LMFDB - Embedded newform 1690.2.l.m.361.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(361,1690)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1690, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,2,6,0,0,0,0,8,-6,0,4,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.6
Root			$-1.07992 + 0.623490i$ of defining polynomial
Character	$\chi$	$=$	1690.361
Dual form			1690.2.l.m.1161.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(0.900969 + 1.56052i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(1.56052 + 0.900969i) q^{6} +(3.12105 + 1.80194i) q^{7} -1.00000i q^{8} +(-0.123490 + 0.213891i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(3.84952 - 2.22252i) q^{11} +1.80194 q^{12} +3.60388 q^{14} +(1.56052 - 0.900969i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.57942 + 2.73563i) q^{17} +0.246980i q^{18} +(-0.309081 - 0.178448i) q^{19} +(-0.866025 - 0.500000i) q^{20} +6.49396i q^{21} +(2.22252 - 3.84952i) q^{22} +(-3.24698 - 5.62393i) q^{23} +(1.56052 - 0.900969i) q^{24} -1.00000 q^{25} +4.96077 q^{27} +(3.12105 - 1.80194i) q^{28} +(1.44504 + 2.50289i) q^{29} +(0.900969 - 1.56052i) q^{30} -3.82371i q^{31} +(-0.866025 - 0.500000i) q^{32} +(6.93659 + 4.00484i) q^{33} +3.15883i q^{34} +(1.80194 - 3.12105i) q^{35} +(0.123490 + 0.213891i) q^{36} +(-6.47950 + 3.74094i) q^{37} -0.356896 q^{38} -1.00000 q^{40} +(-1.76602 + 1.01961i) q^{41} +(3.24698 + 5.62393i) q^{42} +(5.00753 - 8.67330i) q^{43} -4.44504i q^{44} +(0.213891 + 0.123490i) q^{45} +(-5.62393 - 3.24698i) q^{46} +11.7017i q^{47} +(0.900969 - 1.56052i) q^{48} +(2.99396 + 5.18569i) q^{49} +(-0.866025 + 0.500000i) q^{50} -5.69202 q^{51} -12.3720 q^{53} +(4.29615 - 2.48039i) q^{54} +(-2.22252 - 3.84952i) q^{55} +(1.80194 - 3.12105i) q^{56} -0.643104i q^{57} +(2.50289 + 1.44504i) q^{58} +(10.3902 + 5.99880i) q^{59} -1.80194i q^{60} +(6.18598 - 10.7144i) q^{61} +(-1.91185 - 3.31143i) q^{62} +(-0.770835 + 0.445042i) q^{63} -1.00000 q^{64} +8.00969 q^{66} +(-12.1223 + 6.99880i) q^{67} +(1.57942 + 2.73563i) q^{68} +(5.85086 - 10.1340i) q^{69} -3.60388i q^{70} +(11.0952 + 6.40581i) q^{71} +(0.213891 + 0.123490i) q^{72} +6.96615i q^{73} +(-3.74094 + 6.47950i) q^{74} +(-0.900969 - 1.56052i) q^{75} +(-0.309081 + 0.178448i) q^{76} +16.0194 q^{77} -5.87800 q^{79} +(-0.866025 + 0.500000i) q^{80} +(4.83997 + 8.38307i) q^{81} +(-1.01961 + 1.76602i) q^{82} -4.67456i q^{83} +(5.62393 + 3.24698i) q^{84} +(2.73563 + 1.57942i) q^{85} -10.0151i q^{86} +(-2.60388 + 4.51004i) q^{87} +(-2.22252 - 3.84952i) q^{88} +(6.94706 - 4.01089i) q^{89} +0.246980 q^{90} -6.49396 q^{92} +(5.96699 - 3.44504i) q^{93} +(5.85086 + 10.1340i) q^{94} +(-0.178448 + 0.309081i) q^{95} -1.80194i q^{96} +(3.42174 + 1.97554i) q^{97} +(5.18569 + 2.99396i) q^{98} +1.09783i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} + 6 q^{4} + 8 q^{9} - 6 q^{10} + 4 q^{12} + 8 q^{14} - 6 q^{16} - 2 q^{17} + 26 q^{22} - 20 q^{23} - 12 q^{25} + 8 q^{27} + 16 q^{29} + 2 q^{30} + 4 q^{35} - 8 q^{36} + 12 q^{38} - 12 q^{40}+ \cdots + 6 q^{95}+O(q^{100}) $ 12 * q + 2 * q^3 + 6 * q^4 + 8 * q^9 - 6 * q^10 + 4 * q^12 + 8 * q^14 - 6 * q^16 - 2 * q^17 + 26 * q^22 - 20 * q^23 - 12 * q^25 + 8 * q^27 + 16 * q^29 + 2 * q^30 + 4 * q^35 - 8 * q^36 + 12 * q^38 - 12 * q^40 + 20 * q^42 + 10 * q^43 + 2 * q^48 - 2 * q^49 - 48 * q^51 - 32 * q^53 - 26 * q^55 + 4 * q^56 + 16 * q^61 - 8 * q^62 - 12 * q^64 + 8 * q^66 + 2 * q^68 + 16 * q^69 + 12 * q^74 - 2 * q^75 + 16 * q^77 + 8 * q^79 + 10 * q^81 - 38 * q^82 + 4 * q^87 - 26 * q^88 - 16 * q^90 - 40 * q^92 + 16 * q^94 + 6 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	0.900969	+	1.56052i	0.520175	+	0.900969i	0.999725	+	0.0234545i	$0.00746647\pi$
$3$	0.900969	+	1.56052i	0.520175	+	0.900969i	−0.479550	+	0.877514i	$0.659200\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.56052	+	0.900969i	0.637081	+	0.367819i
$7$	3.12105	+	1.80194i	1.17965	+	0.681068i	0.955932	−	0.293587i	$-0.0948489\pi$
$7$	3.12105	+	1.80194i	1.17965	+	0.681068i	0.223713	+	0.974655i	$0.428182\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.123490	+	0.213891i	−0.0411633	+	0.0712969i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	3.84952	−	2.22252i	1.16067	−	0.670115i	0.209208	−	0.977871i	$-0.432911\pi$
$11$	3.84952	−	2.22252i	1.16067	−	0.670115i	0.951465	+	0.307756i	$0.0995780\pi$
$12$	1.80194			0.520175
$13$		0			0
$13$		0			0
$14$	3.60388			0.963176
$15$	1.56052	−	0.900969i	0.402926	−	0.232629i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.57942	+	2.73563i	−0.383065	+	0.663488i	−0.991499	−	0.130117i	$-0.958465\pi$
$17$	−1.57942	+	2.73563i	−0.383065	+	0.663488i	0.608434	+	0.793605i	$0.291798\pi$
$18$			0.246980i			0.0582137i
$19$	−0.309081	−	0.178448i	−0.0709080	−	0.0409388i	0.464127	−	0.885769i	$-0.346368\pi$
$19$	−0.309081	−	0.178448i	−0.0709080	−	0.0409388i	−0.535035	+	0.844830i	$0.679702\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$			6.49396i			1.41710i
$22$	2.22252	−	3.84952i	0.473843	−	0.820720i
$23$	−3.24698	−	5.62393i	−0.677042	−	1.17267i	−0.975868	−	0.218363i	$-0.929928\pi$
$23$	−3.24698	−	5.62393i	−0.677042	−	1.17267i	0.298825	−	0.954308i	$-0.403405\pi$
$24$	1.56052	−	0.900969i	0.318541	−	0.183910i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	4.96077			0.954701
$28$	3.12105	−	1.80194i	0.589823	−	0.340534i
$29$	1.44504	+	2.50289i	0.268338	+	0.464774i	0.968433	−	0.249275i	$-0.0801924\pi$
$29$	1.44504	+	2.50289i	0.268338	+	0.464774i	−0.700095	+	0.714050i	$0.746859\pi$
$30$	0.900969	−	1.56052i	0.164494	−	0.284911i
$31$		−	3.82371i		−	0.686758i	−0.939197	−	0.343379i	$-0.888428\pi$
$31$		−	3.82371i		−	0.686758i	0.939197	−	0.343379i	$-0.111572\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	6.93659	+	4.00484i	1.20751	+	0.697154i
$34$			3.15883i			0.541735i
$35$	1.80194	−	3.12105i	0.304583	−	0.527553i
$36$	0.123490	+	0.213891i	0.0205816	+	0.0356484i
$37$	−6.47950	+	3.74094i	−1.06522	+	0.615007i	−0.926872	−	0.375377i	$-0.877513\pi$
$37$	−6.47950	+	3.74094i	−1.06522	+	0.615007i	−0.138350	+	0.990383i	$0.544180\pi$
$38$	−0.356896			−0.0578962
$39$		0			0
$40$	−1.00000			−0.158114
$41$	−1.76602	+	1.01961i	−0.275807	+	0.159237i	−0.631523	−	0.775357i	$-0.717570\pi$
$41$	−1.76602	+	1.01961i	−0.275807	+	0.159237i	0.355717	+	0.934594i	$0.384237\pi$
$42$	3.24698	+	5.62393i	0.501020	+	0.867792i
$43$	5.00753	−	8.67330i	0.763642	−	1.32267i	−0.177320	−	0.984153i	$-0.556743\pi$
$43$	5.00753	−	8.67330i	0.763642	−	1.32267i	0.940962	−	0.338513i	$-0.109924\pi$
$44$		−	4.44504i		−	0.670115i
$45$	0.213891	+	0.123490i	0.0318849	+	0.0184088i
$46$	−5.62393	−	3.24698i	−0.829204	−	0.478741i
$47$			11.7017i			1.70687i	0.521199	+	0.853435i	$0.325485\pi$
$47$			11.7017i			1.70687i	−0.521199	+	0.853435i	$0.674515\pi$
$48$	0.900969	−	1.56052i	0.130044	−	0.225242i
$49$	2.99396	+	5.18569i	0.427708	+	0.740813i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	−5.69202			−0.797042
$52$		0			0
$53$	−12.3720			−1.69942			−0.849710	−	0.527251i	$-0.823223\pi$
$53$	−12.3720			−1.69942			−0.849710	+	0.527251i	$0.823223\pi$
$54$	4.29615	−	2.48039i	0.584633	−	0.337538i
$55$	−2.22252	−	3.84952i	−0.299685	−	0.519069i
$56$	1.80194	−	3.12105i	0.240794	−	0.417068i
$57$		−	0.643104i		−	0.0851812i
$58$	2.50289	+	1.44504i	0.328645	+	0.189743i
$59$	10.3902	+	5.99880i	1.35269	+	0.780978i	0.988626	−	0.150395i	$-0.0480546\pi$
$59$	10.3902	+	5.99880i	1.35269	+	0.780978i	0.364067	+	0.931373i	$0.381388\pi$
$60$		−	1.80194i		−	0.232629i
$61$	6.18598	−	10.7144i	0.792034	−	1.37184i	−0.132672	−	0.991160i	$-0.542356\pi$
$61$	6.18598	−	10.7144i	0.792034	−	1.37184i	0.924706	−	0.380683i	$-0.124311\pi$
$62$	−1.91185	−	3.31143i	−0.242806	−	0.420552i
$63$	−0.770835	+	0.445042i	−0.0971161	+	0.0560700i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	8.00969			0.985925
$67$	−12.1223	+	6.99880i	−1.48097	+	0.855040i	−0.999767	−	0.0215680i	$-0.993134\pi$
$67$	−12.1223	+	6.99880i	−1.48097	+	0.855040i	−0.481205	+	0.876608i	$0.659801\pi$
$68$	1.57942	+	2.73563i	0.191532	+	0.331744i
$69$	5.85086	−	10.1340i	0.704360	−	1.21999i
$70$		−	3.60388i		−	0.430746i
$71$	11.0952	+	6.40581i	1.31676	+	0.760230i	0.983206	−	0.182502i	$-0.0584195\pi$
$71$	11.0952	+	6.40581i	1.31676	+	0.760230i	0.333552	+	0.942732i	$0.391753\pi$
