LMFDB - Embedded newform 370.2.b.c.149.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [370,2,Mod(149,370)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("370.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(370, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-4,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.1
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	370.149
Dual form			370.2.b.c.149.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -2.44949i q^{3} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -2.44949 q^{6} -4.44949i q^{7} +1.00000i q^{8} -3.00000 q^{9} +(-1.00000 + 2.00000i) q^{10} +4.89898 q^{11} +2.44949i q^{12} +4.00000i q^{13} -4.44949 q^{14} +(-2.44949 + 4.89898i) q^{15} +1.00000 q^{16} +4.89898i q^{17} +3.00000i q^{18} -3.55051 q^{19} +(2.00000 + 1.00000i) q^{20} -10.8990 q^{21} -4.89898i q^{22} -8.89898i q^{23} +2.44949 q^{24} +(3.00000 + 4.00000i) q^{25} +4.00000 q^{26} +4.44949i q^{28} +(4.89898 + 2.44949i) q^{30} -1.55051 q^{31} -1.00000i q^{32} -12.0000i q^{33} +4.89898 q^{34} +(-4.44949 + 8.89898i) q^{35} +3.00000 q^{36} -1.00000i q^{37} +3.55051i q^{38} +9.79796 q^{39} +(1.00000 - 2.00000i) q^{40} +2.00000 q^{41} +10.8990i q^{42} +4.00000i q^{43} -4.89898 q^{44} +(6.00000 + 3.00000i) q^{45} -8.89898 q^{46} -4.44949i q^{47} -2.44949i q^{48} -12.7980 q^{49} +(4.00000 - 3.00000i) q^{50} +12.0000 q^{51} -4.00000i q^{52} -11.7980i q^{53} +(-9.79796 - 4.89898i) q^{55} +4.44949 q^{56} +8.69694i q^{57} +3.55051 q^{59} +(2.44949 - 4.89898i) q^{60} +12.0000 q^{61} +1.55051i q^{62} +13.3485i q^{63} -1.00000 q^{64} +(4.00000 - 8.00000i) q^{65} -12.0000 q^{66} +5.55051i q^{67} -4.89898i q^{68} -21.7980 q^{69} +(8.89898 + 4.44949i) q^{70} +4.89898 q^{71} -3.00000i q^{72} +4.00000i q^{73} -1.00000 q^{74} +(9.79796 - 7.34847i) q^{75} +3.55051 q^{76} -21.7980i q^{77} -9.79796i q^{78} -6.44949 q^{79} +(-2.00000 - 1.00000i) q^{80} -9.00000 q^{81} -2.00000i q^{82} -9.55051i q^{83} +10.8990 q^{84} +(4.89898 - 9.79796i) q^{85} +4.00000 q^{86} +4.89898i q^{88} -15.7980 q^{89} +(3.00000 - 6.00000i) q^{90} +17.7980 q^{91} +8.89898i q^{92} +3.79796i q^{93} -4.44949 q^{94} +(7.10102 + 3.55051i) q^{95} -2.44949 q^{96} +2.00000i q^{97} +12.7980i q^{98} -14.6969 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 8 q^{5} - 12 q^{9} - 4 q^{10} - 8 q^{14} + 4 q^{16} - 24 q^{19} + 8 q^{20} - 24 q^{21} + 12 q^{25} + 16 q^{26} - 16 q^{31} - 8 q^{35} + 12 q^{36} + 4 q^{40} + 8 q^{41} + 24 q^{45} - 16 q^{46}+ \cdots + 48 q^{95}+O(q^{100}) $ 4 * q - 4 * q^4 - 8 * q^5 - 12 * q^9 - 4 * q^10 - 8 * q^14 + 4 * q^16 - 24 * q^19 + 8 * q^20 - 24 * q^21 + 12 * q^25 + 16 * q^26 - 16 * q^31 - 8 * q^35 + 12 * q^36 + 4 * q^40 + 8 * q^41 + 24 * q^45 - 16 * q^46 - 12 * q^49 + 16 * q^50 + 48 * q^51 + 8 * q^56 + 24 * q^59 + 48 * q^61 - 4 * q^64 + 16 * q^65 - 48 * q^66 - 48 * q^69 + 16 * q^70 - 4 * q^74 + 24 * q^76 - 16 * q^79 - 8 * q^80 - 36 * q^81 + 24 * q^84 + 16 * q^86 - 24 * q^89 + 12 * q^90 + 32 * q^91 - 8 * q^94 + 48 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	2.44949i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$3$		−	2.44949i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$4$	−1.00000			−0.500000
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$	−2.44949			−1.00000
$7$		−	4.44949i		−	1.68175i	−0.541230	−	0.840875i	$-0.682041\pi$
$7$		−	4.44949i		−	1.68175i	0.541230	−	0.840875i	$-0.317959\pi$
$8$			1.00000i			0.353553i
$9$	−3.00000			−1.00000
$10$	−1.00000	+	2.00000i	−0.316228	+	0.632456i
$11$	4.89898			1.47710			0.738549	−	0.674200i	$-0.235511\pi$
$11$	4.89898			1.47710			0.738549	+	0.674200i	$0.235511\pi$
$12$			2.44949i			0.707107i
$13$			4.00000i			1.10940i	0.832050	+	0.554700i	$0.187167\pi$
$13$			4.00000i			1.10940i	−0.832050	+	0.554700i	$0.812833\pi$
$14$	−4.44949			−1.18918
$15$	−2.44949	+	4.89898i	−0.632456	+	1.26491i
$16$	1.00000			0.250000
$17$			4.89898i			1.18818i	0.804400	+	0.594089i	$0.202487\pi$
$17$			4.89898i			1.18818i	−0.804400	+	0.594089i	$0.797513\pi$
$18$			3.00000i			0.707107i
$19$	−3.55051			−0.814543			−0.407271	−	0.913307i	$-0.633520\pi$
$19$	−3.55051			−0.814543			−0.407271	+	0.913307i	$0.633520\pi$
$20$	2.00000	+	1.00000i	0.447214	+	0.223607i
$21$	−10.8990			−2.37835
$22$		−	4.89898i		−	1.04447i
$23$		−	8.89898i		−	1.85557i	−0.373121	−	0.927783i	$-0.621712\pi$
$23$		−	8.89898i		−	1.85557i	0.373121	−	0.927783i	$-0.378288\pi$
$24$	2.44949			0.500000
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	4.00000			0.784465
$27$		0			0
$28$			4.44949i			0.840875i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	4.89898	+	2.44949i	0.894427	+	0.447214i
$31$	−1.55051			−0.278480			−0.139240	−	0.990259i	$-0.544466\pi$
$31$	−1.55051			−0.278480			−0.139240	+	0.990259i	$0.544466\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	12.0000i		−	2.08893i
$34$	4.89898			0.840168
$35$	−4.44949	+	8.89898i	−0.752101	+	1.50420i
$36$	3.00000			0.500000
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$			3.55051i			0.575969i
$39$	9.79796			1.56893
$40$	1.00000	−	2.00000i	0.158114	−	0.316228i
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$			10.8990i			1.68175i
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	−4.89898			−0.738549
$45$	6.00000	+	3.00000i	0.894427	+	0.447214i
$46$	−8.89898			−1.31208
$47$		−	4.44949i		−	0.649025i	−0.945881	−	0.324512i	$-0.894800\pi$
$47$		−	4.44949i		−	0.649025i	0.945881	−	0.324512i	$-0.105200\pi$
$48$		−	2.44949i		−	0.353553i
$49$	−12.7980			−1.82828
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$	12.0000			1.68034
$52$		−	4.00000i		−	0.554700i
$53$		−	11.7980i		−	1.62057i	−0.586033	−	0.810287i	$-0.699311\pi$
$53$		−	11.7980i		−	1.62057i	0.586033	−	0.810287i	$-0.300689\pi$
$54$		0			0
$55$	−9.79796	−	4.89898i	−1.32116	−	0.660578i
$56$	4.44949			0.594588
$57$			8.69694i			1.15194i
$58$		0			0
$59$	3.55051			0.462237			0.231119	−	0.972926i	$-0.425761\pi$
$59$	3.55051			0.462237			0.231119	+	0.972926i	$0.425761\pi$
$60$	2.44949	−	4.89898i	0.316228	−	0.632456i
$61$	12.0000			1.53644			0.768221	−	0.640184i	$-0.221142\pi$
$61$	12.0000			1.53644			0.768221	+	0.640184i	$0.221142\pi$
$62$			1.55051i			0.196915i
$63$			13.3485i			1.68175i
$64$	−1.00000			−0.125000
$65$	4.00000	−	8.00000i	0.496139	−	0.992278i
$66$	−12.0000			−1.47710
$67$			5.55051i			0.678103i	0.940768	+	0.339051i	$0.110106\pi$
$67$			5.55051i			0.678103i	−0.940768	+	0.339051i	$0.889894\pi$
$68$		−	4.89898i		−	0.594089i
$69$	−21.7980			−2.62417
$70$	8.89898	+	4.44949i	1.06363	+	0.531816i
$71$	4.89898			0.581402			0.290701	−	0.956814i	$-0.406112\pi$
$71$	4.89898			0.581402			0.290701	+	0.956814i	$0.406112\pi$
