LMFDB - Embedded newform 1690.2.e.r.191.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(191,1690)] 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, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.191"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,3,1,-3,6,-1,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.3
Root			$0.900969 - 1.56052i$ of defining polynomial
Character	$\chi$	$=$	1690.191
Dual form			1690.2.e.r.991.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(0.900969 - 1.56052i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.900969 - 1.56052i) q^{6} +(1.80194 + 3.12105i) q^{7} -1.00000 q^{8} +(-0.123490 - 0.213891i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.22252 + 3.84952i) q^{11} -1.80194 q^{12} +3.60388 q^{14} +(0.900969 - 1.56052i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.57942 + 2.73563i) q^{17} -0.246980 q^{18} +(0.178448 + 0.309081i) q^{19} +(-0.500000 - 0.866025i) q^{20} +6.49396 q^{21} +(2.22252 + 3.84952i) q^{22} +(3.24698 - 5.62393i) q^{23} +(-0.900969 + 1.56052i) q^{24} +1.00000 q^{25} +4.96077 q^{27} +(1.80194 - 3.12105i) q^{28} +(1.44504 - 2.50289i) q^{29} +(-0.900969 - 1.56052i) q^{30} +3.82371 q^{31} +(0.500000 + 0.866025i) q^{32} +(4.00484 + 6.93659i) q^{33} +3.15883 q^{34} +(1.80194 + 3.12105i) q^{35} +(-0.123490 + 0.213891i) q^{36} +(3.74094 - 6.47950i) q^{37} +0.356896 q^{38} -1.00000 q^{40} +(-1.01961 + 1.76602i) q^{41} +(3.24698 - 5.62393i) q^{42} +(-5.00753 - 8.67330i) q^{43} +4.44504 q^{44} +(-0.123490 - 0.213891i) q^{45} +(-3.24698 - 5.62393i) q^{46} +11.7017 q^{47} +(0.900969 + 1.56052i) q^{48} +(-2.99396 + 5.18569i) q^{49} +(0.500000 - 0.866025i) q^{50} +5.69202 q^{51} -12.3720 q^{53} +(2.48039 - 4.29615i) q^{54} +(-2.22252 + 3.84952i) q^{55} +(-1.80194 - 3.12105i) q^{56} +0.643104 q^{57} +(-1.44504 - 2.50289i) q^{58} +(5.99880 + 10.3902i) q^{59} -1.80194 q^{60} +(6.18598 + 10.7144i) q^{61} +(1.91185 - 3.31143i) q^{62} +(0.445042 - 0.770835i) q^{63} +1.00000 q^{64} +8.00969 q^{66} +(-6.99880 + 12.1223i) q^{67} +(1.57942 - 2.73563i) q^{68} +(-5.85086 - 10.1340i) q^{69} +3.60388 q^{70} +(-6.40581 - 11.0952i) q^{71} +(0.123490 + 0.213891i) q^{72} +6.96615 q^{73} +(-3.74094 - 6.47950i) q^{74} +(0.900969 - 1.56052i) q^{75} +(0.178448 - 0.309081i) q^{76} -16.0194 q^{77} -5.87800 q^{79} +(-0.500000 + 0.866025i) q^{80} +(4.83997 - 8.38307i) q^{81} +(1.01961 + 1.76602i) q^{82} +4.67456 q^{83} +(-3.24698 - 5.62393i) q^{84} +(1.57942 + 2.73563i) q^{85} -10.0151 q^{86} +(-2.60388 - 4.51004i) q^{87} +(2.22252 - 3.84952i) q^{88} +(-4.01089 + 6.94706i) q^{89} -0.246980 q^{90} -6.49396 q^{92} +(3.44504 - 5.96699i) q^{93} +(5.85086 - 10.1340i) q^{94} +(0.178448 + 0.309081i) q^{95} +1.80194 q^{96} +(-1.97554 - 3.42174i) q^{97} +(2.99396 + 5.18569i) q^{98} +1.09783 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + q^{3} - 3 q^{4} + 6 q^{5} - q^{6} + 2 q^{7} - 6 q^{8} + 4 q^{9} + 3 q^{10} - 13 q^{11} - 2 q^{12} + 4 q^{14} + q^{15} - 3 q^{16} + q^{17} + 8 q^{18} - 3 q^{19} - 3 q^{20} + 20 q^{21}+ \cdots - 30 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 + q^3 - 3 * q^4 + 6 * q^5 - q^6 + 2 * q^7 - 6 * q^8 + 4 * q^9 + 3 * q^10 - 13 * q^11 - 2 * q^12 + 4 * q^14 + q^15 - 3 * q^16 + q^17 + 8 * q^18 - 3 * q^19 - 3 * q^20 + 20 * q^21 + 13 * q^22 + 10 * q^23 - q^24 + 6 * q^25 + 4 * q^27 + 2 * q^28 + 8 * q^29 - q^30 + 8 * q^31 + 3 * q^32 + 2 * q^33 + 2 * q^34 + 2 * q^35 + 4 * q^36 - 6 * q^37 - 6 * q^38 - 6 * q^40 - 19 * q^41 + 10 * q^42 - 5 * q^43 + 26 * q^44 + 4 * q^45 - 10 * q^46 + 16 * q^47 + q^48 + q^49 + 3 * q^50 + 24 * q^51 - 16 * q^53 + 2 * q^54 - 13 * q^55 - 2 * q^56 + 12 * q^57 - 8 * q^58 - 5 * q^59 - 2 * q^60 + 8 * q^61 + 4 * q^62 + 2 * q^63 + 6 * q^64 + 4 * q^66 - q^67 + q^68 - 8 * q^69 + 4 * q^70 - 12 * q^71 - 4 * q^72 + 10 * q^73 + 6 * q^74 + q^75 - 3 * q^76 - 8 * q^77 + 4 * q^79 - 3 * q^80 + 5 * q^81 + 19 * q^82 - 14 * q^83 - 10 * q^84 + q^85 - 10 * q^86 + 2 * q^87 + 13 * q^88 - 21 * q^89 + 8 * q^90 - 20 * q^92 + 20 * q^93 + 8 * q^94 - 3 * q^95 + 2 * q^96 - 21 * q^97 - q^98 - 30 * q^99