$72$	0.213891	+	0.123490i	0.0252073	+	0.0145534i
$73$			6.96615i			0.815326i	0.913132	+	0.407663i	$0.133656\pi$
$73$			6.96615i			0.815326i	−0.913132	+	0.407663i	$0.866344\pi$
$74$	−3.74094	+	6.47950i	−0.434875	+	0.753226i
$75$	−0.900969	−	1.56052i	−0.104035	−	0.180194i
$76$	−0.309081	+	0.178448i	−0.0354540	+	0.0204694i
$77$	16.0194			1.82558
$78$		0			0
$79$	−5.87800			−0.661327			−0.330663	−	0.943749i	$-0.607272\pi$
$79$	−5.87800			−0.661327			−0.330663	+	0.943749i	$0.607272\pi$
$80$	−0.866025	+	0.500000i	−0.0968246	+	0.0559017i
$81$	4.83997	+	8.38307i	0.537774	+	0.931453i
$82$	−1.01961	+	1.76602i	−0.112598	+	0.195025i
$83$		−	4.67456i		−	0.513100i	−0.966531	−	0.256550i	$-0.917414\pi$
$83$		−	4.67456i		−	0.513100i	0.966531	−	0.256550i	$-0.0825858\pi$
$84$	5.62393	+	3.24698i	0.613621	+	0.354275i
$85$	2.73563	+	1.57942i	0.296721	+	0.171312i
$86$		−	10.0151i		−	1.07995i
$87$	−2.60388	+	4.51004i	−0.279165	+	0.483528i
$88$	−2.22252	−	3.84952i	−0.236922	−	0.410360i
$89$	6.94706	−	4.01089i	0.736387	−	0.425153i	−0.0843675	−	0.996435i	$-0.526887\pi$
$89$	6.94706	−	4.01089i	0.736387	−	0.425153i	0.820754	+	0.571282i	$0.193554\pi$
$90$	0.246980			0.0260339
$91$		0			0
$92$	−6.49396			−0.677042
$93$	5.96699	−	3.44504i	0.618748	−	0.357234i
$94$	5.85086	+	10.1340i	0.603470	+	1.04524i
$95$	−0.178448	+	0.309081i	−0.0183084	+	0.0317110i
$96$		−	1.80194i		−	0.183910i
$97$	3.42174	+	1.97554i	0.347425	+	0.200586i	0.663550	−	0.748132i	$-0.269049\pi$
$97$	3.42174	+	1.97554i	0.347425	+	0.200586i	−0.316126	+	0.948717i	$0.602382\pi$
$98$	5.18569	+	2.99396i	0.523834	+	0.302436i
$99$			1.09783i			0.110337i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	7.52111	+	13.0269i	0.748378	+	1.29623i	0.948600	+	0.316478i	$0.102500\pi$
$101$	7.52111	+	13.0269i	0.748378	+	1.29623i	−0.200222	+	0.979751i	$0.564166\pi$
$102$	−4.92944	+	2.84601i	−0.488087	+	0.281797i
$103$	−7.82371			−0.770893			−0.385446	−	0.922730i	$-0.625953\pi$
$103$	−7.82371			−0.770893			−0.385446	+	0.922730i	$0.625953\pi$
$104$		0			0
$105$	6.49396			0.633746
$106$	−10.7144	+	6.18598i	−1.04068	+	0.600836i
$107$	−4.65064	−	8.05514i	−0.449594	−	0.778720i	0.548765	−	0.835976i	$-0.315098\pi$
$107$	−4.65064	−	8.05514i	−0.449594	−	0.778720i	−0.998359	+	0.0572566i	$0.981765\pi$
$108$	2.48039	−	4.29615i	0.238675	−	0.413398i
$109$		−	0.811626i		−	0.0777397i	−0.999244	−	0.0388699i	$-0.987624\pi$
$109$		−	0.811626i		−	0.0777397i	0.999244	−	0.0388699i	$-0.0123758\pi$
$110$	−3.84952	−	2.22252i	−0.367037	−	0.211909i
$111$	−11.6756	−	6.74094i	−1.10820	−	0.639822i
$112$		−	3.60388i		−	0.340534i
$113$	−3.50484	+	6.07057i	−0.329708	+	0.571071i	−0.982454	−	0.186506i	$-0.940284\pi$
$113$	−3.50484	+	6.07057i	−0.329708	+	0.571071i	0.652746	+	0.757577i	$0.273617\pi$
$114$	−0.321552	−	0.556945i	−0.0301161	−	0.0521626i
$115$	−5.62393	+	3.24698i	−0.524435	+	0.302782i
$116$	2.89008			0.268338
$117$		0			0
$118$	11.9976			1.10447
$119$	−9.85887	+	5.69202i	−0.903761	+	0.521787i
$120$	−0.900969	−	1.56052i	−0.0822468	−	0.142456i
$121$	4.37920	−	7.58499i	0.398109	−	0.689545i
$122$		−	12.3720i		−	1.12010i
$123$	−3.18226	−	1.83728i	−0.286935	−	0.165662i
$124$	−3.31143	−	1.91185i	−0.297375	−	0.171690i
$125$			1.00000i			0.0894427i
$126$	−0.445042	+	0.770835i	−0.0396475	+	0.0686715i
$127$	−5.82908	−	10.0963i	−0.517248	−	0.895899i	−0.999799	−	0.0200317i	$-0.993623\pi$
$127$	−5.82908	−	10.0963i	−0.517248	−	0.895899i	0.482552	−	0.875867i	$-0.339710\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	18.0465			1.58891
$130$		0			0
$131$	−1.34481			−0.117497			−0.0587485	−	0.998273i	$-0.518711\pi$
$131$	−1.34481			−0.117497			−0.0587485	+	0.998273i	$0.518711\pi$
$132$	6.93659	−	4.00484i	0.603753	−	0.348577i
$133$	−0.643104	−	1.11389i	−0.0557642	−	0.0965864i
$134$	−6.99880	+	12.1223i	−0.604605	+	1.04721i
$135$		−	4.96077i		−	0.426955i
$136$	2.73563	+	1.57942i	0.234578	+	0.135434i
$137$	−6.75668	−	3.90097i	−0.577262	−	0.333282i	0.182783	−	0.983153i	$-0.441490\pi$
$137$	−6.75668	−	3.90097i	−0.577262	−	0.333282i	−0.760044	+	0.649871i	$0.774823\pi$
$138$		−	11.7017i		−	0.996116i
$139$	−6.93631	+	12.0140i	−0.588330	+	1.01902i	0.406121	+	0.913819i	$0.366881\pi$
$139$	−6.93631	+	12.0140i	−0.588330	+	1.01902i	−0.994451	+	0.105199i	$0.966452\pi$
$140$	−1.80194	−	3.12105i	−0.152292	−	0.263777i
$141$	−18.2608	+	10.5429i	−1.53784	+	0.887870i
$142$	12.8116			1.07513
$143$		0			0
$144$	0.246980			0.0205816
$145$	2.50289	−	1.44504i	0.207853	−	0.120004i
$146$	3.48307	+	6.03286i	0.288261	+	0.499283i
$147$	−5.39493	+	9.34429i	−0.444966	+	0.770704i
$148$			7.48188i			0.615007i
$149$	10.9728	+	6.33513i	0.898923	+	0.518994i	0.876851	−	0.480763i	$-0.159640\pi$
$149$	10.9728	+	6.33513i	0.898923	+	0.518994i	0.0220727	+	0.999756i	$0.492973\pi$
$150$	−1.56052	−	0.900969i	−0.127416	−	0.0735638i
$151$		−	4.86592i		−	0.395983i	−0.980204	−	0.197991i	$-0.936558\pi$
$151$		−	4.86592i		−	0.395983i	0.980204	−	0.197991i	$-0.0634418\pi$
$152$	−0.178448	+	0.309081i	−0.0144740	+	0.0250698i
$153$	−0.390084	−	0.675645i	−0.0315364	−	0.0546226i
$154$	13.8732	−	8.00969i	1.11793	−	0.645439i
$155$	−3.82371			−0.307128
$156$		0			0
$157$	−9.42758			−0.752403			−0.376202	−	0.926538i	$-0.622770\pi$
$157$	−9.42758			−0.752403			−0.376202	+	0.926538i	$0.622770\pi$
$158$	−5.09050	+	2.93900i	−0.404978	+	0.233814i
$159$	−11.1468	−	19.3067i	−0.883995	−	1.53112i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$		−	23.4034i		−	1.84445i
$162$	8.38307	+	4.83997i	0.658636	+	0.380264i
$163$	−4.74279	−	2.73825i	−0.371484	−	0.214476i	0.302623	−	0.953110i	$-0.402138\pi$
$163$	−4.74279	−	2.73825i	−0.371484	−	0.214476i	−0.674107	+	0.738634i	$0.735471\pi$
$164$			2.03923i			0.159237i
$165$	4.00484	−	6.93659i	0.311777	−	0.540013i
$166$	−2.33728	−	4.04829i	−0.181408	−	0.314208i
$167$	−2.32929	+	1.34481i	−0.180246	+	0.104065i	−0.587408	−	0.809291i	$-0.699852\pi$
$167$	−2.32929	+	1.34481i	−0.180246	+	0.104065i	0.407162	+	0.913356i	$0.366518\pi$
$168$	6.49396			0.501020
$169$		0			0
$170$	3.15883			0.242271
$171$	0.0763367	−	0.0440730i	0.00583761	−	0.00337035i
$172$	−5.00753	−	8.67330i	−0.381821	−	0.661333i
$173$	5.45473	−	9.44787i	0.414715	−	0.718308i	−0.580683	−	0.814130i	$-0.697214\pi$
$173$	5.45473	−	9.44787i	0.414715	−	0.718308i	0.995399	+	0.0958214i	$0.0305478\pi$
$174$			5.20775i			0.394799i
$175$	−3.12105	−	1.80194i	−0.235929	−	0.136214i
$176$	−3.84952	−	2.22252i	−0.290168	−	0.167529i
$177$			21.6189i			1.62498i
$178$	4.01089	−	6.94706i	0.300629	−	0.520704i
$179$	6.49127	+	11.2432i	0.485180	+	0.840357i	0.999855	−	0.0170285i	$-0.00542061\pi$
$179$	6.49127	+	11.2432i	0.485180	+	0.840357i	−0.514675	+	0.857386i	$0.672087\pi$
$180$	0.213891	−	0.123490i	0.0159425	−	0.00920439i
$181$	−22.7332			−1.68974			−0.844872	−	0.534969i	$-0.820323\pi$
$181$	−22.7332			−1.68974			−0.844872	+	0.534969i	$0.820323\pi$
$182$		0			0
$183$	22.2935			1.64798
$184$	−5.62393	+	3.24698i	−0.414602	+	0.239371i
$185$	3.74094	+	6.47950i	0.275039	+	0.476382i
$186$	3.44504	−	5.96699i	0.252603	−	0.437521i
$187$			14.0411i			1.02679i
$188$	10.1340	+	5.85086i	0.739096	+	0.426717i
$189$	15.4828	+	8.93900i	1.12621	+	0.650217i
$190$			0.356896i			0.0258919i
$191$	−9.10992	+	15.7788i	−0.659170	+	1.14172i	0.321660	+	0.946855i	$0.395759\pi$
$191$	−9.10992	+	15.7788i	−0.659170	+	1.14172i	−0.980831	+	0.194862i	$0.937574\pi$
$192$	−0.900969	−	1.56052i	−0.0650218	−	0.112621i
$193$	16.2364	−	9.37412i	1.16873	−	0.674764i	0.215346	−	0.976538i	$-0.430912\pi$
$193$	16.2364	−	9.37412i	1.16873	−	0.674764i	0.953379	+	0.301774i	$0.0975789\pi$
$194$	3.95108			0.283671
$195$		0			0
$196$	5.98792			0.427708
$197$	−19.4124	+	11.2078i	−1.38308	+	0.798519i	−0.992523	−	0.122061i	$-0.961050\pi$
$197$	−19.4124	+	11.2078i	−1.38308	+	0.798519i	−0.390553	+	0.920580i	$0.627716\pi$
$198$	0.548917	+	0.950753i	0.0390099	+	0.0675671i
$199$	8.54288	−	14.7967i	0.605588	−	1.04891i	−0.386370	−	0.922344i	$-0.626271\pi$
$199$	8.54288	−	14.7967i	0.605588	−	1.04891i	0.991958	−	0.126566i	$-0.0403956\pi$
$200$			1.00000i			0.0707107i
$201$	−21.8436	−	12.6114i	−1.54073	−	0.889540i
$202$	13.0269	+	7.52111i	0.916572	+	0.529183i
$203$			10.4155i			0.731025i
$204$	−2.84601	+	4.92944i	−0.199261	+	0.345129i
$205$	1.01961	+	1.76602i	0.0712130	+	0.123344i
