.1227	−	27.2814i	−0.991149	−	0.868816i
$987$	6.20516			0.197512
$988$	−197.824			−6.29363
$989$			37.7793i			1.20131i
$990$	−26.4696			−0.841258
$991$			1.81341i			0.0576047i	0.999585	+	0.0288024i	$0.00916935\pi$
$991$			1.81341i			0.0576047i	−0.999585	+	0.0288024i	$0.990831\pi$
$992$			37.4208i			1.18811i
$993$		−	15.6460i		−	0.496512i
$994$	−78.1469			−2.47867
$995$	39.0953			1.23940
$996$			79.8801i			2.53110i
$997$			13.3367i			0.422379i	0.977445	+	0.211189i	$0.0677337\pi$
$997$			13.3367i			0.422379i	−0.977445	+	0.211189i	$0.932266\pi$
$998$			107.057i			3.38883i
$999$	33.3398			1.05483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	799.2.b.c.424.3	✓	40
17.16	even	2	inner	799.2.b.c.424.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.2.b.c.424.3	✓	40	1.1	even	1	trivial
799.2.b.c.424.4	yes	40	17.16	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 799 = 17 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	799.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.67224 q^{2} -1.20994i q^{3} +5.14087 q^{4} +1.97515i q^{5} +3.23326i q^{6} +5.12847i q^{7} -8.39315 q^{8} +1.53604 q^{9} +O(q^{10})\)	\(q-2.67224 q^{2} -1.20994i q^{3} +5.14087 q^{4} +1.97515i q^{5} +3.23326i q^{6} +5.12847i q^{7} -8.39315 q^{8} +1.53604 q^{9} -5.27807i q^{10} -3.26489i q^{11} -6.22015i q^{12} +6.27909 q^{13} -13.7045i q^{14} +2.38982 q^{15} +12.1468 q^{16} +(2.71785 - 3.10053i) q^{17} -4.10466 q^{18} -6.12840 q^{19} +10.1540i q^{20} +6.20516 q^{21} +8.72458i q^{22} +3.97734i q^{23} +10.1552i q^{24} +1.09878 q^{25} -16.7792 q^{26} -5.48835i q^{27} +26.3648i q^{28} +3.75635i q^{29} -6.38617 q^{30} -2.38763i q^{31} -15.6728 q^{32} -3.95034 q^{33} +(-7.26274 + 8.28536i) q^{34} -10.1295 q^{35} +7.89657 q^{36} +6.07466i q^{37} +16.3765 q^{38} -7.59734i q^{39} -16.5777i q^{40} +0.399791i q^{41} -16.5817 q^{42} +9.49861 q^{43} -16.7844i q^{44} +3.03390i q^{45} -10.6284i q^{46} +1.00000 q^{47} -14.6969i q^{48} -19.3012 q^{49} -2.93622 q^{50} +(-3.75147 - 3.28844i) q^{51} +32.2800 q^{52} +2.70871 q^{53} +14.6662i q^{54} +6.44866 q^{55} -43.0440i q^{56} +7.41501i q^{57} -10.0379i q^{58} -2.20822 q^{59} +12.2857 q^{60} +10.7270i q^{61} +6.38032i q^{62} +7.87753i q^{63} +17.5879 q^{64} +12.4021i q^{65} +10.5562 q^{66} -2.26153 q^{67} +(13.9721 - 15.9394i) q^{68} +4.81236 q^{69} +27.0685 q^{70} -5.70228i q^{71} -12.8922 q^{72} +5.66356i q^{73} -16.2329i q^{74} -1.32947i q^{75} -31.5053 q^{76} +16.7439 q^{77} +20.3019i q^{78} -1.26216i q^{79} +23.9917i q^{80} -2.03247 q^{81} -1.06834i q^{82} -12.8421 q^{83} +31.8999 q^{84} +(6.12401 + 5.36816i) q^{85} -25.3826 q^{86} +4.54497 q^{87} +27.4027i q^{88} +15.5223 q^{89} -8.10732i q^{90} +32.2022i q^{91} +20.4470i q^{92} -2.88890 q^{93} -2.67224 q^{94} -12.1045i q^{95} +18.9632i q^{96} +0.0910806i q^{97} +51.5775 q^{98} -5.01500i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 6 q^{2} + 46 q^{4} - 18 q^{8} - 46 q^{9}+O(q^{10}) \) 40 * q - 6 * q^2 + 46 * q^4 - 18 * q^8 - 46 * q^9	\( 40 q - 6 q^{2} + 46 q^{4} - 18 q^{8} - 46 q^{9} + 14 q^{13} - 18 q^{15} + 58 q^{16} + 2 q^{17} - 10 q^{18} - 22 q^{19} + 24 q^{21} - 58 q^{25} - 6 q^{26} + 34 q^{30} - 92 q^{32} + 50 q^{33} + 8 q^{34} - 18 q^{35} - 68 q^{36} + 6 q^{38} + 36 q^{42} - 26 q^{43} + 40 q^{47} - 78 q^{49} + 50 q^{50} + 20 q^{51} - 24 q^{52} - 22 q^{53} + 22 q^{55} + 18 q^{59} - 74 q^{60} + 94 q^{64} - 96 q^{66} + 52 q^{67} + 71 q^{68} - 26 q^{69} + 2 q^{70} + 16 q^{72} - 2 q^{76} - 60 q^{77} + 96 q^{81} + 10 q^{83} + 138 q^{84} + 38 q^{85} - 152 q^{86} - 10 q^{87} - 6 q^{89} + 14 q^{93} - 6 q^{94} + 60 q^{98}+O(q^{100}) \) 40 * q - 6 * q^2 + 46 * q^4 - 18 * q^8 - 46 * q^9 + 14 * q^13 - 18 * q^15 + 58 * q^16 + 2 * q^17 - 10 * q^18 - 22 * q^19 + 24 * q^21 - 58 * q^25 - 6 * q^26 + 34 * q^30 - 92 * q^32 + 50 * q^33 + 8 * q^34 - 18 * q^35 - 68 * q^36 + 6 * q^38 + 36 * q^42 - 26 * q^43 + 40 * q^47 - 78 * q^49 + 50 * q^50 + 20 * q^51 - 24 * q^52 - 22 * q^53 + 22 * q^55 + 18 * q^59 - 74 * q^60 + 94 * q^64 - 96 * q^66 + 52 * q^67 + 71 * q^68 - 26 * q^69 + 2 * q^70 + 16 * q^72 - 2 * q^76 - 60 * q^77 + 96 * q^81 + 10 * q^83 + 138 * q^84 + 38 * q^85 - 152 * q^86 - 10 * q^87 - 6 * q^89 + 14 * q^93 - 6 * q^94 + 60 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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