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.900969	−	1.56052i	0.520175	−	0.900969i	−0.479550	−	0.877514i	$-0.659200\pi$
$3$	0.900969	−	1.56052i	0.520175	−	0.900969i	0.999725	−	0.0234545i	$-0.00746647\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.900969	−	1.56052i	−0.367819	−	0.637081i
$7$	1.80194	+	3.12105i	0.681068	+	1.17965i	0.974655	+	0.223713i	$0.0718177\pi$
$7$	1.80194	+	3.12105i	0.681068	+	1.17965i	−0.293587	+	0.955932i	$0.594849\pi$
$8$	−1.00000			−0.353553
$9$	−0.123490	−	0.213891i	−0.0411633	−	0.0712969i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−2.22252	+	3.84952i	−0.670115	+	1.16067i	0.307756	+	0.951465i	$0.400422\pi$
$11$	−2.22252	+	3.84952i	−0.670115	+	1.16067i	−0.977871	+	0.209208i	$0.932911\pi$
$12$	−1.80194			−0.520175
$13$		0			0
$13$		0			0
$14$	3.60388			0.963176
$15$	0.900969	−	1.56052i	0.232629	−	0.402926i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.57942	+	2.73563i	0.383065	+	0.663488i	0.991499	−	0.130117i	$-0.0415352\pi$
$17$	1.57942	+	2.73563i	0.383065	+	0.663488i	−0.608434	+	0.793605i	$0.708202\pi$
$18$	−0.246980			−0.0582137
$19$	0.178448	+	0.309081i	0.0409388	+	0.0709080i	0.885769	−	0.464127i	$-0.153632\pi$
$19$	0.178448	+	0.309081i	0.0409388	+	0.0709080i	−0.844830	+	0.535035i	$0.820298\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	6.49396			1.41710
$22$	2.22252	+	3.84952i	0.473843	+	0.820720i
$23$	3.24698	−	5.62393i	0.677042	−	1.17267i	−0.298825	−	0.954308i	$-0.596595\pi$
$23$	3.24698	−	5.62393i	0.677042	−	1.17267i	0.975868	−	0.218363i	$-0.0700718\pi$
$24$	−0.900969	+	1.56052i	−0.183910	+	0.318541i
$25$	1.00000			0.200000
$26$		0			0
$27$	4.96077			0.954701
$28$	1.80194	−	3.12105i	0.340534	−	0.589823i
$29$	1.44504	−	2.50289i	0.268338	−	0.464774i	−0.700095	−	0.714050i	$-0.746859\pi$
$29$	1.44504	−	2.50289i	0.268338	−	0.464774i	0.968433	+	0.249275i	$0.0801924\pi$
$30$	−0.900969	−	1.56052i	−0.164494	−	0.284911i
$31$	3.82371			0.686758			0.343379	−	0.939197i	$-0.388428\pi$
$31$	3.82371			0.686758			0.343379	+	0.939197i	$0.388428\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	4.00484	+	6.93659i	0.697154	+	1.20751i
$34$	3.15883			0.541735
$35$	1.80194	+	3.12105i	0.304583	+	0.527553i
$36$	−0.123490	+	0.213891i	−0.0205816	+	0.0356484i
$37$	3.74094	−	6.47950i	0.615007	−	1.06522i	−0.375377	−	0.926872i	$-0.622487\pi$
$37$	3.74094	−	6.47950i	0.615007	−	1.06522i	0.990383	−	0.138350i	$-0.0441800\pi$
$38$	0.356896			0.0578962
$39$		0			0
$40$	−1.00000			−0.158114
$41$	−1.01961	+	1.76602i	−0.159237	+	0.275807i	−0.934594	−	0.355717i	$-0.884237\pi$
$41$	−1.01961	+	1.76602i	−0.159237	+	0.275807i	0.775357	+	0.631523i	$0.217570\pi$
$42$	3.24698	−	5.62393i	0.501020	−	0.867792i
$43$	−5.00753	−	8.67330i	−0.763642	−	1.32267i	−0.940962	−	0.338513i	$-0.890076\pi$
$43$	−5.00753	−	8.67330i	−0.763642	−	1.32267i	0.177320	−	0.984153i	$-0.443257\pi$
$44$	4.44504			0.670115
$45$	−0.123490	−	0.213891i	−0.0184088	−	0.0318849i
$46$	−3.24698	−	5.62393i	−0.478741	−	0.829204i
$47$	11.7017			1.70687			0.853435	−	0.521199i	$-0.174515\pi$
$47$	11.7017			1.70687			0.853435	+	0.521199i	$0.174515\pi$
$48$	0.900969	+	1.56052i	0.130044	+	0.225242i
$49$	−2.99396	+	5.18569i	−0.427708	+	0.740813i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	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	$0.823223\pi$
$54$	2.48039	−	4.29615i	0.337538	−	0.584633i
$55$	−2.22252	+	3.84952i	−0.299685	+	0.519069i