$206$	−6.77553	+	3.91185i	−0.472074	+	0.272552i
$207$	1.60388			0.111477
$208$		0			0
$209$	−1.58642			−0.109735
$210$	5.62393	−	3.24698i	0.388088	−	0.224063i
$211$	2.76540	+	4.78981i	0.190378	+	0.329744i	0.945375	−	0.325983i	$-0.105695\pi$
$211$	2.76540	+	4.78981i	0.190378	+	0.329744i	−0.754998	+	0.655727i	$0.772362\pi$
$212$	−6.18598	+	10.7144i	−0.424855	+	0.735870i
$213$			23.0858i			1.58181i
$214$	−8.05514	−	4.65064i	−0.550638	−	0.317911i
$215$	−8.67330	−	5.00753i	−0.591514	−	0.341511i
$216$		−	4.96077i		−	0.337538i
$217$	6.89008	−	11.9340i	0.467729	−	0.810131i
$218$	−0.405813	−	0.702889i	−0.0274851	−	0.0476057i
$219$	−10.8708	+	6.27628i	−0.734583	+	0.424112i
$220$	−4.44504			−0.299685
$221$		0			0
$222$	−13.4819			−0.904844
$223$	−3.70150	+	2.13706i	−0.247871	+	0.143108i	−0.618789	−	0.785557i	$-0.712376\pi$
$223$	−3.70150	+	2.13706i	−0.247871	+	0.143108i	0.370918	+	0.928666i	$0.379043\pi$
$224$	−1.80194	−	3.12105i	−0.120397	−	0.208534i
$225$	0.123490	−	0.213891i	0.00823265	−	0.0142594i
$226$			7.00969i			0.466278i
$227$	−8.62047	−	4.97703i	−0.572161	−	0.330337i	0.185851	−	0.982578i	$-0.440496\pi$
$227$	−8.62047	−	4.97703i	−0.572161	−	0.330337i	−0.758012	+	0.652241i	$0.773829\pi$
$228$	−0.556945	−	0.321552i	−0.0368846	−	0.0212953i
$229$		−	23.0315i		−	1.52196i	−0.648774	−	0.760981i	$-0.724718\pi$
$229$		−	23.0315i		−	1.52196i	0.648774	−	0.760981i	$-0.275282\pi$
$230$	−3.24698	+	5.62393i	−0.214099	+	0.370831i
$231$	14.4330	+	24.9986i	0.949619	+	1.64479i
$232$	2.50289	−	1.44504i	0.164323	−	0.0948716i
$233$	−18.5700			−1.21656			−0.608281	−	0.793721i	$-0.708141\pi$
$233$	−18.5700			−1.21656			−0.608281	+	0.793721i	$0.708141\pi$
$234$		0			0
$235$	11.7017			0.763335
$236$	10.3902	−	5.99880i	0.676347	−	0.390489i
$237$	−5.29590	−	9.17276i	−0.344005	−	0.595835i
$238$	−5.69202	+	9.85887i	−0.368959	+	0.639056i
$239$			18.9530i			1.22597i	0.790095	+	0.612984i	$0.210031\pi$
$239$			18.9530i			1.22597i	−0.790095	+	0.612984i	$0.789969\pi$
$240$	−1.56052	−	0.900969i	−0.100731	−	0.0581573i
$241$	−19.6968	−	11.3720i	−1.26878	−	0.732532i	−0.294026	−	0.955798i	$-0.594995\pi$
$241$	−19.6968	−	11.3720i	−1.26878	−	0.732532i	−0.974758	+	0.223265i	$0.928328\pi$
$242$		−	8.75840i		−	0.563011i
$243$	−1.28017	+	2.21732i	−0.0821228	+	0.142241i
$244$	−6.18598	−	10.7144i	−0.396017	−	0.685921i
$245$	5.18569	−	2.99396i	0.331302	−	0.191277i
$246$	−3.67456			−0.234282
$247$		0			0
$248$	−3.82371			−0.242806
$249$	7.29477	−	4.21164i	0.462287	−	0.266902i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	7.28352	−	12.6154i	0.459732	−	0.796279i	−0.539215	−	0.842168i	$-0.681279\pi$
$251$	7.28352	−	12.6154i	0.459732	−	0.796279i	0.998947	+	0.0458896i	$0.0146122\pi$
$252$			0.890084i			0.0560700i
$253$	−24.9986	−	14.4330i	−1.57165	−	0.907392i
$254$	−10.0963	−	5.82908i	−0.633496	−	0.365749i
$255$			5.69202i			0.356448i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.00216	+	1.73578i	0.0625128	+	0.108275i	0.895588	−	0.444884i	$-0.146755\pi$
$257$	1.00216	+	1.73578i	0.0625128	+	0.108275i	−0.833075	+	0.553160i	$0.813422\pi$
$258$	15.6287	−	9.02326i	0.973003	−	0.561764i
$259$	−26.9638			−1.67545
$260$		0			0
$261$	−0.713792			−0.0441826
$262$	−1.16464	+	0.672407i	−0.0719519	+	0.0415415i
$263$	−2.20775	−	3.82394i	−0.136136	−	0.235794i	0.789895	−	0.613242i	$-0.210135\pi$
$263$	−2.20775	−	3.82394i	−0.136136	−	0.235794i	−0.926031	+	0.377448i	$0.876802\pi$
$264$	4.00484	−	6.93659i	0.246481	−	0.426918i
$265$			12.3720i			0.760004i
$266$	−1.11389	−	0.643104i	−0.0682969	−	0.0394312i
$267$	12.5182	+	7.22737i	0.766099	+	0.442308i
$268$			13.9976i			0.855040i
$269$	9.07606	−	15.7202i	0.553377	−	0.958478i	−0.444650	−	0.895704i	$-0.646672\pi$
$269$	9.07606	−	15.7202i	0.553377	−	0.958478i	0.998028	−	0.0627736i	$-0.0199946\pi$
$270$	−2.48039	−	4.29615i	−0.150951	−	0.261456i
$271$	−16.8625	+	9.73556i	−1.02432	+	0.591393i	−0.915353	−	0.402652i	$-0.868089\pi$
$271$	−16.8625	+	9.73556i	−1.02432	+	0.591393i	−0.108970	+	0.994045i	$0.534755\pi$
$272$	3.15883			0.191532
$273$		0			0
$274$	−7.80194			−0.471332
$275$	−3.84952	+	2.22252i	−0.232135	+	0.134023i
$276$	−5.85086	−	10.1340i	−0.352180	−	0.609994i
$277$	−9.19806	+	15.9315i	−0.552658	+	0.957232i	0.445424	+	0.895320i	$0.353053\pi$
$277$	−9.19806	+	15.9315i	−0.552658	+	0.957232i	−0.998082	+	0.0619118i	$0.980280\pi$
$278$			13.8726i			0.832025i
$279$	0.817855	+	0.472189i	0.0489637	+	0.0282692i
$280$	−3.12105	−	1.80194i	−0.186518	−	0.107686i
$281$		−	15.9463i		−	0.951276i	−0.879641	−	0.475638i	$-0.842217\pi$
$281$		−	15.9463i		−	0.951276i	0.879641	−	0.475638i	$-0.157783\pi$
$282$	−10.5429	+	18.2608i	−0.627819	+	1.08741i
$283$	−13.9955	−	24.2408i	−0.831943	−	1.44097i	−0.896495	−	0.443054i	$-0.853895\pi$
$283$	−13.9955	−	24.2408i	−0.831943	−	1.44097i	0.0645519	−	0.997914i	$-0.479438\pi$
$284$	11.0952	−	6.40581i	0.658379	−	0.380115i
$285$	−0.643104			−0.0380942
$286$		0			0
$287$	−7.34913			−0.433805
$288$	0.213891	−	0.123490i	0.0126036	−	0.00727671i
$289$	3.51089	+	6.08103i	0.206523	+	0.357708i
$290$	1.44504	−	2.50289i	0.0848558	−	0.146975i
$291$			7.11960i			0.417359i
$292$	6.03286	+	3.48307i	0.353047	+	0.203831i
$293$	11.7436	+	6.78017i	0.686068	+	0.396102i	0.802137	−	0.597140i	$-0.203696\pi$
$293$	11.7436	+	6.78017i	0.686068	+	0.396102i	−0.116069	+	0.993241i	$0.537029\pi$
$294$			10.7899i			0.629277i
$295$	5.99880	−	10.3902i	0.349264	−	0.604943i
$296$	3.74094	+	6.47950i	0.217438	+	0.376613i
$297$	19.0966	−	11.0254i	1.10810	−	0.639760i
$298$	12.6703			0.733968
$299$		0			0
$300$	−1.80194			−0.104035
$301$	31.2575	−	18.0465i	1.80165	−	1.04018i
$302$	−2.43296	−	4.21401i	−0.140001	−	0.242489i
$303$	−13.5526	+	23.4737i	−0.778575	+	1.34853i
$304$			0.356896i			0.0204694i
$305$	−10.7144	−	6.18598i	−0.613507	−	0.354208i
$306$	−0.675645	−	0.390084i	−0.0386240	−	0.0222996i
$307$		−	15.1588i		−	0.865160i	−0.901595	−	0.432580i	$-0.857603\pi$
$307$		−	15.1588i		−	0.865160i	0.901595	−	0.432580i	$-0.142397\pi$
$308$	8.00969	−	13.8732i	0.456394	−	0.790498i
$309$	−7.04892	−	12.2091i	−0.400999	−	0.694550i
$310$	−3.31143	+	1.91185i	−0.188076	+	0.108586i
$311$	−5.38404			−0.305301			−0.152651	−	0.988280i	$-0.548781\pi$
$311$	−5.38404			−0.305301			−0.152651	+	0.988280i	$0.548781\pi$
$312$		0			0
$313$	−16.5864			−0.937520			−0.468760	−	0.883326i	$-0.655299\pi$
$313$	−16.5864			−0.937520			−0.468760	+	0.883326i	$0.655299\pi$
$314$	−8.16453	+	4.71379i	−0.460751	+	0.266015i
$315$	0.445042	+	0.770835i	0.0250753	+	0.0434316i
$316$	−2.93900	+	5.09050i	−0.165332	+	0.286363i
$317$		−	12.1086i		−	0.680086i	−0.940410	−	0.340043i	$-0.889558\pi$
$317$		−	12.1086i		−	0.680086i	0.940410	−	0.340043i	$-0.110442\pi$
$318$	−19.3067	−	11.1468i	−1.08267	−	0.625079i
$319$	11.1254	+	6.42327i	0.622905	+	0.359634i
$320$			1.00000i			0.0559017i
$321$	8.38016	−	14.5149i	0.467735	−	0.810140i
$322$	−11.7017	−	20.2680i	−0.652111	−	1.12949i
$323$	0.976335	−	0.563687i	0.0543247	−	0.0313644i
$324$	9.67994			0.537774
$325$		0			0
$326$	−5.47650			−0.303315
$327$	1.26656	−	0.731250i	0.0700411	−	0.0404382i
$328$	1.01961	+	1.76602i	0.0562988	+	0.0975124i
$329$	−21.0858	+	36.5216i	−1.16250	+	2.01350i
$330$		−	8.00969i		−	0.440919i
$331$	12.6536	+	7.30559i	0.695507	+	0.401551i	0.805672	−	0.592362i	$-0.201804\pi$
$331$	12.6536	+	7.30559i	0.695507	+	0.401551i	−0.110165	+	0.993913i	$0.535138\pi$
$332$	−4.04829	−	2.33728i	−0.222179	−	0.128275i
$333$		−	1.84787i		−	0.101263i
$334$	−1.34481	+	2.32929i	−0.0735850	+	0.127453i
$335$	6.99880	+	12.1223i	0.382385	+	0.662311i
$336$	5.62393	−	3.24698i	0.306811	−	0.177137i
$337$	4.45952			0.242925			0.121463	−	0.992596i	$-0.461242\pi$
$337$	4.45952			0.242925			0.121463	+	0.992596i	$0.461242\pi$
$338$		0			0
$339$	−12.6310			−0.686023
$340$	2.73563	−	1.57942i	0.148360	−	0.0856559i
$341$	−8.49827	−	14.7194i	−0.460207	−	0.797102i
$342$	0.0440730	−	0.0763367i	0.00238319	−	0.00412781i
$343$		−	3.64742i		−	0.196942i
$344$	−8.67330	−	5.00753i	−0.467633	−	0.269988i
$345$	−10.1340	−	5.85086i	−0.545595	−	0.314999i
$346$		−	10.9095i		−	0.586496i
$347$	−14.2935	+	24.7571i	−0.767316	+	1.32903i	0.171698	+	0.985150i	$0.445075\pi$
$347$	−14.2935	+	24.7571i	−0.767316	+	1.32903i	−0.939014	+	0.343880i	$0.888259\pi$
$348$	2.60388	+	4.51004i	0.139582	+	0.241764i