$72$		−	3.00000i		−	0.353553i
$73$			4.00000i			0.468165i	0.972217	+	0.234082i	$0.0752085\pi$
$73$			4.00000i			0.468165i	−0.972217	+	0.234082i	$0.924791\pi$
$74$	−1.00000			−0.116248
$75$	9.79796	−	7.34847i	1.13137	−	0.848528i
$76$	3.55051			0.407271
$77$		−	21.7980i		−	2.48411i
$78$		−	9.79796i		−	1.10940i
$79$	−6.44949			−0.725624			−0.362812	−	0.931862i	$-0.618183\pi$
$79$	−6.44949			−0.725624			−0.362812	+	0.931862i	$0.618183\pi$
$80$	−2.00000	−	1.00000i	−0.223607	−	0.111803i
$81$	−9.00000			−1.00000
$82$		−	2.00000i		−	0.220863i
$83$		−	9.55051i		−	1.04830i	−0.851625	−	0.524152i	$-0.824382\pi$
$83$		−	9.55051i		−	1.04830i	0.851625	−	0.524152i	$-0.175618\pi$
$84$	10.8990			1.18918
$85$	4.89898	−	9.79796i	0.531369	−	1.06274i
$86$	4.00000			0.431331
$87$		0			0
$88$			4.89898i			0.522233i
$89$	−15.7980			−1.67458			−0.837290	−	0.546759i	$-0.815861\pi$
$89$	−15.7980			−1.67458			−0.837290	+	0.546759i	$0.815861\pi$
$90$	3.00000	−	6.00000i	0.316228	−	0.632456i
$91$	17.7980			1.86573
$92$			8.89898i			0.927783i
$93$			3.79796i			0.393830i
$94$	−4.44949			−0.458930
$95$	7.10102	+	3.55051i	0.728549	+	0.364275i
$96$	−2.44949			−0.250000
$97$			2.00000i			0.203069i	0.994832	+	0.101535i	$0.0323753\pi$
$97$			2.00000i			0.203069i	−0.994832	+	0.101535i	$0.967625\pi$
$98$			12.7980i			1.29279i
$99$	−14.6969			−1.47710
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$	10.6969			1.06439			0.532193	−	0.846623i	$-0.321368\pi$
$101$	10.6969			1.06439			0.532193	+	0.846623i	$0.321368\pi$
$102$		−	12.0000i		−	1.18818i
$103$			9.79796i			0.965422i	0.875780	+	0.482711i	$0.160348\pi$
$103$			9.79796i			0.965422i	−0.875780	+	0.482711i	$0.839652\pi$
$104$	−4.00000			−0.392232
$105$	21.7980	+	10.8990i	2.12726	+	1.06363i
$106$	−11.7980			−1.14592
$107$			5.55051i			0.536588i	0.963337	+	0.268294i	$0.0864599\pi$
$107$			5.55051i			0.536588i	−0.963337	+	0.268294i	$0.913540\pi$
$108$		0			0
$109$	5.79796			0.555344			0.277672	−	0.960676i	$-0.410437\pi$
$109$	5.79796			0.555344			0.277672	+	0.960676i	$0.410437\pi$
$110$	−4.89898	+	9.79796i	−0.467099	+	0.934199i
$111$	−2.44949			−0.232495
$112$		−	4.44949i		−	0.420437i
$113$		−	3.10102i		−	0.291719i	−0.989305	−	0.145860i	$-0.953405\pi$
$113$		−	3.10102i		−	0.291719i	0.989305	−	0.145860i	$-0.0465948\pi$
$114$	8.69694			0.814543
$115$	−8.89898	+	17.7980i	−0.829834	+	1.65967i
$116$		0			0
$117$		−	12.0000i		−	1.10940i
$118$		−	3.55051i		−	0.326851i
$119$	21.7980			1.99822
$120$	−4.89898	−	2.44949i	−0.447214	−	0.223607i
$121$	13.0000			1.18182
$122$		−	12.0000i		−	1.08643i
$123$		−	4.89898i		−	0.441726i
$124$	1.55051			0.139240
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$	13.3485			1.18918
$127$			2.65153i			0.235285i	0.993056	+	0.117643i	$0.0375337\pi$
$127$			2.65153i			0.235285i	−0.993056	+	0.117643i	$0.962466\pi$
$128$			1.00000i			0.0883883i
$129$	9.79796			0.862662
$130$	−8.00000	−	4.00000i	−0.701646	−	0.350823i
$131$	−10.2474			−0.895324			−0.447662	−	0.894203i	$-0.647743\pi$
$131$	−10.2474			−0.895324			−0.447662	+	0.894203i	$0.647743\pi$
$132$			12.0000i			1.04447i
$133$			15.7980i			1.36986i
$134$	5.55051			0.479491
$135$		0			0
$136$	−4.89898			−0.420084
$137$		−	19.5959i		−	1.67419i	−0.547056	−	0.837096i	$-0.684251\pi$
$137$		−	19.5959i		−	1.67419i	0.547056	−	0.837096i	$-0.315749\pi$
$138$			21.7980i			1.85557i
$139$	5.79796			0.491776			0.245888	−	0.969298i	$-0.420920\pi$
$139$	5.79796			0.491776			0.245888	+	0.969298i	$0.420920\pi$
$140$	4.44949	−	8.89898i	0.376051	−	0.752101i
$141$	−10.8990			−0.917860
$142$		−	4.89898i		−	0.411113i
$143$			19.5959i			1.63869i
$144$	−3.00000			−0.250000
$145$		0			0
$146$	4.00000			0.331042
$147$			31.3485i			2.58558i
$148$			1.00000i			0.0821995i
$149$	18.6969			1.53171			0.765856	−	0.643012i	$-0.222315\pi$
$149$	18.6969			1.53171			0.765856	+	0.643012i	$0.222315\pi$
$150$	−7.34847	−	9.79796i	−0.600000	−	0.800000i
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$		−	3.55051i		−	0.287984i
$153$		−	14.6969i		−	1.18818i
$154$	−21.7980			−1.75653
$155$	3.10102	+	1.55051i	0.249080	+	0.124540i
$156$	−9.79796			−0.784465
$157$			7.79796i			0.622345i	0.950353	+	0.311172i	$0.100722\pi$
$157$			7.79796i			0.622345i	−0.950353	+	0.311172i	$0.899278\pi$
$158$			6.44949i			0.513094i
$159$	−28.8990			−2.29184
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$	−39.5959			−3.12060
$162$			9.00000i			0.707107i
$163$		−	21.7980i		−	1.70735i	−0.520808	−	0.853674i	$-0.674369\pi$
$163$		−	21.7980i		−	1.70735i	0.520808	−	0.853674i	$-0.325631\pi$
$164$	−2.00000			−0.156174
$165$	−12.0000	+	24.0000i	−0.934199	+	1.86840i
$166$	−9.55051			−0.741263
$167$		−	8.00000i		−	0.619059i	−0.950890	−	0.309529i	$-0.899829\pi$
$167$		−	8.00000i		−	0.619059i	0.950890	−	0.309529i	$-0.100171\pi$
$168$		−	10.8990i		−	0.840875i
$169$	−3.00000			−0.230769
$170$	−9.79796	−	4.89898i	−0.751469	−	0.375735i
$171$	10.6515			0.814543
$172$		−	4.00000i		−	0.304997i
$173$			19.7980i			1.50521i	0.658472	+	0.752605i	$0.271203\pi$
$173$			19.7980i			1.50521i	−0.658472	+	0.752605i	$0.728797\pi$
$174$		0			0
$175$	17.7980	−	13.3485i	1.34540	−	1.00905i
$176$	4.89898			0.369274
$177$		−	8.69694i		−	0.653702i
$178$			15.7980i			1.18411i
$179$	9.34847			0.698737			0.349369	−	0.936985i	$-0.386396\pi$
$179$	9.34847			0.698737			0.349369	+	0.936985i	$0.386396\pi$
$180$	−6.00000	−	3.00000i	−0.447214	−	0.223607i
$181$	10.6969			0.795097			0.397549	−	0.917581i	$-0.369861\pi$
$181$	10.6969			0.795097			0.397549	+	0.917581i	$0.369861\pi$
$182$		−	17.7980i		−	1.31927i
$183$		−	29.3939i		−	2.17286i
$184$	8.89898			0.656041
$185$	−1.00000	+	2.00000i	−0.0735215	+	0.147043i
$186$	3.79796			0.278480
$187$			24.0000i			1.75505i
$188$			4.44949i			0.324512i
$189$		0			0
$190$	3.55051	−	7.10102i	0.257581	−	0.515162i
$191$	11.3485			0.821146			0.410573	−	0.911828i	$-0.365329\pi$
$191$	11.3485			0.821146			0.410573	+	0.911828i	$0.365329\pi$
$192$			2.44949i			0.176777i
$193$			14.0000i			1.00774i	0.863779	+	0.503871i	$0.168091\pi$
$193$			14.0000i			1.00774i	−0.863779	+	0.503871i	$0.831909\pi$
$194$	2.00000			0.143592
$195$	−19.5959	−	9.79796i	−1.40329	−	0.701646i
$196$	12.7980			0.914140
$197$			2.00000i			0.142494i	0.997459	+	0.0712470i	$0.0226979\pi$
$197$			2.00000i			0.142494i	−0.997459	+	0.0712470i	$0.977302\pi$
$198$			14.6969i			1.04447i
$199$	−6.44949			−0.457192			−0.228596	−	0.973521i	$-0.573414\pi$
$199$	−6.44949			−0.457192			−0.228596	+	0.973521i	$0.573414\pi$
$200$	−4.00000	+	3.00000i	−0.282843	+	0.212132i
$201$	13.5959			0.958982
$202$		−	10.6969i		−	0.752634i
$203$		0			0
$204$	−12.0000			−0.840168
$205$	−4.00000	−	2.00000i	−0.279372	−	0.139686i
$206$	9.79796			0.682656