$56$	−1.80194	−	3.12105i	−0.240794	−	0.417068i
$57$	0.643104			0.0851812
$58$	−1.44504	−	2.50289i	−0.189743	−	0.328645i
$59$	5.99880	+	10.3902i	0.780978	+	1.35269i	0.931373	+	0.364067i	$0.118612\pi$
$59$	5.99880	+	10.3902i	0.780978	+	1.35269i	−0.150395	+	0.988626i	$0.548055\pi$
$60$	−1.80194			−0.232629
$61$	6.18598	+	10.7144i	0.792034	+	1.37184i	0.924706	+	0.380683i	$0.124311\pi$
$61$	6.18598	+	10.7144i	0.792034	+	1.37184i	−0.132672	+	0.991160i	$0.542356\pi$
$62$	1.91185	−	3.31143i	0.242806	−	0.420552i
$63$	0.445042	−	0.770835i	0.0560700	−	0.0971161i
$64$	1.00000			0.125000
$65$		0			0
$66$	8.00969			0.985925
$67$	−6.99880	+	12.1223i	−0.855040	+	1.48097i	0.0215680	+	0.999767i	$0.493134\pi$
$67$	−6.99880	+	12.1223i	−0.855040	+	1.48097i	−0.876608	+	0.481205i	$0.840199\pi$
$68$	1.57942	−	2.73563i	0.191532	−	0.331744i
$69$	−5.85086	−	10.1340i	−0.704360	−	1.21999i
$70$	3.60388			0.430746
$71$	−6.40581	−	11.0952i	−0.760230	−	1.31676i	−0.942732	−	0.333552i	$-0.891753\pi$
$71$	−6.40581	−	11.0952i	−0.760230	−	1.31676i	0.182502	−	0.983206i	$-0.441581\pi$
$72$	0.123490	+	0.213891i	0.0145534	+	0.0252073i
$73$	6.96615			0.815326			0.407663	−	0.913132i	$-0.366344\pi$
$73$	6.96615			0.815326			0.407663	+	0.913132i	$0.366344\pi$
$74$	−3.74094	−	6.47950i	−0.434875	−	0.753226i
$75$	0.900969	−	1.56052i	0.104035	−	0.180194i
$76$	0.178448	−	0.309081i	0.0204694	−	0.0354540i
$77$	−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	$0.607272\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	4.83997	−	8.38307i	0.537774	−	0.931453i
$82$	1.01961	+	1.76602i	0.112598	+	0.195025i
$83$	4.67456			0.513100			0.256550	−	0.966531i	$-0.417414\pi$
$83$	4.67456			0.513100			0.256550	+	0.966531i	$0.417414\pi$
$84$	−3.24698	−	5.62393i	−0.354275	−	0.613621i
$85$	1.57942	+	2.73563i	0.171312	+	0.296721i
$86$	−10.0151			−1.07995
$87$	−2.60388	−	4.51004i	−0.279165	−	0.483528i
$88$	2.22252	−	3.84952i	0.236922	−	0.410360i
$89$	−4.01089	+	6.94706i	−0.425153	+	0.736387i	−0.996435	−	0.0843675i	$-0.973113\pi$
$89$	−4.01089	+	6.94706i	−0.425153	+	0.736387i	0.571282	+	0.820754i	$0.306446\pi$
$90$	−0.246980			−0.0260339
$91$		0			0
$92$	−6.49396			−0.677042
$93$	3.44504	−	5.96699i	0.357234	−	0.618748i
$94$	5.85086	−	10.1340i	0.603470	−	1.04524i
$95$	0.178448	+	0.309081i	0.0183084	+	0.0317110i
$96$	1.80194			0.183910
$97$	−1.97554	−	3.42174i	−0.200586	−	0.347425i	0.748132	−	0.663550i	$-0.230951\pi$
$97$	−1.97554	−	3.42174i	−0.200586	−	0.347425i	−0.948717	+	0.316126i	$0.897618\pi$
$98$	2.99396	+	5.18569i	0.302436	+	0.523834i
$99$	1.09783			0.110337
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−7.52111	+	13.0269i	−0.748378	+	1.29623i	0.200222	+	0.979751i	$0.435834\pi$
$101$	−7.52111	+	13.0269i	−0.748378	+	1.29623i	−0.948600	+	0.316478i	$0.897500\pi$
$102$	2.84601	−	4.92944i	0.281797	−	0.488087i
$103$	7.82371			0.770893			0.385446	−	0.922730i	$-0.374047\pi$
$103$	7.82371			0.770893			0.385446	+	0.922730i	$0.374047\pi$
$104$		0			0
$105$	6.49396			0.633746
$106$	−6.18598	+	10.7144i	−0.600836	+	1.04068i
$107$	−4.65064	+	8.05514i	−0.449594	+	0.778720i	−0.998359	−	0.0572566i	$-0.981765\pi$
$107$	−4.65064	+	8.05514i	−0.449594	+	0.778720i	0.548765	+	0.835976i	$0.315098\pi$
$108$	−2.48039	−	4.29615i	−0.238675	−	0.413398i
$109$	0.811626			0.0777397			0.0388699	−	0.999244i	$-0.487624\pi$
$109$	0.811626			0.0777397			0.0388699	+	0.999244i	$0.487624\pi$
$110$	2.22252	+	3.84952i	0.211909	+	0.367037i
$111$	−6.74094	−	11.6756i	−0.639822	−	1.10820i
$112$	−3.60388			−0.340534
$113$	−3.50484	−	6.07057i	−0.329708	−	0.571071i	0.652746	−	0.757577i	$-0.273617\pi$
$113$	−3.50484	−	6.07057i	−0.329708	−	0.571071i	−0.982454	+	0.186506i	$0.940284\pi$
$114$	0.321552	−	0.556945i	0.0301161	−	0.0521626i