$349$	−4.22562	+	2.43967i	−0.226192	+	0.130592i	−0.608814	−	0.793313i	$-0.708355\pi$
$349$	−4.22562	+	2.43967i	−0.226192	+	0.130592i	0.382622	+	0.923905i	$0.375021\pi$
$350$	−3.60388			−0.192635
$351$		0			0
$352$	−4.44504			−0.236922
$353$	3.51578	−	2.02984i	0.187126	−	0.108037i	−0.403510	−	0.914975i	$-0.632210\pi$
$353$	3.51578	−	2.02984i	0.187126	−	0.108037i	0.590636	+	0.806938i	$0.298877\pi$
$354$	10.8095	+	18.7226i	0.574517	+	0.995092i
$355$	6.40581	−	11.0952i	0.339985	−	0.588872i
$356$		−	8.02177i		−	0.425153i
$357$	−17.7651	−	10.2567i	−0.940227	−	0.542840i
$358$	11.2432	+	6.49127i	0.594222	+	0.343074i
$359$		−	5.12067i		−	0.270259i	−0.990828	−	0.135129i	$-0.956855\pi$
$359$		−	5.12067i		−	0.270259i	0.990828	−	0.135129i	$-0.0431450\pi$
$360$	0.123490	−	0.213891i	0.00650848	−	0.0112730i
$361$	−9.43631	−	16.3442i	−0.496648	−	0.860220i
$362$	−19.6875	+	11.3666i	−1.03475	+	0.597414i
$363$	15.7821			0.828345
$364$		0			0
$365$	6.96615			0.364625
$366$	19.3067	−	11.1468i	1.00918	−	0.582650i
$367$	4.64310	+	8.04209i	0.242368	+	0.419794i	0.961388	−	0.275195i	$-0.0887425\pi$
$367$	4.64310	+	8.04209i	0.242368	+	0.419794i	−0.719020	+	0.694989i	$0.755409\pi$
$368$	−3.24698	+	5.62393i	−0.169261	+	0.293168i
$369$		−	0.503648i		−	0.0262189i
$370$	6.47950	+	3.74094i	0.336853	+	0.194482i
$371$	−38.6135	−	22.2935i	−2.00471	−	1.15742i
$372$		−	6.89008i		−	0.357234i
$373$	3.65279	−	6.32682i	0.189134	−	0.327590i	−0.755827	−	0.654771i	$-0.772765\pi$
$373$	3.65279	−	6.32682i	0.189134	−	0.327590i	0.944962	+	0.327180i	$0.106098\pi$
$374$	7.02057	+	12.1600i	0.363025	+	0.628778i
$375$	−1.56052	+	0.900969i	−0.0805851	+	0.0465258i
$376$	11.7017			0.603470
$377$		0			0
$378$	17.8780			0.919545
$379$	26.4744	−	15.2850i	1.35990	−	0.785138i	0.370290	−	0.928916i	$-0.379258\pi$
$379$	26.4744	−	15.2850i	1.35990	−	0.785138i	0.989610	+	0.143778i	$0.0459252\pi$
$380$	0.178448	+	0.309081i	0.00915419	+	0.0158555i
$381$	10.5036	−	18.1929i	0.538118	−	0.932048i
$382$			18.2198i			0.932208i
$383$	6.86957	+	3.96615i	0.351019	+	0.202661i	0.665134	−	0.746724i	$-0.268374\pi$
$383$	6.86957	+	3.96615i	0.351019	+	0.202661i	−0.314115	+	0.949385i	$0.601708\pi$
$384$	−1.56052	−	0.900969i	−0.0796351	−	0.0459774i
$385$		−	16.0194i		−	0.816423i
$386$	9.37412	−	16.2364i	0.477130	−	0.826413i
$387$	1.23676	+	2.14213i	0.0628680	+	0.108891i
$388$	3.42174	−	1.97554i	0.173712	−	0.100293i
$389$	−1.35988			−0.0689486			−0.0344743	−	0.999406i	$-0.510976\pi$
$389$	−1.35988			−0.0689486			−0.0344743	+	0.999406i	$0.510976\pi$
$390$		0			0
$391$	20.5133			1.03740
$392$	5.18569	−	2.99396i	0.261917	−	0.151218i
$393$	−1.21164	−	2.09861i	−0.0611189	−	0.105861i
$394$	−11.2078	+	19.4124i	−0.564638	+	0.977982i
$395$			5.87800i			0.295754i
$396$	0.950753	+	0.548917i	0.0477771	+	0.0275841i
$397$	21.3139	+	12.3056i	1.06971	+	0.617600i	0.928103	−	0.372323i	$-0.121439\pi$
$397$	21.3139	+	12.3056i	1.06971	+	0.617600i	0.141611	+	0.989922i	$0.454772\pi$
$398$		−	17.0858i		−	0.856431i
$399$	1.15883	−	2.00716i	0.0580142	−	0.100484i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	4.23959	−	2.44773i	0.211715	−	0.122234i	−0.390393	−	0.920648i	$-0.627661\pi$
$401$	4.23959	−	2.44773i	0.211715	−	0.122234i	0.602108	+	0.798414i	$0.294328\pi$
$402$	−25.2228			−1.25800
$403$		0			0
$404$	15.0422			0.748378
$405$	8.38307	−	4.83997i	0.416558	−	0.240500i
$406$	5.20775	+	9.02009i	0.258456	+	0.447660i
$407$	−16.6286	+	28.8016i	−0.824251	+	1.42764i
$408$			5.69202i			0.281797i
$409$	−3.78830	−	2.18718i	−0.187319	−	0.108149i	0.403408	−	0.915020i	$-0.367826\pi$
$409$	−3.78830	−	2.18718i	−0.187319	−	0.108149i	−0.590727	+	0.806871i	$0.701159\pi$
$410$	1.76602	+	1.01961i	0.0872177	+	0.0503552i
$411$		−	14.0586i		−	0.693460i
$412$	−3.91185	+	6.77553i	−0.192723	+	0.333806i
$413$	21.6189	+	37.4451i	1.06380	+	1.84255i
$414$	1.38900	−	0.801938i	0.0682655	−	0.0394131i
$415$	−4.67456			−0.229465
$416$		0			0
$417$	−24.9976			−1.22414
$418$	−1.37388	+	0.793209i	−0.0671985	+	0.0387971i
$419$	−8.37196	−	14.5007i	−0.408997	−	0.708404i	0.585781	−	0.810470i	$-0.300788\pi$
$419$	−8.37196	−	14.5007i	−0.408997	−	0.708404i	−0.994778	+	0.102066i	$0.967455\pi$
$420$	3.24698	−	5.62393i	0.158436	−	0.274420i
$421$		−	0.483206i		−	0.0235500i	−0.999931	−	0.0117750i	$-0.996252\pi$
$421$		−	0.483206i		−	0.0235500i	0.999931	−	0.0117750i	$-0.00374819\pi$
$422$	4.78981	+	2.76540i	0.233164	+	0.134617i
$423$	−2.50289	−	1.44504i	−0.121694	−	0.0702603i
$424$			12.3720i			0.600836i
$425$	1.57942	−	2.73563i	0.0766130	−	0.132698i
$426$	11.5429	+	19.9928i	0.559254	+	0.968657i
$427$	38.6135	−	22.2935i	1.86864	−	1.07886i
$428$	−9.30127			−0.449594
$429$		0			0
$430$	−10.0151			−0.482969
$431$	10.3714	−	5.98792i	0.499572	−	0.288428i	−0.228965	−	0.973435i	$-0.573534\pi$
$431$	10.3714	−	5.98792i	0.499572	−	0.288428i	0.728537	+	0.685007i	$0.240201\pi$
$432$	−2.48039	−	4.29615i	−0.119338	−	0.206699i
$433$	−2.07726	+	3.59792i	−0.0998268	+	0.172905i	−0.911613	−	0.411050i	$-0.865162\pi$
$433$	−2.07726	+	3.59792i	−0.0998268	+	0.172905i	0.811786	+	0.583955i	$0.198496\pi$
$434$		−	13.7802i		−	0.661469i
$435$	4.51004	+	2.60388i	0.216240	+	0.124846i
$436$	−0.702889	−	0.405813i	−0.0336623	−	0.0194349i
$437$			2.31767i			0.110869i
$438$	−6.27628	+	10.8708i	−0.299892	+	0.519429i
$439$	−6.25667	−	10.8369i	−0.298614	−	0.517215i	0.677205	−	0.735795i	$-0.263191\pi$
$439$	−6.25667	−	10.8369i	−0.298614	−	0.517215i	−0.975819	+	0.218579i	$0.929858\pi$
$440$	−3.84952	+	2.22252i	−0.183519	+	0.105955i
$441$	−1.47889			−0.0704235
$442$		0			0
$443$	−2.27950			−0.108302			−0.0541512	−	0.998533i	$-0.517245\pi$
$443$	−2.27950			−0.108302			−0.0541512	+	0.998533i	$0.517245\pi$
$444$	−11.6756	+	6.74094i	−0.554102	+	0.319911i
$445$	−4.01089	−	6.94706i	−0.190134	−	0.329322i
$446$	−2.13706	+	3.70150i	−0.101193	+	0.175271i
$447$			22.8310i			1.07987i
$448$	−3.12105	−	1.80194i	−0.147456	−	0.0851336i
$449$	−17.7143	−	10.2274i	−0.835990	−	0.482659i	0.0199090	−	0.999802i	$-0.493662\pi$
$449$	−17.7143	−	10.2274i	−0.835990	−	0.482659i	−0.855899	+	0.517143i	$0.826996\pi$
$450$		−	0.246980i		−	0.0116427i
$451$	−4.53223	+	7.85005i	−0.213414	+	0.369644i
$452$	3.50484	+	6.07057i	0.164854	+	0.285536i
$453$	7.59339	−	4.38404i	0.356768	−	0.205980i
$454$	−9.95407			−0.467167
$455$		0			0
$456$	−0.643104			−0.0301161
$457$	−15.4526	+	8.92154i	−0.722841	+	0.417332i	−0.815797	−	0.578338i	$-0.803702\pi$
$457$	−15.4526	+	8.92154i	−0.722841	+	0.417332i	0.0929568	+	0.995670i	$0.470368\pi$
$458$	−11.5157	−	19.9458i	−0.538095	−	0.932007i
$459$	−7.83513	+	13.5708i	−0.365712	+	0.633432i
$460$			6.49396i			0.302782i
$461$	3.05310	+	1.76271i	0.142197	+	0.0820975i	0.569411	−	0.822053i	$-0.307171\pi$
$461$	3.05310	+	1.76271i	0.142197	+	0.0820975i	−0.427214	+	0.904151i	$0.640505\pi$
$462$	24.9986	+	14.4330i	1.16304	+	0.671482i
$463$			3.72587i			0.173156i	0.996245	+	0.0865780i	$0.0275932\pi$
$463$			3.72587i			0.173156i	−0.996245	+	0.0865780i	$0.972407\pi$
$464$	1.44504	−	2.50289i	0.0670844	−	0.116194i
$465$	−3.44504	−	5.96699i	−0.159760	−	0.276712i
$466$	−16.0821	+	9.28501i	−0.744989	+	0.430120i
$467$	12.8576			0.594977			0.297488	−	0.954725i	$-0.403851\pi$
$467$	12.8576			0.594977			0.297488	+	0.954725i	$0.403851\pi$
$468$		0			0
$469$	−50.4456			−2.32936
$470$	10.1340	−	5.85086i	0.467446	−	0.269880i
$471$	−8.49396	−	14.7120i	−0.391381	−	0.677892i
$472$	5.99880	−	10.3902i	0.276117	−	0.478249i
$473$		−	44.5174i		−	2.04691i
$474$	−9.17276	−	5.29590i	−0.421319	−	0.243249i
$475$	0.309081	+	0.178448i	0.0141816	+	0.00818775i
$476$			11.3840i			0.521787i
$477$	1.52781	−	2.64625i	0.0699537	−	0.121163i
$478$	9.47650	+	16.4138i	0.433445	+	0.750749i
$479$	−29.4407	+	16.9976i	−1.34518	+	0.776640i	−0.987562	−	0.157227i	$-0.949744\pi$
$479$	−29.4407	+	16.9976i	−1.34518	+	0.776640i	−0.357618	+	0.933868i	$0.616411\pi$
$480$	−1.80194			−0.0822468
$481$		0			0
$482$	−22.7439			−1.03596
$483$	36.5216	−	21.0858i	1.66179	−	0.959435i
$484$	−4.37920	−	7.58499i	−0.199054	−	0.344772i
$485$	1.97554	−	3.42174i	0.0897047	−	0.155373i
$486$			2.56033i			0.116139i
$487$	22.0680	+	12.7409i	0.999994	+	0.577347i	0.908247	−	0.418435i	$-0.137421\pi$
$487$	22.0680	+	12.7409i	0.999994	+	0.577347i	0.0917478	+	0.995782i	$0.470755\pi$
$488$	−10.7144	−	6.18598i	−0.485020	−	0.280026i