$207$			26.6969i			1.85557i
$208$			4.00000i			0.277350i
$209$	−17.3939			−1.20316
$210$	10.8990	−	21.7980i	0.752101	−	1.50420i
$211$	−6.69694			−0.461036			−0.230518	−	0.973068i	$-0.574042\pi$
$211$	−6.69694			−0.461036			−0.230518	+	0.973068i	$0.574042\pi$
$212$			11.7980i			0.810287i
$213$		−	12.0000i		−	0.822226i
$214$	5.55051			0.379425
$215$	4.00000	−	8.00000i	0.272798	−	0.545595i
$216$		0			0
$217$			6.89898i			0.468333i
$218$		−	5.79796i		−	0.392687i
$219$	9.79796			0.662085
$220$	9.79796	+	4.89898i	0.660578	+	0.330289i
$221$	−19.5959			−1.31816
$222$			2.44949i			0.164399i
$223$			0.449490i			0.0301001i	0.999887	+	0.0150500i	$0.00479075\pi$
$223$			0.449490i			0.0301001i	−0.999887	+	0.0150500i	$0.995209\pi$
$224$	−4.44949			−0.297294
$225$	−9.00000	−	12.0000i	−0.600000	−	0.800000i
$226$	−3.10102			−0.206277
$227$			24.8990i			1.65260i	0.563228	+	0.826302i	$0.309559\pi$
$227$			24.8990i			1.65260i	−0.563228	+	0.826302i	$0.690441\pi$
$228$		−	8.69694i		−	0.575969i
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$	17.7980	+	8.89898i	1.17356	+	0.586781i
$231$	−53.3939			−3.51306
$232$		0			0
$233$			9.79796i			0.641886i	0.947099	+	0.320943i	$0.104000\pi$
$233$			9.79796i			0.641886i	−0.947099	+	0.320943i	$0.896000\pi$
$234$	−12.0000			−0.784465
$235$	−4.44949	+	8.89898i	−0.290253	+	0.580505i
$236$	−3.55051			−0.231119
$237$			15.7980i			1.02619i
$238$		−	21.7980i		−	1.41295i
$239$	18.0454			1.16726			0.583630	−	0.812020i	$-0.301632\pi$
$239$	18.0454			1.16726			0.583630	+	0.812020i	$0.301632\pi$
$240$	−2.44949	+	4.89898i	−0.158114	+	0.316228i
$241$	7.79796			0.502311			0.251155	−	0.967947i	$-0.419189\pi$
$241$	7.79796			0.502311			0.251155	+	0.967947i	$0.419189\pi$
$242$		−	13.0000i		−	0.835672i
$243$			22.0454i			1.41421i
$244$	−12.0000			−0.768221
$245$	25.5959	+	12.7980i	1.63526	+	0.817632i
$246$	−4.89898			−0.312348
$247$		−	14.2020i		−	0.903654i
$248$		−	1.55051i		−	0.0984575i
$249$	−23.3939			−1.48253
$250$	−11.0000	+	2.00000i	−0.695701	+	0.126491i
$251$	21.3485			1.34750			0.673752	−	0.738958i	$-0.264682\pi$
$251$	21.3485			1.34750			0.673752	+	0.738958i	$0.264682\pi$
$252$		−	13.3485i		−	0.840875i
$253$		−	43.5959i		−	2.74085i
$254$	2.65153			0.166372
$255$	−24.0000	−	12.0000i	−1.50294	−	0.751469i
$256$	1.00000			0.0625000
$257$			4.89898i			0.305590i	0.988258	+	0.152795i	$0.0488274\pi$
$257$			4.89898i			0.305590i	−0.988258	+	0.152795i	$0.951173\pi$
$258$		−	9.79796i		−	0.609994i
$259$	−4.44949			−0.276478
$260$	−4.00000	+	8.00000i	−0.248069	+	0.496139i
$261$		0			0
$262$			10.2474i			0.633089i
$263$			1.75255i			0.108067i	0.998539	+	0.0540335i	$0.0172078\pi$
$263$			1.75255i			0.108067i	−0.998539	+	0.0540335i	$0.982792\pi$
$264$	12.0000			0.738549
$265$	−11.7980	+	23.5959i	−0.724743	+	1.44949i
$266$	15.7980			0.968635
$267$			38.6969i			2.36821i
$268$		−	5.55051i		−	0.339051i
$269$	18.6969			1.13997			0.569986	−	0.821654i	$-0.306949\pi$
$269$	18.6969			1.13997			0.569986	+	0.821654i	$0.306949\pi$
$270$		0			0
$271$	−32.4949			−1.97392			−0.986962	−	0.160952i	$-0.948544\pi$
$271$	−32.4949			−1.97392			−0.986962	+	0.160952i	$0.948544\pi$
$272$			4.89898i			0.297044i
$273$		−	43.5959i		−	2.63854i
$274$	−19.5959			−1.18383
$275$	14.6969	+	19.5959i	0.886259	+	1.18168i
$276$	21.7980			1.31208
$277$		−	19.5959i		−	1.17740i	−0.808350	−	0.588702i	$-0.799639\pi$
$277$		−	19.5959i		−	1.17740i	0.808350	−	0.588702i	$-0.200361\pi$
$278$		−	5.79796i		−	0.347738i
$279$	4.65153			0.278480
$280$	−8.89898	−	4.44949i	−0.531816	−	0.265908i
$281$	27.7980			1.65829			0.829144	−	0.559036i	$-0.188829\pi$
$281$	27.7980			1.65829			0.829144	+	0.559036i	$0.188829\pi$
$282$			10.8990i			0.649025i
$283$			15.5959i			0.927081i	0.886076	+	0.463541i	$0.153421\pi$
$283$			15.5959i			0.927081i	−0.886076	+	0.463541i	$0.846579\pi$
$284$	−4.89898			−0.290701
$285$	8.69694	−	17.3939i	0.515162	−	1.03032i
$286$	19.5959			1.15873
$287$		−	8.89898i		−	0.525290i
$288$			3.00000i			0.176777i
$289$	−7.00000			−0.411765
$290$		0			0
$291$	4.89898			0.287183
$292$		−	4.00000i		−	0.234082i
$293$			25.5959i			1.49533i	0.664076	+	0.747665i	$0.268825\pi$
$293$			25.5959i			1.49533i	−0.664076	+	0.747665i	$0.731175\pi$
$294$	31.3485			1.82828
$295$	−7.10102	−	3.55051i	−0.413437	−	0.206719i
$296$	1.00000			0.0581238
$297$		0			0
$298$		−	18.6969i		−	1.08308i
$299$	35.5959			2.05857
$300$	−9.79796	+	7.34847i	−0.565685	+	0.424264i
$301$	17.7980			1.02586
$302$			8.00000i			0.460348i
$303$		−	26.2020i		−	1.50527i
$304$	−3.55051			−0.203636
$305$	−24.0000	−	12.0000i	−1.37424	−	0.687118i
$306$	−14.6969			−0.840168
$307$		−	13.1464i		−	0.750306i	−0.926963	−	0.375153i	$-0.877590\pi$
$307$		−	13.1464i		−	0.750306i	0.926963	−	0.375153i	$-0.122410\pi$
$308$			21.7980i			1.24205i
$309$	24.0000			1.36531
$310$	1.55051	−	3.10102i	0.0880631	−	0.176126i
$311$	−7.34847			−0.416693			−0.208347	−	0.978055i	$-0.566808\pi$
$311$	−7.34847			−0.416693			−0.208347	+	0.978055i	$0.566808\pi$
$312$			9.79796i			0.554700i
$313$		−	17.5959i		−	0.994580i	−0.867584	−	0.497290i	$-0.834328\pi$
$313$		−	17.5959i		−	0.994580i	0.867584	−	0.497290i	$-0.165672\pi$
$314$	7.79796			0.440064
$315$	13.3485	−	26.6969i	0.752101	−	1.50420i
$316$	6.44949			0.362812
$317$		−	18.0000i		−	1.01098i	−0.862832	−	0.505490i	$-0.831312\pi$
$317$		−	18.0000i		−	1.01098i	0.862832	−	0.505490i	$-0.168688\pi$
$318$			28.8990i			1.62057i
$319$		0			0
$320$	2.00000	+	1.00000i	0.111803	+	0.0559017i
$321$	13.5959			0.758850
$322$			39.5959i			2.20659i
$323$		−	17.3939i		−	0.967821i
$324$	9.00000			0.500000
$325$	−16.0000	+	12.0000i	−0.887520	+	0.665640i
$326$	−21.7980			−1.20728
$327$		−	14.2020i		−	0.785375i
$328$			2.00000i			0.110432i
$329$	−19.7980			−1.09150
$330$	24.0000	+	12.0000i	1.32116	+	0.660578i
$331$	14.2474			0.783111			0.391555	−	0.920155i	$-0.371937\pi$
$331$	14.2474			0.783111			0.391555	+	0.920155i	$0.371937\pi$
$332$			9.55051i			0.524152i
$333$			3.00000i			0.164399i
$334$	−8.00000			−0.437741
$335$	5.55051	−	11.1010i	0.303257	−	0.606514i
$336$	−10.8990			−0.594588
$337$			3.59592i			0.195882i	0.995192	+	0.0979411i	$0.0312257\pi$
$337$			3.59592i			0.195882i	−0.995192	+	0.0979411i	$0.968774\pi$
$338$			3.00000i			0.163178i
$339$	−7.59592			−0.412554
$340$	−4.89898	+	9.79796i	−0.265684	+	0.531369i
$341$	−7.59592			−0.411342
$342$		−	10.6515i		−	0.575969i
$343$			25.7980i			1.39296i
$344$	−4.00000			−0.215666
$345$	43.5959	+	21.7980i	2.34713	+	1.17356i
$346$	19.7980			1.06434
$347$		−	2.20204i		−	0.118212i	−0.998252	−	0.0591059i	$-0.981175\pi$
$347$		−	2.20204i		−	0.118212i	0.998252	−	0.0591059i	$-0.0188250\pi$
$348$		0			0