$115$	3.24698	−	5.62393i	0.302782	−	0.524435i
$116$	−2.89008			−0.268338
$117$		0			0
$118$	11.9976			1.10447
$119$	−5.69202	+	9.85887i	−0.521787	+	0.903761i
$120$	−0.900969	+	1.56052i	−0.0822468	+	0.142456i
$121$	−4.37920	−	7.58499i	−0.398109	−	0.689545i
$122$	12.3720			1.12010
$123$	1.83728	+	3.18226i	0.165662	+	0.286935i
$124$	−1.91185	−	3.31143i	−0.171690	−	0.297375i
$125$	1.00000			0.0894427
$126$	−0.445042	−	0.770835i	−0.0396475	−	0.0686715i
$127$	5.82908	−	10.0963i	0.517248	−	0.895899i	−0.482552	−	0.875867i	$-0.660290\pi$
$127$	5.82908	−	10.0963i	0.517248	−	0.895899i	0.999799	−	0.0200317i	$-0.00637672\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−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	$0.518711\pi$
$132$	4.00484	−	6.93659i	0.348577	−	0.603753i
$133$	−0.643104	+	1.11389i	−0.0557642	+	0.0965864i
$134$	6.99880	+	12.1223i	0.604605	+	1.04721i
$135$	4.96077			0.426955
$136$	−1.57942	−	2.73563i	−0.135434	−	0.234578i
$137$	−3.90097	−	6.75668i	−0.333282	−	0.577262i	0.649871	−	0.760044i	$-0.274823\pi$
$137$	−3.90097	−	6.75668i	−0.333282	−	0.577262i	−0.983153	+	0.182783i	$0.941490\pi$
$138$	−11.7017			−0.996116
$139$	−6.93631	−	12.0140i	−0.588330	−	1.01902i	−0.994451	−	0.105199i	$-0.966452\pi$
$139$	−6.93631	−	12.0140i	−0.588330	−	1.01902i	0.406121	−	0.913819i	$-0.366881\pi$
$140$	1.80194	−	3.12105i	0.152292	−	0.263777i
$141$	10.5429	−	18.2608i	0.887870	−	1.53784i
$142$	−12.8116			−1.07513
$143$		0			0
$144$	0.246980			0.0205816
$145$	1.44504	−	2.50289i	0.120004	−	0.207853i
$146$	3.48307	−	6.03286i	0.288261	−	0.499283i
$147$	5.39493	+	9.34429i	0.444966	+	0.770704i
$148$	−7.48188			−0.615007
$149$	−6.33513	−	10.9728i	−0.518994	−	0.898923i	−0.999756	−	0.0220727i	$-0.992973\pi$
$149$	−6.33513	−	10.9728i	−0.518994	−	0.898923i	0.480763	−	0.876851i	$-0.340360\pi$
$150$	−0.900969	−	1.56052i	−0.0735638	−	0.127416i
$151$	−4.86592			−0.395983			−0.197991	−	0.980204i	$-0.563442\pi$
$151$	−4.86592			−0.395983			−0.197991	+	0.980204i	$0.563442\pi$
$152$	−0.178448	−	0.309081i	−0.0144740	−	0.0250698i
$153$	0.390084	−	0.675645i	0.0315364	−	0.0546226i
$154$	−8.00969	+	13.8732i	−0.645439	+	1.11793i
$155$	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	$0.622770\pi$
$158$	−2.93900	+	5.09050i	−0.233814	+	0.404978i
$159$	−11.1468	+	19.3067i	−0.883995	+	1.53112i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	23.4034			1.84445
$162$	−4.83997	−	8.38307i	−0.380264	−	0.658636i
$163$	−2.73825	−	4.74279i	−0.214476	−	0.371484i	0.738634	−	0.674107i	$-0.235471\pi$
$163$	−2.73825	−	4.74279i	−0.214476	−	0.371484i	−0.953110	+	0.302623i	$0.902138\pi$
$164$	2.03923			0.159237
$165$	4.00484	+	6.93659i	0.311777	+	0.540013i
$166$	2.33728	−	4.04829i	0.181408	−	0.314208i
$167$	1.34481	−	2.32929i	0.104065	−	0.180246i	−0.809291	−	0.587408i	$-0.800148\pi$
$167$	1.34481	−	2.32929i	0.104065	−	0.180246i	0.913356	+	0.407162i	$0.133482\pi$
$168$	−6.49396			−0.501020
$169$		0			0
$170$	3.15883			0.242271
$171$	0.0440730	−	0.0763367i	0.00337035	−	0.00583761i
$172$	−5.00753	+	8.67330i	−0.381821	+	0.661333i
$173$	−5.45473	−	9.44787i	−0.414715	−	0.718308i	0.580683	−	0.814130i	$-0.302786\pi$
$173$	−5.45473	−	9.44787i	−0.414715	−	0.718308i	−0.995399	+	0.0958214i	$0.969452\pi$
$174$	−5.20775			−0.394799
$175$	1.80194	+	3.12105i	0.136214	+	0.235929i
$176$	−2.22252	−	3.84952i	−0.167529	−	0.290168i
$177$	21.6189			1.62498
$178$	4.01089	+	6.94706i	0.300629	+	0.520704i
$179$	−6.49127	+	11.2432i	−0.485180	+	0.840357i	−0.999855	−	0.0170285i	$-0.994579\pi$
$179$	−6.49127	+	11.2432i	−0.485180	+	0.840357i	0.514675	+	0.857386i	$0.327913\pi$
$180$	−0.123490	+	0.213891i	−0.00920439	+	0.0159425i
$181$	22.7332			1.68974			0.844872	−	0.534969i	$-0.179677\pi$
$181$	22.7332			1.68974			0.844872	+	0.534969i	$0.179677\pi$