$489$		−	9.86831i		−	0.446261i
$490$	2.99396	−	5.18569i	0.135253	−	0.234266i
$491$	12.8889	+	22.3242i	0.581667	+	1.00748i	0.995282	+	0.0970253i	$0.0309328\pi$
$491$	12.8889	+	22.3242i	0.581667	+	1.00748i	−0.413615	+	0.910452i	$0.635734\pi$
$492$	−3.18226	+	1.83728i	−0.143468	+	0.0828310i
$493$	−9.12929			−0.411163
$494$		0			0
$495$	1.09783			0.0493440
$496$	−3.31143	+	1.91185i	−0.148688	+	0.0858448i
$497$	23.0858	+	39.9857i	1.03554	+	1.79360i
$498$	4.21164	−	7.29477i	0.188728	−	0.326886i
$499$			21.6286i			0.968230i	0.875004	+	0.484115i	$0.160858\pi$
$499$			21.6286i			0.968230i	−0.875004	+	0.484115i	$0.839142\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	−4.19723	−	2.42327i	−0.187518	−	0.108264i
$502$		−	14.5670i		−	0.650159i
$503$	−13.3666	+	23.1516i	−0.595987	+	1.03228i	0.397420	+	0.917637i	$0.369906\pi$
$503$	−13.3666	+	23.1516i	−0.595987	+	1.03228i	−0.993407	+	0.114642i	$0.963428\pi$
$504$	0.445042	+	0.770835i	0.0198237	+	0.0343357i
$505$	13.0269	−	7.52111i	0.579691	−	0.334685i
$506$	−28.8659			−1.28325
$507$		0			0
$508$	−11.6582			−0.517248
$509$	−30.5546	+	17.6407i	−1.35431	+	0.781911i	−0.988850	−	0.148916i	$-0.952421\pi$
$509$	−30.5546	+	17.6407i	−1.35431	+	0.781911i	−0.365459	+	0.930827i	$0.619088\pi$
$510$	2.84601	+	4.92944i	0.126023	+	0.218279i
$511$	−12.5526	+	21.7417i	−0.555293	+	0.961795i
$512$			1.00000i			0.0441942i
$513$	−1.53328	−	0.885239i	−0.0676959	−	0.0390843i
$514$	1.73578	+	1.00216i	0.0765622	+	0.0442032i
$515$			7.82371i			0.344754i
$516$	9.02326	−	15.6287i	0.397227	−	0.688017i
$517$	26.0073	+	45.0460i	1.14380	+	1.98112i
$518$	−23.3513	+	13.4819i	−1.02600	+	0.592360i
$519$	19.6582			0.862898
$520$		0			0
$521$	12.5700			0.550703			0.275351	−	0.961344i	$-0.411206\pi$
$521$	12.5700			0.550703			0.275351	+	0.961344i	$0.411206\pi$
$522$	−0.618162	+	0.356896i	−0.0270562	+	0.0156209i
$523$	−2.69471	−	4.66737i	−0.117831	−	0.204090i	0.801077	−	0.598562i	$-0.204261\pi$
$523$	−2.69471	−	4.66737i	−0.117831	−	0.204090i	−0.918908	+	0.394472i	$0.870928\pi$
$524$	−0.672407	+	1.16464i	−0.0293742	+	0.0508777i
$525$		−	6.49396i		−	0.283420i
$526$	−3.82394	−	2.20775i	−0.166732	−	0.0962625i
$527$	10.4603	+	6.03923i	0.455656	+	0.263073i
$528$		−	8.00969i		−	0.348577i
$529$	−9.58575	+	16.6030i	−0.416772	+	0.721870i
$530$	6.18598	+	10.7144i	0.268702	+	0.465405i
$531$	−2.56618	+	1.48158i	−0.111363	+	0.0642952i
$532$	−1.28621			−0.0557642
$533$		0			0
$534$	14.4547			0.625517
$535$	−8.05514	+	4.65064i	−0.348254	+	0.201065i
$536$	6.99880	+	12.1223i	0.302302	+	0.523603i
$537$	−11.6969	+	20.2596i	−0.504757	+	0.874265i
$538$		−	18.1521i		−	0.782594i
$539$	23.0506	+	13.3083i	0.992860	+	0.573228i
$540$	−4.29615	−	2.48039i	−0.184877	−	0.106739i
$541$			22.7332i			0.977375i	0.872459	+	0.488688i	$0.162524\pi$
$541$			22.7332i			0.977375i	−0.872459	+	0.488688i	$0.837476\pi$
$542$	−9.73556	+	16.8625i	−0.418178	+	0.724306i
$543$	−20.4819	−	35.4757i	−0.878961	−	1.52241i
$544$	2.73563	−	1.57942i	0.117289	−	0.0677169i
$545$	−0.811626			−0.0347663
$546$		0			0
$547$	31.9734			1.36709			0.683543	−	0.729910i	$-0.260438\pi$
$547$	31.9734			1.36709			0.683543	+	0.729910i	$0.260438\pi$
$548$	−6.75668	+	3.90097i	−0.288631	+	0.166641i
$549$	1.52781	+	2.64625i	0.0652054	+	0.112939i
$550$	−2.22252	+	3.84952i	−0.0947686	+	0.164144i
$551$		−	1.03146i		−	0.0439416i
$552$	−10.1340	−	5.85086i	−0.431331	−	0.249029i
$553$	−18.3455	−	10.5918i	−0.780131	−	0.450409i
$554$			18.3961i			0.781576i
$555$	−6.74094	+	11.6756i	−0.286137	+	0.495604i
$556$	6.93631	+	12.0140i	0.294165	+	0.509509i
$557$	23.5701	−	13.6082i	0.998696	−	0.576597i	0.0908338	−	0.995866i	$-0.471047\pi$
$557$	23.5701	−	13.6082i	0.998696	−	0.576597i	0.907862	+	0.419269i	$0.137713\pi$
$558$	0.944378			0.0399787
$559$		0			0
$560$	−3.60388			−0.152292
$561$	−21.9115	+	12.6506i	−0.925106	+	0.534110i
$562$	−7.97315	−	13.8099i	−0.336327	−	0.582535i
$563$	−5.87800	+	10.1810i	−0.247728	+	0.429078i	−0.962895	−	0.269876i	$-0.913017\pi$
$563$	−5.87800	+	10.1810i	−0.247728	+	0.429078i	0.715167	+	0.698954i	$0.246351\pi$
$564$			21.0858i			0.887870i
$565$	6.07057	+	3.50484i	0.255391	+	0.147450i
$566$	−24.2408	−	13.9955i	−1.01892	−	0.588273i
$567$			34.8853i			1.46504i
$568$	6.40581	−	11.0952i	0.268782	−	0.465544i
$569$	−9.63653	−	16.6910i	−0.403984	−	0.699721i	0.590218	−	0.807244i	$-0.299042\pi$
$569$	−9.63653	−	16.6910i	−0.403984	−	0.699721i	−0.994203	+	0.107522i	$0.965708\pi$
$570$	−0.556945	+	0.321552i	−0.0233278	+	0.0134683i
$571$	−32.6329			−1.36565			−0.682823	−	0.730584i	$-0.739248\pi$
$571$	−32.6329			−1.36565			−0.682823	+	0.730584i	$0.739248\pi$
$572$		0			0
$573$	−32.8310			−1.37153
$574$	−6.36453	+	3.67456i	−0.265650	+	0.153373i
$575$	3.24698	+	5.62393i	0.135408	+	0.234534i
$576$	0.123490	−	0.213891i	0.00514541	−	0.00891211i
$577$			31.4534i			1.30942i	0.755879	+	0.654711i	$0.227210\pi$
$577$			31.4534i			1.30942i	−0.755879	+	0.654711i	$0.772790\pi$
$578$	6.08103	+	3.51089i	0.252938	+	0.146034i
$579$	29.2571	+	16.8916i	1.21588	+	0.701990i
$580$		−	2.89008i		−	0.120004i
$581$	8.42327	−	14.5895i	0.349456	−	0.605276i
$582$	3.55980	+	6.16576i	0.147559	+	0.255579i
$583$	−47.6261	+	27.4969i	−1.97247	+	1.13881i
$584$	6.96615			0.288261
$585$		0			0
$586$	13.5603			0.560172
$587$	17.9801	−	10.3808i	0.742119	−	0.428462i	−0.0807205	−	0.996737i	$-0.525722\pi$
$587$	17.9801	−	10.3808i	0.742119	−	0.428462i	0.822839	+	0.568274i	$0.192389\pi$
$588$	5.39493	+	9.34429i	0.222483	+	0.385352i
$589$	−0.682333	+	1.18184i	−0.0281150	+	0.0486967i
$590$		−	11.9976i		−	0.493934i
$591$	−34.9799	−	20.1957i	−1.43888	−	0.830739i
$592$	6.47950	+	3.74094i	0.266306	+	0.153752i
$593$		−	31.9028i		−	1.31009i	−0.755590	−	0.655045i	$-0.772650\pi$
$593$		−	31.9028i		−	1.31009i	0.755590	−	0.655045i	$-0.227350\pi$
$594$	11.0254	−	19.0966i	0.452378	−	0.783542i
$595$	5.69202	+	9.85887i	0.233350	+	0.404174i
$596$	10.9728	−	6.33513i	0.449462	−	0.259497i
$597$	30.7875			1.26005
$598$		0			0
$599$	−8.07846			−0.330077			−0.165038	−	0.986287i	$-0.552775\pi$
$599$	−8.07846			−0.330077			−0.165038	+	0.986287i	$0.552775\pi$
$600$	−1.56052	+	0.900969i	−0.0637081	+	0.0367819i
$601$	9.74847	+	16.8848i	0.397648	+	0.688747i	0.993435	−	0.114395i	$-0.0364930\pi$
$601$	9.74847	+	16.8848i	0.397648	+	0.688747i	−0.595787	+	0.803143i	$0.703160\pi$
$602$	18.0465	−	31.2575i	0.735521	−	1.27396i
$603$		−	3.45712i		−	0.140785i
$604$	−4.21401	−	2.43296i	−0.171466	−	0.0989957i
$605$	−7.58499	−	4.37920i	−0.308374	−	0.178040i
$606$			27.1051i			1.10107i
$607$	17.9922	−	31.1635i	0.730282	−	1.26489i	−0.226480	−	0.974016i	$-0.572722\pi$
$607$	17.9922	−	31.1635i	0.730282	−	1.26489i	0.956763	−	0.290870i	$-0.0939447\pi$
$608$	0.178448	+	0.309081i	0.00723702	+	0.0125349i
$609$	−16.2536	+	9.38404i	−0.658631	+	0.380261i
$610$	−12.3720			−0.500926
$611$		0			0
$612$	−0.780167			−0.0315364
$613$	−15.7411	+	9.08815i	−0.635778	+	0.367067i	−0.782986	−	0.622039i	$-0.786305\pi$
$613$	−15.7411	+	9.08815i	−0.635778	+	0.367067i	0.147208	+	0.989106i	$0.452971\pi$
$614$	−7.57942	−	13.1279i	−0.305880	−	0.529800i
$615$	−1.83728	+	3.18226i	−0.0740863	+	0.128321i
$616$		−	16.0194i		−	0.645439i
$617$	37.2852	+	21.5266i	1.50105	+	0.866629i	0.999999	+	0.00120820i	$0.000384582\pi$
$617$	37.2852	+	21.5266i	1.50105	+	0.866629i	0.501046	+	0.865421i	$0.332949\pi$
$618$	−12.2091	−	7.04892i	−0.491121	−	0.283549i
$619$			39.5120i			1.58812i	0.607838	+	0.794061i	$0.292037\pi$
$619$			39.5120i			1.58812i	−0.607838	+	0.794061i	$0.707963\pi$
$620$	−1.91185	+	3.31143i	−0.0767819	+	0.132990i
$621$	−16.1075	−	27.8990i	−0.646373	−	1.11955i
$622$	−4.66272	+	2.69202i	−0.186958	+	0.107940i
$623$	28.9095			1.15823
$624$		0			0
$625$	1.00000			0.0400000
$626$	−14.3643	+	8.29321i	−0.574111	+	0.331463i
$627$	−1.42931	−	2.47564i	−0.0570812	−	0.0988676i
$628$	−4.71379	+	8.16453i	−0.188101	+	0.325800i
$629$		−	23.6340i		−	0.942350i
$630$	0.770835	+	0.445042i	0.0307108	+	0.0177309i
$631$	−19.9719	−	11.5308i	−0.795070	−	0.459034i	0.0466746	−	0.998910i	$-0.485138\pi$
$631$	−19.9719	−	11.5308i	−0.795070	−	0.459034i	−0.841744	+	0.539876i	$0.818471\pi$
$632$			5.87800i			0.233814i
$633$	−4.98307	+	8.63094i	−0.198059	+	0.343049i
$634$	−6.05429	−	10.4863i	−0.240447	−	0.416466i
$635$	−10.0963	+	5.82908i	−0.400658	+	0.231320i