$349$	−7.10102			−0.380109			−0.190054	−	0.981774i	$-0.560866\pi$
$349$	−7.10102			−0.380109			−0.190054	+	0.981774i	$0.560866\pi$
$350$	−13.3485	−	17.7980i	−0.713506	−	0.951341i
$351$		0			0
$352$		−	4.89898i		−	0.261116i
$353$		−	6.00000i		−	0.319348i	−0.987170	−	0.159674i	$-0.948956\pi$
$353$		−	6.00000i		−	0.319348i	0.987170	−	0.159674i	$-0.0510443\pi$
$354$	−8.69694			−0.462237
$355$	−9.79796	−	4.89898i	−0.520022	−	0.260011i
$356$	15.7980			0.837290
$357$		−	53.3939i		−	2.82590i
$358$		−	9.34847i		−	0.494082i
$359$	12.8990			0.680782			0.340391	−	0.940284i	$-0.389441\pi$
$359$	12.8990			0.680782			0.340391	+	0.940284i	$0.389441\pi$
$360$	−3.00000	+	6.00000i	−0.158114	+	0.316228i
$361$	−6.39388			−0.336520
$362$		−	10.6969i		−	0.562219i
$363$		−	31.8434i		−	1.67134i
$364$	−17.7980			−0.932867
$365$	4.00000	−	8.00000i	0.209370	−	0.418739i
$366$	−29.3939			−1.53644
$367$			2.65153i			0.138409i	0.997603	+	0.0692044i	$0.0220461\pi$
$367$			2.65153i			0.138409i	−0.997603	+	0.0692044i	$0.977954\pi$
$368$		−	8.89898i		−	0.463891i
$369$	−6.00000			−0.312348
$370$	2.00000	+	1.00000i	0.103975	+	0.0519875i
$371$	−52.4949			−2.72540
$372$		−	3.79796i		−	0.196915i
$373$		−	11.7980i		−	0.610875i	−0.952212	−	0.305438i	$-0.901197\pi$
$373$		−	11.7980i		−	0.610875i	0.952212	−	0.305438i	$-0.0988027\pi$
$374$	24.0000			1.24101
$375$	−26.9444	+	4.89898i	−1.39140	+	0.252982i
$376$	4.44949			0.229465
$377$		0			0
$378$		0			0
$379$	31.5959			1.62297			0.811487	−	0.584371i	$-0.198659\pi$
$379$	31.5959			1.62297			0.811487	+	0.584371i	$0.198659\pi$
$380$	−7.10102	−	3.55051i	−0.364275	−	0.182137i
$381$	6.49490			0.332744
$382$		−	11.3485i		−	0.580638i
$383$		−	34.6969i		−	1.77293i	−0.462795	−	0.886465i	$-0.653153\pi$
$383$		−	34.6969i		−	1.77293i	0.462795	−	0.886465i	$-0.346847\pi$
$384$	2.44949			0.125000
$385$	−21.7980	+	43.5959i	−1.11093	+	2.22185i
$386$	14.0000			0.712581
$387$		−	12.0000i		−	0.609994i
$388$		−	2.00000i		−	0.101535i
$389$	25.7980			1.30801			0.654004	−	0.756491i	$-0.273088\pi$
$389$	25.7980			1.30801			0.654004	+	0.756491i	$0.273088\pi$
$390$	−9.79796	+	19.5959i	−0.496139	+	0.992278i
$391$	43.5959			2.20474
$392$		−	12.7980i		−	0.646395i
$393$			25.1010i			1.26618i
$394$	2.00000			0.100759
$395$	12.8990	+	6.44949i	0.649018	+	0.324509i
$396$	14.6969			0.738549
$397$			16.2020i			0.813157i	0.913616	+	0.406579i	$0.133278\pi$
$397$			16.2020i			0.813157i	−0.913616	+	0.406579i	$0.866722\pi$
$398$			6.44949i			0.323284i
$399$	38.6969			1.93727
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	−23.7980			−1.18841			−0.594207	−	0.804312i	$-0.702534\pi$
$401$	−23.7980			−1.18841			−0.594207	+	0.804312i	$0.702534\pi$
$402$		−	13.5959i		−	0.678103i
$403$		−	6.20204i		−	0.308946i
$404$	−10.6969			−0.532193
$405$	18.0000	+	9.00000i	0.894427	+	0.447214i
$406$		0			0
$407$		−	4.89898i		−	0.242833i
$408$			12.0000i			0.594089i
$409$	10.0000			0.494468			0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000			0.494468			0.247234	+	0.968956i	$0.420478\pi$
$410$	−2.00000	+	4.00000i	−0.0987730	+	0.197546i
$411$	−48.0000			−2.36767
$412$		−	9.79796i		−	0.482711i
$413$		−	15.7980i		−	0.777367i
$414$	26.6969			1.31208
$415$	−9.55051	+	19.1010i	−0.468816	+	0.937632i
$416$	4.00000			0.196116
$417$		−	14.2020i		−	0.695477i
$418$			17.3939i			0.850762i
$419$	−5.79796			−0.283249			−0.141624	−	0.989920i	$-0.545233\pi$
$419$	−5.79796			−0.283249			−0.141624	+	0.989920i	$0.545233\pi$
$420$	−21.7980	−	10.8990i	−1.06363	−	0.531816i
$421$	−19.5959			−0.955047			−0.477523	−	0.878619i	$-0.658465\pi$
$421$	−19.5959			−0.955047			−0.477523	+	0.878619i	$0.658465\pi$
$422$			6.69694i			0.326002i
$423$			13.3485i			0.649025i
$424$	11.7980			0.572960
$425$	−19.5959	+	14.6969i	−0.950542	+	0.712906i
$426$	−12.0000			−0.581402
$427$		−	53.3939i		−	2.58391i
$428$		−	5.55051i		−	0.268294i
$429$	48.0000			2.31746
$430$	−8.00000	−	4.00000i	−0.385794	−	0.192897i
$431$	−15.7526			−0.758774			−0.379387	−	0.925238i	$-0.623865\pi$
$431$	−15.7526			−0.758774			−0.379387	+	0.925238i	$0.623865\pi$
$432$		0			0
$433$			21.3939i			1.02812i	0.857753	+	0.514062i	$0.171860\pi$
$433$			21.3939i			1.02812i	−0.857753	+	0.514062i	$0.828140\pi$
$434$	6.89898			0.331162
$435$		0			0
$436$	−5.79796			−0.277672
$437$			31.5959i			1.51144i
$438$		−	9.79796i		−	0.468165i
$439$	−20.6515			−0.985644			−0.492822	−	0.870130i	$-0.664035\pi$
$439$	−20.6515			−0.985644			−0.492822	+	0.870130i	$0.664035\pi$
$440$	4.89898	−	9.79796i	0.233550	−	0.467099i
$441$	38.3939			1.82828
$442$			19.5959i			0.932083i
$443$			24.6515i			1.17123i	0.810589	+	0.585615i	$0.199147\pi$
$443$			24.6515i			1.17123i	−0.810589	+	0.585615i	$0.800853\pi$
$444$	2.44949			0.116248
$445$	31.5959	+	15.7980i	1.49779	+	0.748895i
$446$	0.449490			0.0212840
$447$		−	45.7980i		−	2.16617i
$448$			4.44949i			0.210219i
$449$	15.7980			0.745552			0.372776	−	0.927921i	$-0.378406\pi$
$449$	15.7980			0.745552			0.372776	+	0.927921i	$0.378406\pi$
$450$	−12.0000	+	9.00000i	−0.565685	+	0.424264i
$451$	9.79796			0.461368
$452$			3.10102i			0.145860i
$453$			19.5959i			0.920697i
$454$	24.8990			1.16857
$455$	−35.5959	−	17.7980i	−1.66876	−	0.834381i
$456$	−8.69694			−0.407271
$457$			2.00000i			0.0935561i	0.998905	+	0.0467780i	$0.0148953\pi$
$457$			2.00000i			0.0935561i	−0.998905	+	0.0467780i	$0.985105\pi$
$458$		−	10.0000i		−	0.467269i
$459$		0			0
$460$	8.89898	−	17.7980i	0.414917	−	0.829834i
$461$	−33.7980			−1.57413			−0.787064	−	0.616871i	$-0.788400\pi$
$461$	−33.7980			−1.57413			−0.787064	+	0.616871i	$0.788400\pi$
$462$			53.3939i			2.48411i
$463$		−	20.4949i		−	0.952479i	−0.879316	−	0.476239i	$-0.842000\pi$
$463$		−	20.4949i		−	0.952479i	0.879316	−	0.476239i	$-0.158000\pi$
$464$		0			0
$465$	3.79796	−	7.59592i	0.176126	−	0.352252i
$466$	9.79796			0.453882
$467$			12.0000i			0.555294i	0.960683	+	0.277647i	$0.0895545\pi$
$467$			12.0000i			0.555294i	−0.960683	+	0.277647i	$0.910445\pi$
$468$			12.0000i			0.554700i
$469$	24.6969			1.14040
$470$	8.89898	+	4.44949i	0.410479	+	0.205240i
$471$	19.1010			0.880129
$472$			3.55051i			0.163425i
$473$			19.5959i			0.901021i
$474$	15.7980			0.725624
$475$	−10.6515	−	14.2020i	−0.488726	−	0.651634i
$476$	−21.7980			−0.999108
$477$			35.3939i			1.62057i
$478$		−	18.0454i		−	0.825378i
$479$	−5.14643			−0.235146			−0.117573	−	0.993064i	$-0.537511\pi$
$479$	−5.14643			−0.235146			−0.117573	+	0.993064i	$0.537511\pi$
$480$	4.89898	+	2.44949i	0.223607	+	0.111803i
$481$	4.00000			0.182384
$482$		−	7.79796i		−	0.355187i
$483$			96.9898i			4.41319i
$484$	−13.0000			−0.590909
$485$	2.00000	−	4.00000i	0.0908153	−	0.181631i
$486$	22.0454			1.00000
$487$			29.3939i			1.33196i	0.745968	+	0.665982i	$0.231987\pi$