$182$		0			0
$183$	22.2935			1.64798
$184$	−3.24698	+	5.62393i	−0.239371	+	0.414602i
$185$	3.74094	−	6.47950i	0.275039	−	0.476382i
$186$	−3.44504	−	5.96699i	−0.252603	−	0.437521i
$187$	−14.0411			−1.02679
$188$	−5.85086	−	10.1340i	−0.426717	−	0.739096i
$189$	8.93900	+	15.4828i	0.650217	+	1.12621i
$190$	0.356896			0.0258919
$191$	−9.10992	−	15.7788i	−0.659170	−	1.14172i	−0.980831	−	0.194862i	$-0.937574\pi$
$191$	−9.10992	−	15.7788i	−0.659170	−	1.14172i	0.321660	−	0.946855i	$-0.395759\pi$
$192$	0.900969	−	1.56052i	0.0650218	−	0.112621i
$193$	−9.37412	+	16.2364i	−0.674764	+	1.16873i	0.301774	+	0.953379i	$0.402421\pi$
$193$	−9.37412	+	16.2364i	−0.674764	+	1.16873i	−0.976538	+	0.215346i	$0.930912\pi$
$194$	−3.95108			−0.283671
$195$		0			0
$196$	5.98792			0.427708
$197$	−11.2078	+	19.4124i	−0.798519	+	1.38308i	0.122061	+	0.992523i	$0.461050\pi$
$197$	−11.2078	+	19.4124i	−0.798519	+	1.38308i	−0.920580	+	0.390553i	$0.872284\pi$
$198$	0.548917	−	0.950753i	0.0390099	−	0.0675671i
$199$	−8.54288	−	14.7967i	−0.605588	−	1.04891i	−0.991958	−	0.126566i	$-0.959604\pi$
$199$	−8.54288	−	14.7967i	−0.605588	−	1.04891i	0.386370	−	0.922344i	$-0.373729\pi$
$200$	−1.00000			−0.0707107
$201$	12.6114	+	21.8436i	0.889540	+	1.54073i
$202$	7.52111	+	13.0269i	0.529183	+	0.916572i
$203$	10.4155			0.731025
$204$	−2.84601	−	4.92944i	−0.199261	−	0.345129i
$205$	−1.01961	+	1.76602i	−0.0712130	+	0.123344i
$206$	3.91185	−	6.77553i	0.272552	−	0.472074i
$207$	−1.60388			−0.111477
$208$		0			0
$209$	−1.58642			−0.109735
$210$	3.24698	−	5.62393i	0.224063	−	0.388088i
$211$	2.76540	−	4.78981i	0.190378	−	0.329744i	−0.754998	−	0.655727i	$-0.772362\pi$
$211$	2.76540	−	4.78981i	0.190378	−	0.329744i	0.945375	+	0.325983i	$0.105695\pi$
$212$	6.18598	+	10.7144i	0.424855	+	0.735870i
$213$	−23.0858			−1.58181
$214$	4.65064	+	8.05514i	0.317911	+	0.550638i
$215$	−5.00753	−	8.67330i	−0.341511	−	0.591514i
$216$	−4.96077			−0.337538
$217$	6.89008	+	11.9340i	0.467729	+	0.810131i
$218$	0.405813	−	0.702889i	0.0274851	−	0.0476057i
$219$	6.27628	−	10.8708i	0.424112	−	0.734583i
$220$	4.44504			0.299685
$221$		0			0
$222$	−13.4819			−0.904844
$223$	−2.13706	+	3.70150i	−0.143108	+	0.247871i	−0.928666	−	0.370918i	$-0.879043\pi$
$223$	−2.13706	+	3.70150i	−0.143108	+	0.247871i	0.785557	+	0.618789i	$0.212376\pi$
$224$	−1.80194	+	3.12105i	−0.120397	+	0.208534i
$225$	−0.123490	−	0.213891i	−0.00823265	−	0.0142594i
$226$	−7.00969			−0.466278
$227$	4.97703	+	8.62047i	0.330337	+	0.572161i	0.982578	−	0.185851i	$-0.0595042\pi$
$227$	4.97703	+	8.62047i	0.330337	+	0.572161i	−0.652241	+	0.758012i	$0.726171\pi$
$228$	−0.321552	−	0.556945i	−0.0212953	−	0.0368846i
$229$	−23.0315			−1.52196			−0.760981	−	0.648774i	$-0.775282\pi$
$229$	−23.0315			−1.52196			−0.760981	+	0.648774i	$0.775282\pi$
$230$	−3.24698	−	5.62393i	−0.214099	−	0.370831i
$231$	−14.4330	+	24.9986i	−0.949619	+	1.64479i
$232$	−1.44504	+	2.50289i	−0.0948716	+	0.164323i
$233$	18.5700			1.21656			0.608281	−	0.793721i	$-0.291859\pi$
$233$	18.5700			1.21656			0.608281	+	0.793721i	$0.291859\pi$
$234$		0			0
$235$	11.7017			0.763335
$236$	5.99880	−	10.3902i	0.390489	−	0.676347i
$237$	−5.29590	+	9.17276i	−0.344005	+	0.595835i
$238$	5.69202	+	9.85887i	0.368959	+	0.639056i
$239$	−18.9530			−1.22597			−0.612984	−	0.790095i	$-0.710031\pi$
$239$	−18.9530			−1.22597			−0.612984	+	0.790095i	$0.710031\pi$
$240$	0.900969	+	1.56052i	0.0581573	+	0.100731i
$241$	−11.3720	−	19.6968i	−0.732532	−	1.26878i	−0.955798	−	0.294026i	$-0.905005\pi$
$241$	−11.3720	−	19.6968i	−0.732532	−	1.26878i	0.223265	−	0.974758i	$-0.428328\pi$
$242$	−8.75840			−0.563011
$243$	−1.28017	−	2.21732i	−0.0821228	−	0.142241i
$244$	6.18598	−	10.7144i	0.396017	−	0.685921i
$245$	−2.99396	+	5.18569i	−0.191277	+	0.331302i