$636$	−22.2935			−0.883995
$637$		0			0
$638$	12.8465			0.508600
$639$	−2.74029	+	1.58211i	−0.108404	+	0.0625871i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	17.3523	−	30.0551i	0.685377	−	1.18711i	−0.287942	−	0.957648i	$-0.592971\pi$
$641$	17.3523	−	30.0551i	0.685377	−	1.18711i	0.973318	−	0.229459i	$-0.0736957\pi$
$642$		−	16.7603i		−	0.661477i
$643$	29.6274	+	17.1054i	1.16839	+	0.674570i	0.953300	−	0.302025i	$-0.0976625\pi$
$643$	29.6274	+	17.1054i	1.16839	+	0.674570i	0.215089	+	0.976594i	$0.430996\pi$
$644$	−20.2680	−	11.7017i	−0.798669	−	0.461112i
$645$		−	18.0465i		−	0.710581i
$646$	0.563687	−	0.976335i	0.0221780	−	0.0384134i
$647$	2.22952	+	3.86164i	0.0876515	+	0.151817i	0.906518	−	0.422167i	$-0.138730\pi$
$647$	2.22952	+	3.86164i	0.0876515	+	0.151817i	−0.818866	+	0.573984i	$0.805397\pi$
$648$	8.38307	−	4.83997i	0.329318	−	0.190132i
$649$	53.3299			2.09338
$650$		0			0
$651$	24.8310			0.973204
$652$	−4.74279	+	2.73825i	−0.185742	+	0.107238i
$653$	−4.72348	−	8.18131i	−0.184844	−	0.320159i	0.758680	−	0.651464i	$-0.225845\pi$
$653$	−4.72348	−	8.18131i	−0.184844	−	0.320159i	−0.943524	+	0.331304i	$0.892511\pi$
$654$	0.731250	−	1.26656i	0.0285941	−	0.0495265i
$655$			1.34481i			0.0525462i
$656$	1.76602	+	1.01961i	0.0689516	+	0.0398093i
$657$	−1.48999	−	0.860248i	−0.0581302	−	0.0335615i
$658$			42.1715i			1.64402i
$659$	8.88889	−	15.3960i	0.346262	−	0.599743i	−0.639320	−	0.768941i	$-0.720784\pi$
$659$	8.88889	−	15.3960i	0.346262	−	0.599743i	0.985582	+	0.169197i	$0.0541175\pi$
$660$	−4.00484	−	6.93659i	−0.155888	−	0.270007i
$661$	27.0905	−	15.6407i	1.05370	−	0.608353i	0.130016	−	0.991512i	$-0.458497\pi$
$661$	27.0905	−	15.6407i	1.05370	−	0.608353i	0.923683	+	0.383159i	$0.125164\pi$
$662$	14.6112			0.567879
$663$		0			0
$664$	−4.67456			−0.181408
$665$	−1.11389	+	0.643104i	−0.0431948	+	0.0249385i
$666$	−0.923936	−	1.60030i	−0.0358018	−	0.0620105i
$667$	9.38404	−	16.2536i	0.363352	−	0.629343i
$668$			2.68963i			0.104065i
$669$	−6.66988	−	3.85086i	−0.257872	−	0.148883i
$670$	12.1223	+	6.99880i	0.468325	+	0.270387i
$671$		−	54.9939i		−	2.12302i
$672$	3.24698	−	5.62393i	0.125255	−	0.216948i
$673$	−7.23072	−	12.5240i	−0.278724	−	0.482764i	0.692344	−	0.721567i	$-0.256578\pi$
$673$	−7.23072	−	12.5240i	−0.278724	−	0.482764i	−0.971068	+	0.238804i	$0.923245\pi$
$674$	3.86205	−	2.22976i	0.148761	−	0.0858871i
$675$	−4.96077			−0.190940
$676$		0			0
$677$	19.8974			0.764718			0.382359	−	0.924014i	$-0.375112\pi$
$677$	19.8974			0.764718			0.382359	+	0.924014i	$0.375112\pi$
$678$	−10.9388	+	6.31551i	−0.420102	+	0.242546i
$679$	7.11960	+	12.3315i	0.273225	+	0.473240i
$680$	1.57942	−	2.73563i	0.0605679	−	0.104907i
$681$		−	17.9366i		−	0.687332i
$682$	−14.7194	−	8.49827i	−0.563636	−	0.325416i
$683$	34.9041	+	20.1519i	1.33557	+	0.771091i	0.986147	−	0.165875i	$-0.0530448\pi$
$683$	34.9041	+	20.1519i	1.33557	+	0.771091i	0.349421	+	0.936966i	$0.386378\pi$
$684$		−	0.0881460i		−	0.00337035i
$685$	−3.90097	+	6.75668i	−0.149048	+	0.258159i
$686$	−1.82371	−	3.15875i	−0.0696295	−	0.120602i
$687$	35.9411	−	20.7506i	1.37124	−	0.791686i
$688$	−10.0151			−0.381821
$689$		0			0
$690$	−11.7017			−0.445476
$691$	−0.647990	+	0.374117i	−0.0246507	+	0.0142321i	−0.512275	−	0.858822i	$-0.671197\pi$
$691$	−0.647990	+	0.374117i	−0.0246507	+	0.0142321i	0.487624	+	0.873054i	$0.337864\pi$
$692$	−5.45473	−	9.44787i	−0.207358	−	0.359154i
$693$	−1.97823	+	3.42639i	−0.0751467	+	0.130158i
$694$			28.5870i			1.08515i
$695$	12.0140	+	6.93631i	0.455719	+	0.263109i
$696$	4.51004	+	2.60388i	0.170953	+	0.0986996i
$697$		−	6.44158i		−	0.243992i
$698$	−2.43967	+	4.22562i	−0.0923427	+	0.159942i
$699$	−16.7310	−	28.9790i	−0.632825	−	1.09609i
$700$	−3.12105	+	1.80194i	−0.117965	+	0.0681068i
$701$	27.5555			1.04076			0.520379	−	0.853935i	$-0.325791\pi$
$701$	27.5555			1.04076			0.520379	+	0.853935i	$0.325791\pi$
$702$		0			0
$703$	2.67025			0.100710
$704$	−3.84952	+	2.22252i	−0.145084	+	0.0837644i
$705$	10.5429	+	18.2608i	0.397068	+	0.687741i
$706$	2.02984	−	3.51578i	0.0763939	−	0.132318i
$707$			54.2103i			2.03879i
$708$	18.7226	+	10.8095i	0.703637	+	0.406245i
$709$	−6.14059	−	3.54527i	−0.230615	−	0.133145i	0.380241	−	0.924887i	$-0.375841\pi$
$709$	−6.14059	−	3.54527i	−0.230615	−	0.133145i	−0.610856	+	0.791742i	$0.709174\pi$
$710$		−	12.8116i		−	0.480812i
$711$	0.725873	−	1.25725i	0.0272224	−	0.0471505i
$712$	−4.01089	−	6.94706i	−0.150314	−	0.260352i
$713$	−21.5043	+	12.4155i	−0.805342	+	0.464964i
$714$	−20.5133			−0.767692
$715$		0			0
$716$	12.9825			0.485180
$717$	−29.5766	+	17.0761i	−1.10456	+	0.637717i
$718$	−2.56033	−	4.43463i	−0.0955509	−	0.165499i
$719$	−5.35690	+	9.27842i	−0.199779	+	0.346027i	−0.948457	−	0.316907i	$-0.897356\pi$
$719$	−5.35690	+	9.27842i	−0.199779	+	0.346027i	0.748678	+	0.662934i	$0.230689\pi$
$720$		−	0.246980i		−	0.00920439i
$721$	−24.4182	−	14.0978i	−0.909380	−	0.525031i
$722$	−16.3442	−	9.43631i	−0.608267	−	0.351183i
$723$		−	40.9831i		−	1.52418i
$724$	−11.3666	+	19.6875i	−0.422436	+	0.731680i
$725$	−1.44504	−	2.50289i	−0.0536675	−	0.0929548i
$726$	13.6677	−	7.89104i	0.507255	−	0.292864i
$727$	−1.37329			−0.0509325			−0.0254662	−	0.999676i	$-0.508107\pi$
$727$	−1.37329			−0.0509325			−0.0254662	+	0.999676i	$0.508107\pi$
$728$		0			0
$729$	24.4263			0.904676
$730$	6.03286	−	3.48307i	0.223286	−	0.128914i
$731$	15.8180	+	27.3975i	0.585048	+	1.01333i
$732$	11.1468	−	19.3067i	0.411996	−	0.713598i
$733$			12.6160i			0.465981i	0.972479	+	0.232991i	$0.0748511\pi$
$733$			12.6160i			0.465981i	−0.972479	+	0.232991i	$0.925149\pi$
$734$	8.04209	+	4.64310i	0.296839	+	0.171380i
$735$	9.34429	+	5.39493i	0.344669	+	0.198995i
$736$			6.49396i			0.239371i
$737$	−31.1100	+	53.8841i	−1.14595	+	1.98484i
$738$	−0.251824	−	0.436172i	−0.00926977	−	0.0160557i
$739$	32.1622	−	18.5688i	1.18310	−	0.683065i	0.226373	−	0.974041i	$-0.427313\pi$
$739$	32.1622	−	18.5688i	1.18310	−	0.683065i	0.956731	+	0.290975i	$0.0939797\pi$
$740$	7.48188			0.275039
$741$		0			0
$742$	−44.5870			−1.63684
$743$	−13.0363	+	7.52648i	−0.478254	+	0.276120i	−0.719688	−	0.694297i	$-0.755715\pi$
$743$	−13.0363	+	7.52648i	−0.478254	+	0.276120i	0.241435	+	0.970417i	$0.422382\pi$
$744$	−3.44504	−	5.96699i	−0.126301	−	0.218760i
$745$	6.33513	−	10.9728i	0.232101	−	0.402011i
$746$		−	7.30559i		−	0.267476i
$747$	0.999845	+	0.577261i	0.0365824	+	0.0211209i
$748$	12.1600	+	7.02057i	0.444613	+	0.256698i
$749$		−	33.5206i		−	1.22482i
$750$	−0.900969	+	1.56052i	−0.0328987	+	0.0569823i
$751$	−11.1957	−	19.3915i	−0.408536	−	0.707605i	0.586190	−	0.810174i	$-0.300627\pi$
$751$	−11.1957	−	19.3915i	−0.408536	−	0.707605i	−0.994726	+	0.102569i	$0.967294\pi$
$752$	10.1340	−	5.85086i	0.369548	−	0.213359i
$753$	26.2489			0.956563
$754$		0			0
$755$	−4.86592			−0.177089
$756$	15.4828	−	8.93900i	0.563104	−	0.325108i
$757$	7.93661	+	13.7466i	0.288461	+	0.499629i	0.973443	−	0.228931i	$-0.0735231\pi$
$757$	7.93661	+	13.7466i	0.288461	+	0.499629i	−0.684982	+	0.728560i	$0.740190\pi$
$758$	15.2850	−	26.4744i	0.555177	−	0.961594i
$759$		−	52.0146i		−	1.88801i
$760$	0.309081	+	0.178448i	0.0112115	+	0.00647299i
$761$	33.4011	+	19.2841i	1.21079	+	0.699048i	0.962931	−	0.269748i	$-0.0869405\pi$
$761$	33.4011	+	19.2841i	1.21079	+	0.699048i	0.247857	+	0.968797i	$0.420274\pi$
$762$		−	21.0073i		−	0.761014i
$763$	1.46250	−	2.53312i	0.0529461	−	0.0917053i
$764$	9.10992	+	15.7788i	0.329585	+	0.570858i
$765$	−0.675645	+	0.390084i	−0.0244280	+	0.0141035i
$766$	7.93230			0.286606
$767$		0			0
$768$	−1.80194			−0.0650218
$769$	42.4630	−	24.5160i	1.53125	−	0.884070i	0.531951	−	0.846775i	$-0.321459\pi$
$769$	42.4630	−	24.5160i	1.53125	−	0.884070i	0.999304	−	0.0372951i	$-0.0118742\pi$
$770$	−8.00969	−	13.8732i	−0.288649	−	0.499955i
$771$	−1.80582	+	3.12778i	−0.0650351	+	0.112644i
$772$		−	18.7482i		−	0.674764i
$773$	−10.2960	−	5.94438i	−0.370320	−	0.213804i	0.303278	−	0.952902i	$-0.401919\pi$
$773$	−10.2960	−	5.94438i	−0.370320	−	0.213804i	−0.673598	+	0.739098i	$0.735252\pi$
$774$	2.14213	+	1.23676i	0.0769972	+	0.0444544i
$775$			3.82371i			0.137352i
$776$	1.97554	−	3.42174i	0.0709178	−	0.122833i
$777$	−24.2935	−	42.0776i	−0.871525	−	1.50952i
$778$	−1.17769	+	0.679940i	−0.0422222	+	0.0243770i
$779$	0.727792			0.0260759
$780$		0			0
$781$	56.9482			2.03777