$487$			29.3939i			1.33196i	−0.745968	+	0.665982i	$0.768013\pi$
$488$			12.0000i			0.543214i
$489$	−53.3939			−2.41455
$490$	12.7980	−	25.5959i	0.578153	−	1.15631i
$491$	−9.30306			−0.419841			−0.209921	−	0.977718i	$-0.567321\pi$
$491$	−9.30306			−0.419841			−0.209921	+	0.977718i	$0.567321\pi$
$492$			4.89898i			0.220863i
$493$		0			0
$494$	−14.2020			−0.638980
$495$	29.3939	+	14.6969i	1.32116	+	0.660578i
$496$	−1.55051			−0.0696200
$497$		−	21.7980i		−	0.977772i
$498$			23.3939i			1.04830i
$499$	10.6515			0.476828			0.238414	−	0.971164i	$-0.423372\pi$
$499$	10.6515			0.476828			0.238414	+	0.971164i	$0.423372\pi$
$500$	2.00000	+	11.0000i	0.0894427	+	0.491935i
$501$	−19.5959			−0.875481
$502$		−	21.3485i		−	0.952829i
$503$		−	1.79796i		−	0.0801670i	−0.999196	−	0.0400835i	$-0.987238\pi$
$503$		−	1.79796i		−	0.0801670i	0.999196	−	0.0400835i	$-0.0127624\pi$
$504$	−13.3485			−0.594588
$505$	−21.3939	−	10.6969i	−0.952015	−	0.476008i
$506$	−43.5959			−1.93807
$507$			7.34847i			0.326357i
$508$		−	2.65153i		−	0.117643i
$509$	−30.0000			−1.32973			−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000			−1.32973			−0.664863	+	0.746965i	$0.731510\pi$
$510$	−12.0000	+	24.0000i	−0.531369	+	1.06274i
$511$	17.7980			0.787335
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	4.89898			0.216085
$515$	9.79796	−	19.5959i	0.431750	−	0.863499i
$516$	−9.79796			−0.431331
$517$		−	21.7980i		−	0.958673i
$518$			4.44949i			0.195499i
$519$	48.4949			2.12869
$520$	8.00000	+	4.00000i	0.350823	+	0.175412i
$521$	17.7980			0.779743			0.389871	−	0.920869i	$-0.372519\pi$
$521$	17.7980			0.779743			0.389871	+	0.920869i	$0.372519\pi$
$522$		0			0
$523$		−	8.89898i		−	0.389125i	−0.980890	−	0.194563i	$-0.937671\pi$
$523$		−	8.89898i		−	0.389125i	0.980890	−	0.194563i	$-0.0623287\pi$
$524$	10.2474			0.447662
$525$	−32.6969	−	43.5959i	−1.42701	−	1.90268i
$526$	1.75255			0.0764149
$527$		−	7.59592i		−	0.330883i
$528$		−	12.0000i		−	0.522233i
$529$	−56.1918			−2.44312
$530$	23.5959	+	11.7980i	1.02494	+	0.512471i
$531$	−10.6515			−0.462237
$532$		−	15.7980i		−	0.684928i
$533$			8.00000i			0.346518i
$534$	38.6969			1.67458
$535$	5.55051	−	11.1010i	0.239969	−	0.479939i
$536$	−5.55051			−0.239746
$537$		−	22.8990i		−	0.988164i
$538$		−	18.6969i		−	0.806082i
$539$	−62.6969			−2.70055
$540$		0			0
$541$	0.404082			0.0173728			0.00868642	−	0.999962i	$-0.497235\pi$
$541$	0.404082			0.0173728			0.00868642	+	0.999962i	$0.497235\pi$
$542$			32.4949i			1.39578i
$543$		−	26.2020i		−	1.12444i
$544$	4.89898			0.210042
$545$	−11.5959	−	5.79796i	−0.496715	−	0.248357i
$546$	−43.5959			−1.86573
$547$			10.6969i			0.457368i	0.973501	+	0.228684i	$0.0734423\pi$
$547$			10.6969i			0.457368i	−0.973501	+	0.228684i	$0.926558\pi$
$548$			19.5959i			0.837096i
$549$	−36.0000			−1.53644
$550$	19.5959	−	14.6969i	0.835573	−	0.626680i
$551$		0			0
$552$		−	21.7980i		−	0.927783i
$553$			28.6969i			1.22032i
$554$	−19.5959			−0.832551
$555$	4.89898	+	2.44949i	0.207950	+	0.103975i
$556$	−5.79796			−0.245888
$557$			12.0000i			0.508456i	0.967144	+	0.254228i	$0.0818214\pi$
$557$			12.0000i			0.508456i	−0.967144	+	0.254228i	$0.918179\pi$
$558$		−	4.65153i		−	0.196915i
$559$	−16.0000			−0.676728
$560$	−4.44949	+	8.89898i	−0.188025	+	0.376051i
$561$	58.7878			2.48202
$562$		−	27.7980i		−	1.17259i
$563$		−	34.6969i		−	1.46230i	−0.682216	−	0.731151i	$-0.738984\pi$
$563$		−	34.6969i		−	1.46230i	0.682216	−	0.731151i	$-0.261016\pi$
$564$	10.8990			0.458930
$565$	−3.10102	+	6.20204i	−0.130461	+	0.260922i
$566$	15.5959			0.655545
$567$			40.0454i			1.68175i
$568$			4.89898i			0.205557i
$569$	−21.5959			−0.905348			−0.452674	−	0.891676i	$-0.649530\pi$
$569$	−21.5959			−0.905348			−0.452674	+	0.891676i	$0.649530\pi$
$570$	−17.3939	−	8.69694i	−0.728549	−	0.364275i
$571$	−25.3939			−1.06270			−0.531350	−	0.847152i	$-0.678315\pi$
$571$	−25.3939			−1.06270			−0.531350	+	0.847152i	$0.678315\pi$
$572$		−	19.5959i		−	0.819346i
$573$		−	27.7980i		−	1.16128i
$574$	−8.89898			−0.371436
$575$	35.5959	−	26.6969i	1.48445	−	1.11334i
$576$	3.00000			0.125000
$577$			30.6969i			1.27793i	0.769236	+	0.638965i	$0.220637\pi$
$577$			30.6969i			1.27793i	−0.769236	+	0.638965i	$0.779363\pi$
$578$			7.00000i			0.291162i
$579$	34.2929			1.42516
$580$		0			0
$581$	−42.4949			−1.76299
$582$		−	4.89898i		−	0.203069i
$583$		−	57.7980i		−	2.39375i
$584$	−4.00000			−0.165521
$585$	−12.0000	+	24.0000i	−0.496139	+	0.992278i
$586$	25.5959			1.05736
$587$			12.0000i			0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$		−	31.3485i		−	1.29279i
$589$	5.50510			0.226834
$590$	−3.55051	+	7.10102i	−0.146172	+	0.292344i
$591$	4.89898			0.201517
$592$		−	1.00000i		−	0.0410997i
$593$			24.0000i			0.985562i	0.870153	+	0.492781i	$0.164020\pi$
$593$			24.0000i			0.985562i	−0.870153	+	0.492781i	$0.835980\pi$
$594$		0			0
$595$	−43.5959	−	21.7980i	−1.78726	−	0.893629i
$596$	−18.6969			−0.765856
$597$			15.7980i			0.646567i
$598$		−	35.5959i		−	1.45563i
$599$	−11.5959			−0.473796			−0.236898	−	0.971534i	$-0.576131\pi$
$599$	−11.5959			−0.473796			−0.236898	+	0.971534i	$0.576131\pi$
$600$	7.34847	+	9.79796i	0.300000	+	0.400000i
$601$	−8.00000			−0.326327			−0.163163	−	0.986599i	$-0.552170\pi$
$601$	−8.00000			−0.326327			−0.163163	+	0.986599i	$0.552170\pi$
$602$		−	17.7980i		−	0.725391i
$603$		−	16.6515i		−	0.678103i
$604$	8.00000			0.325515
$605$	−26.0000	−	13.0000i	−1.05705	−	0.528525i
$606$	−26.2020			−1.06439
$607$		−	26.6969i		−	1.08360i	−0.840509	−	0.541798i	$-0.817744\pi$
$607$		−	26.6969i		−	1.08360i	0.840509	−	0.541798i	$-0.182256\pi$
$608$			3.55051i			0.143992i
$609$		0			0
$610$	−12.0000	+	24.0000i	−0.485866	+	0.971732i
$611$	17.7980			0.720028
$612$			14.6969i			0.594089i
$613$			39.7980i			1.60742i	0.595018	+	0.803712i	$0.297145\pi$
$613$			39.7980i			1.60742i	−0.595018	+	0.803712i	$0.702855\pi$
$614$	−13.1464			−0.530547
$615$	−4.89898	+	9.79796i	−0.197546	+	0.395092i
$616$	21.7980			0.878265
$617$		−	19.5959i		−	0.788902i	−0.918917	−	0.394451i	$-0.870935\pi$
$617$		−	19.5959i		−	0.788902i	0.918917	−	0.394451i	$-0.129065\pi$
$618$		−	24.0000i		−	0.965422i
$619$	12.8990			0.518454			0.259227	−	0.965816i	$-0.416532\pi$
$619$	12.8990			0.518454			0.259227	+	0.965816i	$0.416532\pi$
$620$	−3.10102	−	1.55051i	−0.124540	−	0.0622700i
$621$		0			0
$622$			7.34847i			0.294647i
$623$			70.2929i			2.81622i
$624$	9.79796			0.392232
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−17.5959			−0.703274
$627$			42.6061i			1.70152i
$628$		−	7.79796i		−	0.311172i
$629$	4.89898			0.195335
$630$	−26.6969	−	13.3485i	−1.06363	−	0.531816i
$631$	−20.2474			−0.806038			−0.403019	−	0.915192i	$-0.632039\pi$