$246$	3.67456			0.234282
$247$		0			0
$248$	−3.82371			−0.242806
$249$	4.21164	−	7.29477i	0.266902	−	0.462287i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−7.28352	−	12.6154i	−0.459732	−	0.796279i	0.539215	−	0.842168i	$-0.318721\pi$
$251$	−7.28352	−	12.6154i	−0.459732	−	0.796279i	−0.998947	+	0.0458896i	$0.985388\pi$
$252$	−0.890084			−0.0560700
$253$	14.4330	+	24.9986i	0.907392	+	1.57165i
$254$	−5.82908	−	10.0963i	−0.365749	−	0.633496i
$255$	5.69202			0.356448
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.00216	+	1.73578i	−0.0625128	+	0.108275i	−0.895588	−	0.444884i	$-0.853245\pi$
$257$	−1.00216	+	1.73578i	−0.0625128	+	0.108275i	0.833075	+	0.553160i	$0.186578\pi$
$258$	−9.02326	+	15.6287i	−0.561764	+	0.973003i
$259$	26.9638			1.67545
$260$		0			0
$261$	−0.713792			−0.0441826
$262$	−0.672407	+	1.16464i	−0.0415415	+	0.0719519i
$263$	−2.20775	+	3.82394i	−0.136136	+	0.235794i	−0.926031	−	0.377448i	$-0.876802\pi$
$263$	−2.20775	+	3.82394i	−0.136136	+	0.235794i	0.789895	+	0.613242i	$0.210135\pi$
$264$	−4.00484	−	6.93659i	−0.246481	−	0.426918i
$265$	−12.3720			−0.760004
$266$	0.643104	+	1.11389i	0.0394312	+	0.0682969i
$267$	7.22737	+	12.5182i	0.442308	+	0.766099i
$268$	13.9976			0.855040
$269$	9.07606	+	15.7202i	0.553377	+	0.958478i	0.998028	+	0.0627736i	$0.0199946\pi$
$269$	9.07606	+	15.7202i	0.553377	+	0.958478i	−0.444650	+	0.895704i	$0.646672\pi$
$270$	2.48039	−	4.29615i	0.150951	−	0.261456i
$271$	9.73556	−	16.8625i	0.591393	−	1.02432i	−0.402652	−	0.915353i	$-0.631911\pi$
$271$	9.73556	−	16.8625i	0.591393	−	1.02432i	0.994045	−	0.108970i	$-0.0347552\pi$
$272$	−3.15883			−0.191532
$273$		0			0
$274$	−7.80194			−0.471332
$275$	−2.22252	+	3.84952i	−0.134023	+	0.232135i
$276$	−5.85086	+	10.1340i	−0.352180	+	0.609994i
$277$	9.19806	+	15.9315i	0.552658	+	0.957232i	0.998082	+	0.0619118i	$0.0197197\pi$
$277$	9.19806	+	15.9315i	0.552658	+	0.957232i	−0.445424	+	0.895320i	$0.646947\pi$
$278$	−13.8726			−0.832025
$279$	−0.472189	−	0.817855i	−0.0282692	−	0.0489637i
$280$	−1.80194	−	3.12105i	−0.107686	−	0.186518i
$281$	−15.9463			−0.951276			−0.475638	−	0.879641i	$-0.657783\pi$
$281$	−15.9463			−0.951276			−0.475638	+	0.879641i	$0.657783\pi$
$282$	−10.5429	−	18.2608i	−0.627819	−	1.08741i
$283$	13.9955	−	24.2408i	0.831943	−	1.44097i	−0.0645519	−	0.997914i	$-0.520562\pi$
$283$	13.9955	−	24.2408i	0.831943	−	1.44097i	0.896495	−	0.443054i	$-0.146105\pi$
$284$	−6.40581	+	11.0952i	−0.380115	+	0.658379i
$285$	0.643104			0.0380942
$286$		0			0
$287$	−7.34913			−0.433805
$288$	0.123490	−	0.213891i	0.00727671	−	0.0126036i
$289$	3.51089	−	6.08103i	0.206523	−	0.357708i
$290$	−1.44504	−	2.50289i	−0.0848558	−	0.146975i
$291$	−7.11960			−0.417359
$292$	−3.48307	−	6.03286i	−0.203831	−	0.353047i
$293$	6.78017	+	11.7436i	0.396102	+	0.686068i	0.993241	−	0.116069i	$-0.0370295\pi$
$293$	6.78017	+	11.7436i	0.396102	+	0.686068i	−0.597140	+	0.802137i	$0.703696\pi$
$294$	10.7899			0.629277
$295$	5.99880	+	10.3902i	0.349264	+	0.604943i
$296$	−3.74094	+	6.47950i	−0.217438	+	0.376613i
$297$	−11.0254	+	19.0966i	−0.639760	+	1.10810i
$298$	−12.6703			−0.733968
$299$		0			0
$300$	−1.80194			−0.104035
$301$	18.0465	−	31.2575i	1.04018	−	1.80165i
$302$	−2.43296	+	4.21401i	−0.140001	+	0.242489i
$303$	13.5526	+	23.4737i	0.778575	+	1.34853i
$304$	−0.356896			−0.0204694
$305$	6.18598	+	10.7144i	0.354208	+	0.613507i
$306$	−0.390084	−	0.675645i	−0.0222996	−	0.0386240i
$307$	−15.1588			−0.865160			−0.432580	−	0.901595i	$-0.642397\pi$
$307$	−15.1588			−0.865160			−0.432580	+	0.901595i	$0.642397\pi$
$308$	8.00969	+	13.8732i	0.456394	+	0.790498i
$309$	7.04892	−	12.2091i	0.400999	−	0.694550i
$310$	1.91185	−	3.31143i	0.108586	−	0.188076i
$311$	5.38404			0.305301			0.152651	−	0.988280i	$-0.451219\pi$