$782$	17.7651	−	10.2567i	0.635278	−	0.366778i
$783$	7.16852	+	12.4162i	0.256182	+	0.443720i
$784$	2.99396	−	5.18569i	0.106927	−	0.185203i
$785$			9.42758i			0.336485i
$786$	−2.09861	−	1.21164i	−0.0748551	−	0.0432176i
$787$	2.82036	+	1.62833i	0.100535	+	0.0580438i	0.549424	−	0.835543i	$-0.314847\pi$
$787$	2.82036	+	1.62833i	0.100535	+	0.0580438i	−0.448890	+	0.893587i	$0.648180\pi$
$788$			22.4155i			0.798519i
$789$	3.97823	−	6.89050i	0.141629	−	0.245308i
$790$	2.93900	+	5.09050i	0.104565	+	0.181112i
$791$	−21.8776	+	12.6310i	−0.777877	+	0.449107i
$792$	1.09783			0.0390099
$793$		0			0
$794$	24.6112			0.873418
$795$	−19.3067	+	11.1468i	−0.684740	+	0.395335i
$796$	−8.54288	−	14.7967i	−0.302794	−	0.524455i
$797$	18.4765	−	32.0022i	0.654471	−	1.13358i	−0.327555	−	0.944832i	$-0.606225\pi$
$797$	18.4765	−	32.0022i	0.654471	−	1.13358i	0.982026	−	0.188745i	$-0.0604420\pi$
$798$		−	2.31767i		−	0.0820445i
$799$	−32.0116	−	18.4819i	−1.13249	−	0.653842i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$			1.98121i			0.0700027i
$802$	2.44773	−	4.23959i	0.0864324	−	0.149705i
$803$	15.4824	+	26.8163i	0.546362	+	0.946327i
$804$	−21.8436	+	12.6114i	−0.770364	+	0.444770i
$805$	−23.4034			−0.824862
$806$		0			0
$807$	32.7090			1.15141
$808$	13.0269	−	7.52111i	0.458286	−	0.264592i
$809$	2.08599	+	3.61304i	0.0733395	+	0.127028i	0.900363	−	0.435140i	$-0.143301\pi$
$809$	2.08599	+	3.61304i	0.0733395	+	0.127028i	−0.827023	+	0.562167i	$0.809968\pi$
$810$	4.83997	−	8.38307i	0.170059	−	0.294551i
$811$		−	17.0696i		−	0.599396i	−0.954034	−	0.299698i	$-0.903114\pi$
$811$		−	17.0696i		−	0.599396i	0.954034	−	0.299698i	$-0.0968858\pi$
$812$	9.02009	+	5.20775i	0.316543	+	0.182756i
$813$	−30.3852	−	17.5429i	−1.06565	−	0.615256i
$814$			33.2573i			1.16567i
$815$	−2.73825	+	4.74279i	−0.0959167	+	0.166133i
$816$	2.84601	+	4.92944i	0.0996303	+	0.172565i
$817$	−3.09547	+	1.78717i	−0.108297	+	0.0625251i
$818$	−4.37435			−0.152946
$819$		0			0
$820$	2.03923			0.0712130
$821$	−32.7615	+	18.9148i	−1.14338	+	0.660132i	−0.947266	−	0.320448i	$-0.896167\pi$
$821$	−32.7615	+	18.9148i	−1.14338	+	0.660132i	−0.196117	+	0.980581i	$0.562833\pi$
$822$	−7.02930	−	12.1751i	−0.245175	−	0.424656i
$823$	20.5362	−	35.5697i	0.715846	−	1.23988i	−0.246786	−	0.969070i	$-0.579375\pi$
$823$	20.5362	−	35.5697i	0.715846	−	1.23988i	0.962632	−	0.270812i	$-0.0872921\pi$
$824$			7.82371i			0.272552i
$825$	−6.93659	−	4.00484i	−0.241501	−	0.139431i
$826$	37.4451	+	21.6189i	1.30288	+	0.752219i
$827$			26.9855i			0.938379i	0.883098	+	0.469189i	$0.155454\pi$
$827$			26.9855i			0.938379i	−0.883098	+	0.469189i	$0.844546\pi$
$828$	0.801938	−	1.38900i	0.0278693	−	0.0482710i
$829$	−6.08277	−	10.5357i	−0.211263	−	0.365919i	0.740847	−	0.671674i	$-0.234424\pi$
$829$	−6.08277	−	10.5357i	−0.211263	−	0.365919i	−0.952110	+	0.305755i	$0.901091\pi$
$830$	−4.04829	+	2.33728i	−0.140518	+	0.0811282i
$831$	−33.1487			−1.14991
$832$		0			0
$833$	−18.9148			−0.655360
$834$	−21.6486	+	12.4988i	−0.749628	+	0.432798i
$835$	1.34481	+	2.32929i	0.0465392	+	0.0806083i
$836$	−0.793209	+	1.37388i	−0.0274337	+	0.0475165i
$837$		−	18.9685i		−	0.655649i
$838$	−14.5007	−	8.37196i	−0.500917	−	0.289205i
$839$	−1.61708	−	0.933624i	−0.0558280	−	0.0322323i	0.471826	−	0.881692i	$-0.343595\pi$
$839$	−1.61708	−	0.933624i	−0.0558280	−	0.0322323i	−0.527654	+	0.849459i	$0.676928\pi$
$840$		−	6.49396i		−	0.224063i
$841$	10.3237	−	17.8812i	0.355990	−	0.616593i
$842$	−0.241603	−	0.418468i	−0.00832618	−	0.0144214i
$843$	24.8846	−	14.3671i	0.857070	−	0.494830i
$844$	5.53079			0.190378
$845$		0			0
$846$	−2.89008			−0.0993631
$847$	27.3354	−	15.7821i	0.939255	−	0.542279i
$848$	6.18598	+	10.7144i	0.212427	+	0.367935i
$849$	25.2189	−	43.6805i	0.865511	−	1.49911i
$850$		−	3.15883i		−	0.108347i
$851$	42.0776	+	24.2935i	1.44240	+	0.832771i
$852$	19.9928	+	11.5429i	0.684944	+	0.395452i
$853$			27.7453i			0.949979i	0.879991	+	0.474990i	$0.157548\pi$
$853$			27.7453i			0.949979i	−0.879991	+	0.474990i	$0.842452\pi$
$854$	22.2935	−	38.6135i	0.762868	−	1.32133i
$855$	−0.0440730	−	0.0763367i	−0.00150726	−	0.00261066i
$856$	−8.05514	+	4.65064i	−0.275319	+	0.158955i
$857$	24.2553			0.828547			0.414273	−	0.910153i	$-0.364036\pi$
$857$	24.2553			0.828547			0.414273	+	0.910153i	$0.364036\pi$
$858$		0			0
$859$	26.1089			0.890823			0.445411	−	0.895326i	$-0.353057\pi$
$859$	26.1089			0.890823			0.445411	+	0.895326i	$0.353057\pi$
$860$	−8.67330	+	5.00753i	−0.295757	+	0.170755i
$861$	−6.62133	−	11.4685i	−0.225654	−	0.390845i
$862$	5.98792	−	10.3714i	0.203949	−	0.353251i
$863$		−	39.5905i		−	1.34768i	−0.738880	−	0.673838i	$-0.764645\pi$
$863$		−	39.5905i		−	1.34768i	0.738880	−	0.673838i	$-0.235355\pi$
$864$	−4.29615	−	2.48039i	−0.146158	−	0.0843844i
$865$	−9.44787	−	5.45473i	−0.321237	−	0.185466i
$866$			4.15452i			0.141176i
$867$	−6.32640	+	10.9576i	−0.214856	+	0.372141i
$868$	−6.89008	−	11.9340i	−0.233865	−	0.405066i
$869$	−22.6275	+	13.0640i	−0.767585	+	0.443165i
$870$	5.20775			0.176559
$871$		0			0
$872$	−0.811626			−0.0274851
$873$	−0.845099	+	0.487918i	−0.0286023	+	0.0165135i
$874$	1.15883	+	2.00716i	0.0391981	+	0.0678932i
$875$	−1.80194	+	3.12105i	−0.0609166	+	0.105511i
$876$			12.5526i			0.424112i
$877$	−35.0814	−	20.2543i	−1.18462	−	0.683938i	−0.227538	−	0.973769i	$-0.573068\pi$
$877$	−35.0814	−	20.2543i	−1.18462	−	0.683938i	−0.957078	+	0.289831i	$0.906401\pi$
$878$	−10.8369	−	6.25667i	−0.365727	−	0.211152i
$879$			24.4349i			0.824168i
$880$	−2.22252	+	3.84952i	−0.0749212	+	0.129767i
$881$	−18.1876	−	31.5019i	−0.612756	−	1.06132i	−0.990774	−	0.135526i	$-0.956728\pi$
$881$	−18.1876	−	31.5019i	−0.612756	−	1.06132i	0.378018	−	0.925798i	$-0.376606\pi$
$882$	−1.28076	+	0.739447i	−0.0431254	+	0.0248985i
$883$	−6.51275			−0.219171			−0.109586	−	0.993977i	$-0.534952\pi$
$883$	−6.51275			−0.219171			−0.109586	+	0.993977i	$0.534952\pi$
$884$		0			0
$885$	21.6189			0.726713
$886$	−1.97411	+	1.13975i	−0.0663215	+	0.0382907i
$887$	−1.65817	−	2.87203i	−0.0556759	−	0.0964335i	0.836844	−	0.547441i	$-0.184398\pi$
$887$	−1.65817	−	2.87203i	−0.0556759	−	0.0964335i	−0.892520	+	0.451008i	$0.851065\pi$
$888$	−6.74094	+	11.6756i	−0.226211	+	0.391809i
$889$		−	42.0146i		−	1.40912i
$890$	−6.94706	−	4.01089i	−0.232866	−	0.134445i
$891$	37.2631	+	21.5139i	1.24836	+	0.720742i
$892$			4.27413i			0.143108i
$893$	2.08815	−	3.61677i	0.0698771	−	0.121031i
$894$	11.4155	+	19.7722i	0.381791	+	0.661282i
$895$	11.2432	−	6.49127i	0.375819	−	0.216979i
$896$	−3.60388			−0.120397
$897$		0			0
$898$	−20.4547			−0.682583
$899$	9.57030	−	5.52542i	0.319188	−	0.184283i
$900$	−0.123490	−	0.213891i	−0.00411633	−	0.00712969i
$901$	19.5405	−	33.8451i	0.650988	−	1.12754i
$902$			9.06446i			0.301813i
$903$	56.3241	+	32.5187i	1.87435	+	1.08216i
$904$	6.07057	+	3.50484i	0.201904	+	0.116569i
$905$			22.7332i			0.755676i
$906$	4.38404	−	7.59339i	0.145650	−	0.252273i
$907$	−24.1824	−	41.8851i	−0.802963	−	1.39077i	−0.917658	−	0.397372i	$-0.869922\pi$
$907$	−24.1824	−	41.8851i	−0.802963	−	1.39077i	0.114694	−	0.993401i	$-0.463411\pi$
$908$	−8.62047	+	4.97703i	−0.286080	+	0.165169i
$909$	−3.71512			−0.123223
$910$		0			0
$911$	−18.2634			−0.605093			−0.302546	−	0.953135i	$-0.597837\pi$
$911$	−18.2634			−0.605093			−0.302546	+	0.953135i	$0.597837\pi$
$912$	−0.556945	+	0.321552i	−0.0184423	+	0.0106477i
$913$	−10.3893	−	17.9948i	−0.343836	−	0.595542i
$914$	−8.92154	+	15.4526i	−0.295098	+	0.511125i
$915$		−	22.2935i		−	0.737001i
$916$	−19.9458	−	11.5157i	−0.659029	−	0.380490i
$917$	−4.19723	−	2.42327i	−0.138605	−	0.0800235i
$918$			15.6703i			0.517195i
$919$	−11.0804	+	19.1918i	−0.365508	+	0.633078i	−0.988858	−	0.148865i	$-0.952438\pi$
$919$	−11.0804	+	19.1918i	−0.365508	+	0.633078i	0.623350	+	0.781943i	$0.285771\pi$
$920$	3.24698	+	5.62393i	0.107050	+	0.185416i
$921$	23.6557	−	13.6576i	0.779483	−	0.450034i
$922$	3.52542			0.116103
$923$		0			0
$924$	28.8659			0.949619
$925$	6.47950	−	3.74094i	0.213045	−	0.123001i
$926$	1.86294	+	3.22670i	0.0612199	+	0.106036i
$927$	0.966148	−	1.67342i	0.0317325	−	0.0549622i
$928$		−	2.89008i		−	0.0948716i
$929$	6.86584	+	3.96399i	0.225261	+	0.130054i	0.608384	−	0.793643i	$-0.291818\pi$
$929$	6.86584	+	3.96399i	0.225261	+	0.130054i	−0.383123	+	0.923697i	$0.625151\pi$