$631$	−20.2474			−0.806038			−0.403019	+	0.915192i	$0.632039\pi$
$632$		−	6.44949i		−	0.256547i
$633$			16.4041i			0.652004i
$634$	−18.0000			−0.714871
$635$	2.65153	−	5.30306i	0.105223	−	0.210446i
$636$	28.8990			1.14592
$637$		−	51.1918i		−	2.02829i
$638$		0			0
$639$	−14.6969			−0.581402
$640$	1.00000	−	2.00000i	0.0395285	−	0.0790569i
$641$	17.7980			0.702977			0.351489	−	0.936192i	$-0.385676\pi$
$641$	17.7980			0.702977			0.351489	+	0.936192i	$0.385676\pi$
$642$		−	13.5959i		−	0.536588i
$643$		−	23.1010i		−	0.911015i	−0.890232	−	0.455508i	$-0.849458\pi$
$643$		−	23.1010i		−	0.911015i	0.890232	−	0.455508i	$-0.150542\pi$
$644$	39.5959			1.56030
$645$	−19.5959	−	9.79796i	−0.771589	−	0.385794i
$646$	−17.3939			−0.684353
$647$			32.0000i			1.25805i	0.777385	+	0.629025i	$0.216546\pi$
$647$			32.0000i			1.25805i	−0.777385	+	0.629025i	$0.783454\pi$
$648$		−	9.00000i		−	0.353553i
$649$	17.3939			0.682769
$650$	12.0000	+	16.0000i	0.470679	+	0.627572i
$651$	16.8990			0.662323
$652$			21.7980i			0.853674i
$653$			34.0000i			1.33052i	0.746611	+	0.665261i	$0.231680\pi$
$653$			34.0000i			1.33052i	−0.746611	+	0.665261i	$0.768320\pi$
$654$	−14.2020			−0.555344
$655$	20.4949	+	10.2474i	0.800802	+	0.400401i
$656$	2.00000			0.0780869
$657$		−	12.0000i		−	0.468165i
$658$			19.7980i			0.771805i
$659$	−31.5959			−1.23080			−0.615401	−	0.788214i	$-0.711006\pi$
$659$	−31.5959			−1.23080			−0.615401	+	0.788214i	$0.711006\pi$
$660$	12.0000	−	24.0000i	0.467099	−	0.934199i
$661$	−31.1918			−1.21322			−0.606611	−	0.794999i	$-0.707471\pi$
$661$	−31.1918			−1.21322			−0.606611	+	0.794999i	$0.707471\pi$
$662$		−	14.2474i		−	0.553743i
$663$			48.0000i			1.86417i
$664$	9.55051			0.370632
$665$	15.7980	−	31.5959i	0.612619	−	1.22524i
$666$	3.00000			0.116248
$667$		0			0
$668$			8.00000i			0.309529i
$669$	1.10102			0.0425679
$670$	−11.1010	−	5.55051i	−0.428870	−	0.214435i
$671$	58.7878			2.26948
$672$			10.8990i			0.420437i
$673$			24.0000i			0.925132i	0.886585	+	0.462566i	$0.153071\pi$
$673$			24.0000i			0.925132i	−0.886585	+	0.462566i	$0.846929\pi$
$674$	3.59592			0.138510
$675$		0			0
$676$	3.00000			0.115385
$677$		−	18.0000i		−	0.691796i	−0.938272	−	0.345898i	$-0.887574\pi$
$677$		−	18.0000i		−	0.691796i	0.938272	−	0.345898i	$-0.112426\pi$
$678$			7.59592i			0.291719i
$679$	8.89898			0.341511
$680$	9.79796	+	4.89898i	0.375735	+	0.187867i
$681$	60.9898			2.33713
$682$			7.59592i			0.290863i
$683$			15.5959i			0.596761i	0.954447	+	0.298381i	$0.0964465\pi$
$683$			15.5959i			0.596761i	−0.954447	+	0.298381i	$0.903554\pi$
$684$	−10.6515			−0.407271
$685$	−19.5959	+	39.1918i	−0.748722	+	1.49744i
$686$	25.7980			0.984971
$687$		−	24.4949i		−	0.934539i
$688$			4.00000i			0.152499i
$689$	47.1918			1.79787
$690$	21.7980	−	43.5959i	0.829834	−	1.65967i
$691$	37.7980			1.43790			0.718951	−	0.695061i	$-0.244623\pi$
$691$	37.7980			1.43790			0.718951	+	0.695061i	$0.244623\pi$
$692$		−	19.7980i		−	0.752605i
$693$			65.3939i			2.48411i
$694$	−2.20204			−0.0835883
$695$	−11.5959	−	5.79796i	−0.439858	−	0.219929i
$696$		0			0
$697$			9.79796i			0.371124i
$698$			7.10102i			0.268778i
$699$	24.0000			0.907763
$700$	−17.7980	+	13.3485i	−0.672700	+	0.504525i
$701$	−13.7980			−0.521142			−0.260571	−	0.965455i	$-0.583911\pi$
$701$	−13.7980			−0.521142			−0.260571	+	0.965455i	$0.583911\pi$
$702$		0			0
$703$			3.55051i			0.133910i
$704$	−4.89898			−0.184637
$705$	21.7980	+	10.8990i	0.820959	+	0.410479i
$706$	−6.00000			−0.225813
$707$		−	47.5959i		−	1.79003i
$708$			8.69694i			0.326851i
$709$	−5.79796			−0.217747			−0.108873	−	0.994056i	$-0.534724\pi$
$709$	−5.79796			−0.217747			−0.108873	+	0.994056i	$0.534724\pi$
$710$	−4.89898	+	9.79796i	−0.183855	+	0.367711i
$711$	19.3485			0.725624
$712$		−	15.7980i		−	0.592054i
$713$			13.7980i			0.516738i
$714$	−53.3939			−1.99822
$715$	19.5959	−	39.1918i	0.732846	−	1.46569i
$716$	−9.34847			−0.349369
$717$		−	44.2020i		−	1.65076i
$718$		−	12.8990i		−	0.481386i
$719$	−51.5959			−1.92420			−0.962102	−	0.272692i	$-0.912086\pi$
$719$	−51.5959			−1.92420			−0.962102	+	0.272692i	$0.912086\pi$
$720$	6.00000	+	3.00000i	0.223607	+	0.111803i
$721$	43.5959			1.62360
$722$			6.39388i			0.237955i
$723$		−	19.1010i		−	0.710375i
$724$	−10.6969			−0.397549
$725$		0			0
$726$	−31.8434			−1.18182
$727$		−	0.898979i		−	0.0333413i	−0.999861	−	0.0166707i	$-0.994693\pi$
$727$		−	0.898979i		−	0.0333413i	0.999861	−	0.0166707i	$-0.00530668\pi$
$728$			17.7980i			0.659636i
$729$	27.0000			1.00000
$730$	−8.00000	−	4.00000i	−0.296093	−	0.148047i
$731$	−19.5959			−0.724781
$732$			29.3939i			1.08643i
$733$		−	17.5959i		−	0.649920i	−0.945728	−	0.324960i	$-0.894649\pi$
$733$		−	17.5959i		−	0.649920i	0.945728	−	0.324960i	$-0.105351\pi$
$734$	2.65153			0.0978698
$735$	31.3485	−	62.6969i	1.15631	−	2.31261i
$736$	−8.89898			−0.328021
$737$			27.1918i			1.00162i
$738$			6.00000i			0.220863i
$739$	45.7980			1.68471			0.842353	−	0.538927i	$-0.181170\pi$
$739$	45.7980			1.68471			0.842353	+	0.538927i	$0.181170\pi$
$740$	1.00000	−	2.00000i	0.0367607	−	0.0735215i
$741$	−34.7878			−1.27796
$742$			52.4949i			1.92715i
$743$		−	13.7526i		−	0.504532i	−0.967658	−	0.252266i	$-0.918824\pi$
$743$		−	13.7526i		−	0.504532i	0.967658	−	0.252266i	$-0.0811758\pi$
$744$	−3.79796			−0.139240
$745$	−37.3939	−	18.6969i	−1.37001	−	0.685003i
$746$	−11.7980			−0.431954
$747$			28.6515i			1.04830i
$748$		−	24.0000i		−	0.877527i
$749$	24.6969			0.902406
$750$	4.89898	+	26.9444i	0.178885	+	0.983870i
$751$	30.6969			1.12015			0.560074	−	0.828443i	$-0.310773\pi$
$751$	30.6969			1.12015			0.560074	+	0.828443i	$0.310773\pi$
$752$		−	4.44949i		−	0.162256i
$753$		−	52.2929i		−	1.90566i
$754$		0			0
$755$	16.0000	+	8.00000i	0.582300	+	0.291150i
$756$		0			0
$757$			33.5959i			1.22106i	0.791991	+	0.610532i	$0.209044\pi$
$757$			33.5959i			1.22106i	−0.791991	+	0.610532i	$0.790956\pi$
$758$		−	31.5959i		−	1.14762i
$759$	−106.788			−3.87615
$760$	−3.55051	+	7.10102i	−0.128791	+	0.257581i
$761$	25.1918			0.913203			0.456602	−	0.889671i	$-0.349066\pi$
$761$	25.1918			0.913203			0.456602	+	0.889671i	$0.349066\pi$
$762$		−	6.49490i		−	0.235285i
$763$		−	25.7980i		−	0.933949i
$764$	−11.3485			−0.410573
$765$	−14.6969	+	29.3939i	−0.531369	+	1.06274i
$766$	−34.6969			−1.25365
$767$			14.2020i			0.512806i
$768$		−	2.44949i		−	0.0883883i
$769$	35.7980			1.29091			0.645454	−	0.763799i	$-0.276668\pi$
$769$	35.7980			1.29091			0.645454	+	0.763799i	$0.276668\pi$
$770$	43.5959	+	21.7980i	1.57109	+	0.785544i
$771$	12.0000			0.432169
$772$		−	14.0000i		−	0.503871i
$773$		−	6.00000i		−	0.215805i	−0.994161	−	0.107903i	$-0.965587\pi$
$773$		−	6.00000i		−	0.215805i	0.994161	−	0.107903i	$-0.0344134\pi$