$311$	5.38404			0.305301			0.152651	+	0.988280i	$0.451219\pi$
$312$		0			0
$313$	−16.5864			−0.937520			−0.468760	−	0.883326i	$-0.655299\pi$
$313$	−16.5864			−0.937520			−0.468760	+	0.883326i	$0.655299\pi$
$314$	−4.71379	+	8.16453i	−0.266015	+	0.460751i
$315$	0.445042	−	0.770835i	0.0250753	−	0.0434316i
$316$	2.93900	+	5.09050i	0.165332	+	0.286363i
$317$	12.1086			0.680086			0.340043	−	0.940410i	$-0.389558\pi$
$317$	12.1086			0.680086			0.340043	+	0.940410i	$0.389558\pi$
$318$	11.1468	+	19.3067i	0.625079	+	1.08267i
$319$	6.42327	+	11.1254i	0.359634	+	0.622905i
$320$	1.00000			0.0559017
$321$	8.38016	+	14.5149i	0.467735	+	0.810140i
$322$	11.7017	−	20.2680i	0.652111	−	1.12949i
$323$	−0.563687	+	0.976335i	−0.0313644	+	0.0543247i
$324$	−9.67994			−0.537774
$325$		0			0
$326$	−5.47650			−0.303315
$327$	0.731250	−	1.26656i	0.0404382	−	0.0700411i
$328$	1.01961	−	1.76602i	0.0562988	−	0.0975124i
$329$	21.0858	+	36.5216i	1.16250	+	2.01350i
$330$	8.00969			0.440919
$331$	−7.30559	−	12.6536i	−0.401551	−	0.695507i	0.592362	−	0.805672i	$-0.298196\pi$
$331$	−7.30559	−	12.6536i	−0.401551	−	0.695507i	−0.993913	+	0.110165i	$0.964862\pi$
$332$	−2.33728	−	4.04829i	−0.128275	−	0.222179i
$333$	−1.84787			−0.101263
$334$	−1.34481	−	2.32929i	−0.0735850	−	0.127453i
$335$	−6.99880	+	12.1223i	−0.382385	+	0.662311i
$336$	−3.24698	+	5.62393i	−0.177137	+	0.306811i
$337$	−4.45952			−0.242925			−0.121463	−	0.992596i	$-0.538758\pi$
$337$	−4.45952			−0.242925			−0.121463	+	0.992596i	$0.538758\pi$
$338$		0			0
$339$	−12.6310			−0.686023
$340$	1.57942	−	2.73563i	0.0856559	−	0.148360i
$341$	−8.49827	+	14.7194i	−0.460207	+	0.797102i
$342$	−0.0440730	−	0.0763367i	−0.00238319	−	0.00412781i
$343$	3.64742			0.196942
$344$	5.00753	+	8.67330i	0.269988	+	0.467633i
$345$	−5.85086	−	10.1340i	−0.314999	−	0.545595i
$346$	−10.9095			−0.586496
$347$	−14.2935	−	24.7571i	−0.767316	−	1.32903i	−0.939014	−	0.343880i	$-0.888259\pi$
$347$	−14.2935	−	24.7571i	−0.767316	−	1.32903i	0.171698	−	0.985150i	$-0.445075\pi$
$348$	−2.60388	+	4.51004i	−0.139582	+	0.241764i
$349$	2.43967	−	4.22562i	0.130592	−	0.226192i	−0.793313	−	0.608814i	$-0.791645\pi$
$349$	2.43967	−	4.22562i	0.130592	−	0.226192i	0.923905	+	0.382622i	$0.124979\pi$
$350$	3.60388			0.192635
$351$		0			0
$352$	−4.44504			−0.236922
$353$	2.02984	−	3.51578i	0.108037	−	0.187126i	−0.806938	−	0.590636i	$-0.798877\pi$
$353$	2.02984	−	3.51578i	0.108037	−	0.187126i	0.914975	+	0.403510i	$0.132210\pi$
$354$	10.8095	−	18.7226i	0.574517	−	0.995092i
$355$	−6.40581	−	11.0952i	−0.339985	−	0.588872i
$356$	8.02177			0.425153
$357$	10.2567	+	17.7651i	0.542840	+	0.940227i
$358$	6.49127	+	11.2432i	0.343074	+	0.594222i
$359$	−5.12067			−0.270259			−0.135129	−	0.990828i	$-0.543145\pi$
$359$	−5.12067			−0.270259			−0.135129	+	0.990828i	$0.543145\pi$
$360$	0.123490	+	0.213891i	0.00650848	+	0.0112730i
$361$	9.43631	−	16.3442i	0.496648	−	0.860220i
$362$	11.3666	−	19.6875i	0.597414	−	1.03475i
$363$	−15.7821			−0.828345
$364$		0			0
$365$	6.96615			0.364625
$366$	11.1468	−	19.3067i	0.582650	−	1.00918i
$367$	4.64310	−	8.04209i	0.242368	−	0.419794i	−0.719020	−	0.694989i	$-0.755409\pi$
$367$	4.64310	−	8.04209i	0.242368	−	0.419794i	0.961388	+	0.275195i	$0.0887425\pi$
$368$	3.24698	+	5.62393i	0.169261	+	0.293168i
$369$	0.503648			0.0262189
$370$	−3.74094	−	6.47950i	−0.194482	−	0.336853i
$371$	−22.2935	−	38.6135i	−1.15742	−	2.00471i
$372$	−6.89008			−0.357234
$373$	3.65279	+	6.32682i	0.189134	+	0.327590i	0.944962	−	0.327180i	$-0.106098\pi$
$373$	3.65279	+	6.32682i	0.189134	+	0.327590i	−0.755827	+	0.654771i	$0.772765\pi$
$374$	−7.02057	+	12.1600i	−0.363025	+	0.628778i
$375$	0.900969	−	1.56052i	0.0465258	−	0.0805851i
$376$	−11.7017			−0.603470
$377$		0			0
$378$	17.8780			0.919545