$930$	−5.96699	−	3.44504i	−0.195665	−	0.112967i
$931$		−	2.13706i		−	0.0700394i
$932$	−9.28501	+	16.0821i	−0.304141	+	0.526787i
$933$	−4.85086	−	8.40193i	−0.158810	−	0.275067i
$934$	11.1350	−	6.42878i	0.364347	−	0.210356i
$935$	14.0411			0.459195
$936$		0			0
$937$	28.1758			0.920464			0.460232	−	0.887799i	$-0.347766\pi$
$937$	28.1758			0.920464			0.460232	+	0.887799i	$0.347766\pi$
$938$	−43.6872	+	25.2228i	−1.42644	+	0.823554i
$939$	−14.9438	−	25.8835i	−0.487674	−	0.844676i
$940$	5.85086	−	10.1340i	0.190834	−	0.330534i
$941$			31.4228i			1.02435i	0.858880	+	0.512177i	$0.171161\pi$
$941$			31.4228i			1.02435i	−0.858880	+	0.512177i	$0.828839\pi$
$942$	−14.7120	−	8.49396i	−0.479342	−	0.276748i
$943$	11.4685	+	6.62133i	0.373465	+	0.215620i
$944$		−	11.9976i		−	0.390489i
$945$	8.93900	−	15.4828i	0.290786	−	0.503656i
$946$	−22.2587	−	38.5532i	−0.723693	−	1.25347i
$947$	−6.89423	+	3.98039i	−0.224032	+	0.129345i	−0.607816	−	0.794078i	$-0.707954\pi$
$947$	−6.89423	+	3.98039i	−0.224032	+	0.129345i	0.383784	+	0.923423i	$0.374621\pi$
$948$	−10.5918			−0.344005
$949$		0			0
$950$	0.356896			0.0115792
$951$	18.8957	−	10.9095i	0.612736	−	0.353764i
$952$	5.69202	+	9.85887i	0.184479	+	0.319528i
$953$	−3.45257	+	5.98003i	−0.111840	+	0.193712i	−0.916512	−	0.400007i	$-0.869008\pi$
$953$	−3.45257	+	5.98003i	−0.111840	+	0.193712i	0.804672	+	0.593719i	$0.202341\pi$
$954$		−	3.05562i		−	0.0989294i
$955$	15.7788	+	9.10992i	0.510591	+	0.294790i
$956$	16.4138	+	9.47650i	0.530860	+	0.306492i
$957$			23.1487i			0.748290i
$958$	−16.9976	+	29.4407i	−0.549168	+	0.951186i
$959$	−14.0586	−	24.3502i	−0.453976	−	0.786310i
$960$	−1.56052	+	0.900969i	−0.0503657	+	0.0290786i
$961$	16.3793			0.528363
$962$		0			0
$963$	2.29722			0.0740270
$964$	−19.6968	+	11.3720i	−0.634392	+	0.366266i
$965$	−9.37412	−	16.2364i	−0.301764	−	0.522670i
$966$	21.0858	−	36.5216i	0.678423	−	1.17506i
$967$		−	31.3297i		−	1.00750i	−0.863850	−	0.503748i	$-0.831954\pi$
$967$		−	31.3297i		−	1.00750i	0.863850	−	0.503748i	$-0.168046\pi$
$968$	−7.58499	−	4.37920i	−0.243791	−	0.140753i
$969$	1.75930	+	1.01573i	0.0565167	+	0.0326299i
$970$		−	3.95108i		−	0.126862i
$971$	2.45257	−	4.24798i	0.0787069	−	0.136324i	−0.823985	−	0.566611i	$-0.808254\pi$
$971$	2.45257	−	4.24798i	0.0787069	−	0.136324i	0.902692	+	0.430287i	$0.141588\pi$
$972$	1.28017	+	2.21732i	0.0410614	+	0.0711204i
$973$	−43.2971	+	24.9976i	−1.38804	+	0.801386i
$974$	25.4819			0.816492
$975$		0			0
$976$	−12.3720			−0.396017
$977$	−11.7055	+	6.75816i	−0.374491	+	0.216213i	−0.675419	−	0.737434i	$-0.736037\pi$
$977$	−11.7055	+	6.75816i	−0.374491	+	0.216213i	0.300927	+	0.953647i	$0.402704\pi$
$978$	−4.93416	−	8.54621i	−0.157777	−	0.273278i
$979$	17.8286	−	30.8800i	0.569803	−	0.986928i
$980$		−	5.98792i		−	0.191277i
$981$	0.173599	+	0.100228i	0.00554260	+	0.00320002i
$982$	22.3242	+	12.8889i	0.712394	+	0.411301i
$983$			31.7453i			1.01252i	0.862382	+	0.506258i	$0.168972\pi$
$983$			31.7453i			1.01252i	−0.862382	+	0.506258i	$0.831028\pi$
$984$	−1.83728	+	3.18226i	−0.0585704	+	0.101447i
$985$	11.2078	+	19.4124i	0.357109	+	0.618530i
$986$	−7.90620	+	4.56465i	−0.251785	+	0.145368i
$987$	−75.9904			−2.41880
$988$		0			0
$989$	−65.0374			−2.06807
$990$	0.950753	−	0.548917i	0.0302169	−	0.0174457i
$991$	−6.80492	−	11.7865i	−0.216165	−	0.374410i	0.737467	−	0.675383i	$-0.236022\pi$
$991$	−6.80492	−	11.7865i	−0.216165	−	0.374410i	−0.953632	+	0.300974i	$0.902688\pi$
$992$	−1.91185	+	3.31143i	−0.0607014	+	0.105138i
$993$			26.3284i			0.835507i
$994$	39.9857	+	23.0858i	1.26827	+	0.732236i
$995$	−14.7967	−	8.54288i	−0.469087	−	0.270827i
$996$		−	8.42327i		−	0.266902i
$997$	19.7060	−	34.1318i	0.624096	−	1.08097i	−0.364619	−	0.931157i	$-0.618801\pi$
$997$	19.7060	−	34.1318i	0.624096	−	1.08097i	0.988715	−	0.149809i	$-0.0478659\pi$
$998$	10.8143	+	18.7309i	0.342321	+	0.592918i
$999$	−32.1433	+	18.5579i	−1.01697	+	0.587147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.l.m.361.6		12
13.2	odd	12		1690.2.a.r.1.1	yes	3
13.3	even	3		1690.2.d.i.1351.4		6
13.4	even	6	inner	1690.2.l.m.1161.6		12
13.5	odd	4		1690.2.e.p.991.3		6
13.6	odd	12		1690.2.e.p.191.3		6
13.7	odd	12		1690.2.e.r.191.3		6
13.8	odd	4		1690.2.e.r.991.3		6
13.9	even	3	inner	1690.2.l.m.1161.3		12
13.10	even	6		1690.2.d.i.1351.1		6
13.11	odd	12		1690.2.a.p.1.1	✓	3
13.12	even	2	inner	1690.2.l.m.361.3		12
65.24	odd	12		8450.2.a.cg.1.3		3
65.54	odd	12		8450.2.a.bv.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.a.p.1.1	✓	3	13.11	odd	12
1690.2.a.r.1.1	yes	3	13.2	odd	12
1690.2.d.i.1351.1		6	13.10	even	6
1690.2.d.i.1351.4		6	13.3	even	3
1690.2.e.p.191.3		6	13.6	odd	12
1690.2.e.p.991.3		6	13.5	odd	4
1690.2.e.r.191.3		6	13.7	odd	12
1690.2.e.r.991.3		6	13.8	odd	4
1690.2.l.m.361.3		12	13.12	even	2	inner
1690.2.l.m.361.6		12	1.1	even	1	trivial
1690.2.l.m.1161.3		12	13.9	even	3	inner
1690.2.l.m.1161.6		12	13.4	even	6	inner
8450.2.a.bv.1.3		3	65.54	odd	12
8450.2.a.cg.1.3		3	65.24	odd	12

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:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.900969 + 1.56052i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(1.56052 + 0.900969i) q^{6} +(3.12105 + 1.80194i) q^{7} -1.00000i q^{8} +(-0.123490 + 0.213891i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(3.84952 - 2.22252i) q^{11} +1.80194 q^{12} +3.60388 q^{14} +(1.56052 - 0.900969i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.57942 + 2.73563i) q^{17} +0.246980i q^{18} +(-0.309081 - 0.178448i) q^{19} +(-0.866025 - 0.500000i) q^{20} +6.49396i q^{21} +(2.22252 - 3.84952i) q^{22} +(-3.24698 - 5.62393i) q^{23} +(1.56052 - 0.900969i) q^{24} -1.00000 q^{25} +4.96077 q^{27} +(3.12105 - 1.80194i) q^{28} +(1.44504 + 2.50289i) q^{29} +(0.900969 - 1.56052i) q^{30} -3.82371i q^{31} +(-0.866025 - 0.500000i) q^{32} +(6.93659 + 4.00484i) q^{33} +3.15883i q^{34} +(1.80194 - 3.12105i) q^{35} +(0.123490 + 0.213891i) q^{36} +(-6.47950 + 3.74094i) q^{37} -0.356896 q^{38} -1.00000 q^{40} +(-1.76602 + 1.01961i) q^{41} +(3.24698 + 5.62393i) q^{42} +(5.00753 - 8.67330i) q^{43} -4.44504i q^{44} +(0.213891 + 0.123490i) q^{45} +(-5.62393 - 3.24698i) q^{46} +11.7017i q^{47} +(0.900969 - 1.56052i) q^{48} +(2.99396 + 5.18569i) q^{49} +(-0.866025 + 0.500000i) q^{50} -5.69202 q^{51} -12.3720 q^{53} +(4.29615 - 2.48039i) q^{54} +(-2.22252 - 3.84952i) q^{55} +(1.80194 - 3.12105i) q^{56} -0.643104i q^{57} +(2.50289 + 1.44504i) q^{58} +(10.3902 + 5.99880i) q^{59} -1.80194i q^{60} +(6.18598 - 10.7144i) q^{61} +(-1.91185 - 3.31143i) q^{62} +(-0.770835 + 0.445042i) q^{63} -1.00000 q^{64} +8.00969 q^{66} +(-12.1223 + 6.99880i) q^{67} +(1.57942 + 2.73563i) q^{68} +(5.85086 - 10.1340i) q^{69} -3.60388i q^{70} +(11.0952 + 6.40581i) q^{71} +(0.213891 + 0.123490i) q^{72} +6.96615i q^{73} +(-3.74094 + 6.47950i) q^{74} +(-0.900969 - 1.56052i) q^{75} +(-0.309081 + 0.178448i) q^{76} +16.0194 q^{77} -5.87800 q^{79} +(-0.866025 + 0.500000i) q^{80} +(4.83997 + 8.38307i) q^{81} +(-1.01961 + 1.76602i) q^{82} -4.67456i q^{83} +(5.62393 + 3.24698i) q^{84} +(2.73563 + 1.57942i) q^{85} -10.0151i q^{86} +(-2.60388 + 4.51004i) q^{87} +(-2.22252 - 3.84952i) q^{88} +(6.94706 - 4.01089i) q^{89} +0.246980 q^{90} -6.49396 q^{92} +(5.96699 - 3.44504i) q^{93} +(5.85086 + 10.1340i) q^{94} +(-0.178448 + 0.309081i) q^{95} -1.80194i q^{96} +(3.42174 + 1.97554i) q^{97} +(5.18569 + 2.99396i) q^{98} +1.09783i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} + 6 q^{4} + 8 q^{9} - 6 q^{10} + 4 q^{12} + 8 q^{14} - 6 q^{16} - 2 q^{17} + 26 q^{22} - 20 q^{23} - 12 q^{25} + 8 q^{27} + 16 q^{29} + 2 q^{30} + 4 q^{35} - 8 q^{36} + 12 q^{38} - 12 q^{40}+ \cdots + 6 q^{95}+O(q^{100}) \) 12 * q + 2 * q^3 + 6 * q^4 + 8 * q^9 - 6 * q^10 + 4 * q^12 + 8 * q^14 - 6 * q^16 - 2 * q^17 + 26 * q^22 - 20 * q^23 - 12 * q^25 + 8 * q^27 + 16 * q^29 + 2 * q^30 + 4 * q^35 - 8 * q^36 + 12 * q^38 - 12 * q^40 + 20 * q^42 + 10 * q^43 + 2 * q^48 - 2 * q^49 - 48 * q^51 - 32 * q^53 - 26 * q^55 + 4 * q^56 + 16 * q^61 - 8 * q^62 - 12 * q^64 + 8 * q^66 + 2 * q^68 + 16 * q^69 + 12 * q^74 - 2 * q^75 + 16 * q^77 + 8 * q^79 + 10 * q^81 - 38 * q^82 + 4 * q^87 - 26 * q^88 - 16 * q^90 - 40 * q^92 + 16 * q^94 + 6 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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