$774$	−12.0000			−0.431331
$775$	−4.65153	−	6.20204i	−0.167088	−	0.222784i
$776$	−2.00000			−0.0717958
$777$			10.8990i			0.390999i
$778$		−	25.7980i		−	0.924902i
$779$	−7.10102			−0.254420
$780$	19.5959	+	9.79796i	0.701646	+	0.350823i
$781$	24.0000			0.858788
$782$		−	43.5959i		−	1.55899i
$783$		0			0
$784$	−12.7980			−0.457070
$785$	7.79796	−	15.5959i	0.278321	−	0.556642i
$786$	25.1010			0.895324
$787$			28.7423i			1.02455i	0.858820	+	0.512277i	$0.171198\pi$
$787$			28.7423i			1.02455i	−0.858820	+	0.512277i	$0.828802\pi$
$788$		−	2.00000i		−	0.0712470i
$789$	4.29286			0.152830
$790$	6.44949	−	12.8990i	0.229463	−	0.458925i
$791$	−13.7980			−0.490599
$792$		−	14.6969i		−	0.522233i
$793$			48.0000i			1.70453i
$794$	16.2020			0.574989
$795$	57.7980	+	28.8990i	2.04988	+	1.02494i
$796$	6.44949			0.228596
$797$			43.5959i			1.54425i	0.635473	+	0.772123i	$0.280805\pi$
$797$			43.5959i			1.54425i	−0.635473	+	0.772123i	$0.719195\pi$
$798$		−	38.6969i		−	1.36986i
$799$	21.7980			0.771156
$800$	4.00000	−	3.00000i	0.141421	−	0.106066i
$801$	47.3939			1.67458
$802$			23.7980i			0.840335i
$803$			19.5959i			0.691525i
$804$	−13.5959			−0.479491
$805$	79.1918	+	39.5959i	2.79115	+	1.39557i
$806$	−6.20204			−0.218458
$807$		−	45.7980i		−	1.61216i
$808$			10.6969i			0.376317i
$809$	33.1918			1.16696			0.583481	−	0.812127i	$-0.301690\pi$
$809$	33.1918			1.16696			0.583481	+	0.812127i	$0.301690\pi$
$810$	9.00000	−	18.0000i	0.316228	−	0.632456i
$811$	26.2020			0.920078			0.460039	−	0.887899i	$-0.347835\pi$
$811$	26.2020			0.920078			0.460039	+	0.887899i	$0.347835\pi$
$812$		0			0
$813$			79.5959i			2.79155i
$814$	−4.89898			−0.171709
$815$	−21.7980	+	43.5959i	−0.763549	+	1.52710i
$816$	12.0000			0.420084
$817$		−	14.2020i		−	0.496867i
$818$		−	10.0000i		−	0.349642i
$819$	−53.3939			−1.86573
$820$	4.00000	+	2.00000i	0.139686	+	0.0698430i
$821$	−6.40408			−0.223504			−0.111752	−	0.993736i	$-0.535646\pi$
$821$	−6.40408			−0.223504			−0.111752	+	0.993736i	$0.535646\pi$
$822$			48.0000i			1.67419i
$823$			33.3485i			1.16245i	0.813741	+	0.581227i	$0.197427\pi$
$823$			33.3485i			1.16245i	−0.813741	+	0.581227i	$0.802573\pi$
$824$	−9.79796			−0.341328
$825$	48.0000	−	36.0000i	1.67115	−	1.25336i
$826$	−15.7980			−0.549681
$827$			36.4949i			1.26905i	0.772902	+	0.634526i	$0.218805\pi$
$827$			36.4949i			1.26905i	−0.772902	+	0.634526i	$0.781195\pi$
$828$		−	26.6969i		−	0.927783i
$829$	−8.40408			−0.291886			−0.145943	−	0.989293i	$-0.546622\pi$
$829$	−8.40408			−0.291886			−0.145943	+	0.989293i	$0.546622\pi$
$830$	19.1010	+	9.55051i	0.663006	+	0.331503i
$831$	−48.0000			−1.66510
$832$		−	4.00000i		−	0.138675i
$833$		−	62.6969i		−	2.17232i
$834$	−14.2020			−0.491776
$835$	−8.00000	+	16.0000i	−0.276851	+	0.553703i
$836$	17.3939			0.601580
$837$		0			0
$838$			5.79796i			0.200287i
$839$	−14.2020			−0.490309			−0.245154	−	0.969484i	$-0.578839\pi$
$839$	−14.2020			−0.490309			−0.245154	+	0.969484i	$0.578839\pi$
$840$	−10.8990	+	21.7980i	−0.376051	+	0.752101i
$841$	−29.0000			−1.00000
$842$			19.5959i			0.675320i
$843$		−	68.0908i		−	2.34517i
$844$	6.69694			0.230518
$845$	6.00000	+	3.00000i	0.206406	+	0.103203i
$846$	13.3485			0.458930
$847$		−	57.8434i		−	1.98752i
$848$		−	11.7980i		−	0.405144i
$849$	38.2020			1.31109
$850$	14.6969	+	19.5959i	0.504101	+	0.672134i
$851$	−8.89898			−0.305053
$852$			12.0000i			0.411113i
$853$		−	37.5959i		−	1.28726i	−0.765337	−	0.643630i	$-0.777428\pi$
$853$		−	37.5959i		−	1.28726i	0.765337	−	0.643630i	$-0.222572\pi$
$854$	−53.3939			−1.82710
$855$	−21.3031	−	10.6515i	−0.728549	−	0.364275i
$856$	−5.55051			−0.189713
$857$		−	9.59592i		−	0.327790i	−0.986478	−	0.163895i	$-0.947594\pi$
$857$		−	9.59592i		−	0.327790i	0.986478	−	0.163895i	$-0.0524059\pi$
$858$		−	48.0000i		−	1.63869i
$859$	55.1464			1.88157			0.940786	−	0.339001i	$-0.110089\pi$
$859$	55.1464			1.88157			0.940786	+	0.339001i	$0.110089\pi$
$860$	−4.00000	+	8.00000i	−0.136399	+	0.272798i
$861$	−21.7980			−0.742872
$862$			15.7526i			0.536534i
$863$		−	42.7423i		−	1.45497i	−0.686126	−	0.727483i	$-0.740690\pi$
$863$		−	42.7423i		−	1.45497i	0.686126	−	0.727483i	$-0.259310\pi$
$864$		0			0
$865$	19.7980	−	39.5959i	0.673151	−	1.34630i
$866$	21.3939			0.726994
$867$			17.1464i			0.582323i
$868$		−	6.89898i		−	0.234167i
$869$	−31.5959			−1.07182
$870$		0			0
$871$	−22.2020			−0.752287
$872$			5.79796i			0.196344i
$873$		−	6.00000i		−	0.203069i
$874$	31.5959			1.06875
$875$	−48.9444	+	8.89898i	−1.65462	+	0.300840i
$876$	−9.79796			−0.331042
$877$		−	15.3939i		−	0.519814i	−0.965634	−	0.259907i	$-0.916308\pi$
$877$		−	15.3939i		−	0.519814i	0.965634	−	0.259907i	$-0.0836920\pi$
$878$			20.6515i			0.696955i
$879$	62.6969			2.11472
$880$	−9.79796	−	4.89898i	−0.330289	−	0.165145i
$881$	−5.39388			−0.181724			−0.0908622	−	0.995863i	$-0.528962\pi$
$881$	−5.39388			−0.181724			−0.0908622	+	0.995863i	$0.528962\pi$
$882$		−	38.3939i		−	1.29279i
$883$			42.6969i			1.43687i	0.695596	+	0.718433i	$0.255140\pi$
$883$			42.6969i			1.43687i	−0.695596	+	0.718433i	$0.744860\pi$
$884$	19.5959			0.659082
$885$	−8.69694	+	17.3939i	−0.292344	+	0.584689i
$886$	24.6515			0.828184
$887$			20.0454i			0.673059i	0.941673	+	0.336529i	$0.109253\pi$
$887$			20.0454i			0.673059i	−0.941673	+	0.336529i	$0.890747\pi$
$888$		−	2.44949i		−	0.0821995i
$889$	11.7980			0.395691
$890$	15.7980	−	31.5959i	0.529549	−	1.05910i
$891$	−44.0908			−1.47710
$892$		−	0.449490i		−	0.0150500i
$893$			15.7980i			0.528659i
$894$	−45.7980			−1.53171
$895$	−18.6969	−	9.34847i	−0.624970	−	0.312485i
$896$	4.44949			0.148647
$897$		−	87.1918i		−	2.91125i
$898$		−	15.7980i		−	0.527185i
$899$		0			0
$900$	9.00000	+	12.0000i	0.300000	+	0.400000i
$901$	57.7980			1.92553
$902$		−	9.79796i		−	0.326236i
$903$		−	43.5959i		−	1.45078i
$904$	3.10102			0.103138
$905$	−21.3939	−	10.6969i	−0.711157	−	0.355578i
$906$	19.5959			0.651031
$907$		−	0.898979i		−	0.0298501i	−0.999889	−	0.0149251i	$-0.995249\pi$
$907$		−	0.898979i		−	0.0298501i	0.999889	−	0.0149251i	$-0.00475097\pi$
$908$		−	24.8990i		−	0.826302i
$909$	−32.0908			−1.06439
$910$	−17.7980	+	35.5959i	−0.589997	+	1.17999i
$911$	−31.8434			−1.05502			−0.527509	−	0.849550i	$-0.676874\pi$
$911$	−31.8434			−1.05502			−0.527509	+	0.849550i	$0.676874\pi$
$912$			8.69694i			0.287984i
$913$		−	46.7878i		−	1.54845i
$914$	2.00000			0.0661541
$915$	−29.3939	+	58.7878i	−0.971732	+	1.94346i
$916$	−10.0000			−0.330409
$917$			45.5959i			1.50571i
$918$		0			0
$919$	−25.1464			−0.829504			−0.414752	−	0.909934i	$-0.636132\pi$
$919$	−25.1464			−0.829504			−0.414752	+	0.909934i	$0.636132\pi$
$920$	−17.7980	−	8.89898i	−0.586781	−	0.293391i
$921$	−32.2020			−1.06109
$922$			33.7980i			1.11308i
$923$			19.5959i			0.645007i
$924$	53.3939			1.75653
$925$	4.00000	−	3.00000i	0.131519	−	0.0986394i
$926$	−20.4949			−0.673504
$927$		−	29.3939i		−	0.965422i
$928$		0			0
$929$	1.59592			0.0523604			0.0261802	−	0.999657i	$-0.491666\pi$
$929$	1.59592			0.0523604			0.0261802	+	0.999657i	$0.491666\pi$
$930$	−7.59592	−	3.79796i	−0.249080	−	0.124540i
$931$	45.4393			1.48921
$932$		−	9.79796i		−	0.320943i
$933$			18.0000i			0.589294i
$934$	12.0000			0.392652
$935$	24.0000	−	48.0000i	0.784884	−	1.56977i
$936$	12.0000			0.392232
$937$		−	8.00000i		−	0.261349i	−0.991425	−	0.130674i	$-0.958286\pi$
$937$		−	8.00000i		−	0.261349i	0.991425	−	0.130674i	$-0.0417142\pi$
$938$		−	24.6969i		−	0.806384i
$939$	−43.1010			−1.40655
$940$	4.44949	−	8.89898i	0.145126	−	0.290253i
$941$	−38.2929			−1.24831			−0.624156	−	0.781300i	$-0.714557\pi$
$941$	−38.2929			−1.24831			−0.624156	+	0.781300i	$0.714557\pi$
$942$		−	19.1010i		−	0.622345i
$943$		−	17.7980i		−	0.579581i
$944$	3.55051			0.115559
$945$		0			0
$946$	19.5959			0.637118
$947$		−	25.3939i		−	0.825190i	−0.910915	−	0.412595i	$-0.864622\pi$
$947$		−	25.3939i		−	0.825190i	0.910915	−	0.412595i	$-0.135378\pi$
$948$		−	15.7980i		−	0.513094i
$949$	−16.0000			−0.519382
$950$	−14.2020	+	10.6515i	−0.460775	+	0.345581i
$951$	−44.0908			−1.42974
$952$			21.7980i			0.706476i
$953$		−	21.7980i		−	0.706105i	−0.935603	−	0.353053i	$-0.885144\pi$
$953$		−	21.7980i		−	0.706105i	0.935603	−	0.353053i	$-0.114856\pi$
$954$	35.3939			1.14592
$955$	−22.6969	−	11.3485i	−0.734456	−	0.367228i
$956$	−18.0454			−0.583630
$957$		0			0
$958$			5.14643i			0.166274i
$959$	−87.1918			−2.81557
$960$	2.44949	−	4.89898i	0.0790569	−	0.158114i
$961$	−28.5959			−0.922449
$962$		−	4.00000i		−	0.128965i
$963$		−	16.6515i		−	0.536588i
$964$	−7.79796			−0.251155
$965$	14.0000	−	28.0000i	0.450676	−	0.901352i
$966$	96.9898			3.12060
$967$		−	3.50510i		−	0.112716i	−0.998411	−	0.0563582i	$-0.982051\pi$
$967$		−	3.50510i		−	0.112716i	0.998411	−	0.0563582i	$-0.0179489\pi$
$968$			13.0000i			0.417836i
$969$	−42.6061			−1.36871
$970$	−4.00000	−	2.00000i	−0.128432	−	0.0642161i
$971$	−35.1010			−1.12645			−0.563223	−	0.826305i	$-0.690439\pi$
$971$	−35.1010			−1.12645			−0.563223	+	0.826305i	$0.690439\pi$
$972$		−	22.0454i		−	0.707107i
$973$		−	25.7980i		−	0.827045i
$974$	29.3939			0.941841
$975$	29.3939	+	39.1918i	0.941357	+	1.25514i
$976$	12.0000			0.384111
$977$			10.4041i			0.332856i	0.986054	+	0.166428i	$0.0532233\pi$
$977$			10.4041i			0.332856i	−0.986054	+	0.166428i	$0.946777\pi$
$978$			53.3939i			1.70735i
$979$	−77.3939			−2.47352
$980$	−25.5959	−	12.7980i	−0.817632	−	0.408816i
$981$	−17.3939			−0.555344
$982$			9.30306i			0.296873i
$983$			4.94439i			0.157701i	0.996886	+	0.0788507i	$0.0251250\pi$
$983$			4.94439i			0.157701i	−0.996886	+	0.0788507i	$0.974875\pi$
$984$	4.89898			0.156174
$985$	2.00000	−	4.00000i	0.0637253	−	0.127451i
$986$		0			0
$987$			48.4949i			1.54361i
$988$			14.2020i			0.451827i
$989$	35.5959			1.13188
$990$	14.6969	−	29.3939i	0.467099	−	0.934199i
$991$	−31.8434			−1.01154			−0.505769	−	0.862669i	$-0.668791\pi$
$991$	−31.8434			−1.01154			−0.505769	+	0.862669i	$0.668791\pi$
$992$			1.55051i			0.0492287i
$993$		−	34.8990i		−	1.10749i
$994$	−21.7980			−0.691389
$995$	12.8990	+	6.44949i	0.408925	+	0.204463i
$996$	23.3939			0.741263
$997$			22.0000i			0.696747i	0.937356	+	0.348373i	$0.113266\pi$
$997$			22.0000i			0.696747i	−0.937356	+	0.348373i	$0.886734\pi$
$998$		−	10.6515i		−	0.337168i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.b.c.149.1	✓	4
3.2	odd	2		3330.2.d.m.1999.3		4
5.2	odd	4		1850.2.a.v.1.1		2
5.3	odd	4		1850.2.a.s.1.2		2
5.4	even	2	inner	370.2.b.c.149.4	yes	4
15.14	odd	2		3330.2.d.m.1999.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.b.c.149.1	✓	4	1.1	even	1	trivial
370.2.b.c.149.4	yes	4	5.4	even	2	inner
1850.2.a.s.1.2		2	5.3	odd	4
1850.2.a.v.1.1		2	5.2	odd	4
3330.2.d.m.1999.2		4	15.14	odd	2
3330.2.d.m.1999.3		4	3.2	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -2.44949i q^{3} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -2.44949 q^{6} -4.44949i q^{7} +1.00000i q^{8} -3.00000 q^{9} +(-1.00000 + 2.00000i) q^{10} +4.89898 q^{11} +2.44949i q^{12} +4.00000i q^{13} -4.44949 q^{14} +(-2.44949 + 4.89898i) q^{15} +1.00000 q^{16} +4.89898i q^{17} +3.00000i q^{18} -3.55051 q^{19} +(2.00000 + 1.00000i) q^{20} -10.8990 q^{21} -4.89898i q^{22} -8.89898i q^{23} +2.44949 q^{24} +(3.00000 + 4.00000i) q^{25} +4.00000 q^{26} +4.44949i q^{28} +(4.89898 + 2.44949i) q^{30} -1.55051 q^{31} -1.00000i q^{32} -12.0000i q^{33} +4.89898 q^{34} +(-4.44949 + 8.89898i) q^{35} +3.00000 q^{36} -1.00000i q^{37} +3.55051i q^{38} +9.79796 q^{39} +(1.00000 - 2.00000i) q^{40} +2.00000 q^{41} +10.8990i q^{42} +4.00000i q^{43} -4.89898 q^{44} +(6.00000 + 3.00000i) q^{45} -8.89898 q^{46} -4.44949i q^{47} -2.44949i q^{48} -12.7980 q^{49} +(4.00000 - 3.00000i) q^{50} +12.0000 q^{51} -4.00000i q^{52} -11.7980i q^{53} +(-9.79796 - 4.89898i) q^{55} +4.44949 q^{56} +8.69694i q^{57} +3.55051 q^{59} +(2.44949 - 4.89898i) q^{60} +12.0000 q^{61} +1.55051i q^{62} +13.3485i q^{63} -1.00000 q^{64} +(4.00000 - 8.00000i) q^{65} -12.0000 q^{66} +5.55051i q^{67} -4.89898i q^{68} -21.7980 q^{69} +(8.89898 + 4.44949i) q^{70} +4.89898 q^{71} -3.00000i q^{72} +4.00000i q^{73} -1.00000 q^{74} +(9.79796 - 7.34847i) q^{75} +3.55051 q^{76} -21.7980i q^{77} -9.79796i q^{78} -6.44949 q^{79} +(-2.00000 - 1.00000i) q^{80} -9.00000 q^{81} -2.00000i q^{82} -9.55051i q^{83} +10.8990 q^{84} +(4.89898 - 9.79796i) q^{85} +4.00000 q^{86} +4.89898i q^{88} -15.7980 q^{89} +(3.00000 - 6.00000i) q^{90} +17.7980 q^{91} +8.89898i q^{92} +3.79796i q^{93} -4.44949 q^{94} +(7.10102 + 3.55051i) q^{95} -2.44949 q^{96} +2.00000i q^{97} +12.7980i q^{98} -14.6969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 8 q^{5} - 12 q^{9} - 4 q^{10} - 8 q^{14} + 4 q^{16} - 24 q^{19} + 8 q^{20} - 24 q^{21} + 12 q^{25} + 16 q^{26} - 16 q^{31} - 8 q^{35} + 12 q^{36} + 4 q^{40} + 8 q^{41} + 24 q^{45} - 16 q^{46}+ \cdots + 48 q^{95}+O(q^{100}) \) 4 * q - 4 * q^4 - 8 * q^5 - 12 * q^9 - 4 * q^10 - 8 * q^14 + 4 * q^16 - 24 * q^19 + 8 * q^20 - 24 * q^21 + 12 * q^25 + 16 * q^26 - 16 * q^31 - 8 * q^35 + 12 * q^36 + 4 * q^40 + 8 * q^41 + 24 * q^45 - 16 * q^46 - 12 * q^49 + 16 * q^50 + 48 * q^51 + 8 * q^56 + 24 * q^59 + 48 * q^61 - 4 * q^64 + 16 * q^65 - 48 * q^66 - 48 * q^69 + 16 * q^70 - 4 * q^74 + 24 * q^76 - 16 * q^79 - 8 * q^80 - 36 * q^81 + 24 * q^84 + 16 * q^86 - 24 * q^89 + 12 * q^90 + 32 * q^91 - 8 * q^94 + 48 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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