$379$	15.2850	−	26.4744i	0.785138	−	1.35990i	−0.143778	−	0.989610i	$-0.545925\pi$
$379$	15.2850	−	26.4744i	0.785138	−	1.35990i	0.928916	−	0.370290i	$-0.120742\pi$
$380$	0.178448	−	0.309081i	0.00915419	−	0.0158555i
$381$	−10.5036	−	18.1929i	−0.538118	−	0.932048i
$382$	−18.2198			−0.932208
$383$	−3.96615	−	6.86957i	−0.202661	−	0.351019i	0.746724	−	0.665134i	$-0.231626\pi$
$383$	−3.96615	−	6.86957i	−0.202661	−	0.351019i	−0.949385	+	0.314115i	$0.898292\pi$
$384$	−0.900969	−	1.56052i	−0.0459774	−	0.0796351i
$385$	−16.0194			−0.816423
$386$	9.37412	+	16.2364i	0.477130	+	0.826413i
$387$	−1.23676	+	2.14213i	−0.0628680	+	0.108891i
$388$	−1.97554	+	3.42174i	−0.100293	+	0.173712i
$389$	1.35988			0.0689486			0.0344743	−	0.999406i	$-0.489024\pi$
$389$	1.35988			0.0689486			0.0344743	+	0.999406i	$0.489024\pi$
$390$		0			0
$391$	20.5133			1.03740
$392$	2.99396	−	5.18569i	0.151218	−	0.261917i
$393$	−1.21164	+	2.09861i	−0.0611189	+	0.105861i
$394$	11.2078	+	19.4124i	0.564638	+	0.977982i
$395$	−5.87800			−0.295754
$396$	−0.548917	−	0.950753i	−0.0275841	−	0.0477771i
$397$	12.3056	+	21.3139i	0.617600	+	1.06971i	0.989922	+	0.141611i	$0.0452281\pi$
$397$	12.3056	+	21.3139i	0.617600	+	1.06971i	−0.372323	+	0.928103i	$0.621439\pi$
$398$	−17.0858			−0.856431
$399$	1.15883	+	2.00716i	0.0580142	+	0.100484i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−2.44773	+	4.23959i	−0.122234	+	0.211715i	−0.920648	−	0.390393i	$-0.872339\pi$
$401$	−2.44773	+	4.23959i	−0.122234	+	0.211715i	0.798414	+	0.602108i	$0.205672\pi$
$402$	25.2228			1.25800
$403$		0			0
$404$	15.0422			0.748378
$405$	4.83997	−	8.38307i	0.240500	−	0.416558i
$406$	5.20775	−	9.02009i	0.258456	−	0.447660i
$407$	16.6286	+	28.8016i	0.824251	+	1.42764i
$408$	−5.69202			−0.281797
$409$	2.18718	+	3.78830i	0.108149	+	0.187319i	0.915020	−	0.403408i	$-0.132174\pi$
$409$	2.18718	+	3.78830i	0.108149	+	0.187319i	−0.806871	+	0.590727i	$0.798841\pi$
$410$	1.01961	+	1.76602i	0.0503552	+	0.0872177i
$411$	−14.0586			−0.693460
$412$	−3.91185	−	6.77553i	−0.192723	−	0.333806i
$413$	−21.6189	+	37.4451i	−1.06380	+	1.84255i
$414$	−0.801938	+	1.38900i	−0.0394131	+	0.0682655i
$415$	4.67456			0.229465
$416$		0			0
$417$	−24.9976			−1.22414
$418$	−0.793209	+	1.37388i	−0.0387971	+	0.0671985i
$419$	−8.37196	+	14.5007i	−0.408997	+	0.708404i	−0.994778	−	0.102066i	$-0.967455\pi$
$419$	−8.37196	+	14.5007i	−0.408997	+	0.708404i	0.585781	+	0.810470i	$0.300788\pi$
$420$	−3.24698	−	5.62393i	−0.158436	−	0.274420i
$421$	0.483206			0.0235500			0.0117750	−	0.999931i	$-0.496252\pi$
$421$	0.483206			0.0235500			0.0117750	+	0.999931i	$0.496252\pi$
$422$	−2.76540	−	4.78981i	−0.134617	−	0.233164i
$423$	−1.44504	−	2.50289i	−0.0702603	−	0.121694i
$424$	12.3720			0.600836
$425$	1.57942	+	2.73563i	0.0766130	+	0.132698i
$426$	−11.5429	+	19.9928i	−0.559254	+	0.968657i
$427$	−22.2935	+	38.6135i	−1.07886	+	1.86864i
$428$	9.30127			0.449594
$429$		0			0
$430$	−10.0151			−0.482969
$431$	5.98792	−	10.3714i	0.288428	−	0.499572i	−0.685007	−	0.728537i	$-0.740201\pi$
$431$	5.98792	−	10.3714i	0.288428	−	0.499572i	0.973435	+	0.228965i	$0.0735341\pi$
$432$	−2.48039	+	4.29615i	−0.119338	+	0.206699i
$433$	2.07726	+	3.59792i	0.0998268	+	0.172905i	0.911613	−	0.411050i	$-0.134838\pi$
$433$	2.07726	+	3.59792i	0.0998268	+	0.172905i	−0.811786	+	0.583955i	$0.801504\pi$
$434$	13.7802			0.661469
$435$	−2.60388	−	4.51004i	−0.124846	−	0.216240i
$436$	−0.405813	−	0.702889i	−0.0194349	−	0.0336623i
$437$	2.31767			0.110869
$438$	−6.27628	−	10.8708i	−0.299892	−	0.519429i
$439$	6.25667	−	10.8369i	0.298614	−	0.517215i	−0.677205	−	0.735795i	$-0.736809\pi$
$439$	6.25667	−	10.8369i	0.298614	−	0.517215i	0.975819	+	0.218579i	$0.0701422\pi$
$440$	2.22252	−	3.84952i	0.105955	−	0.183519i
$441$	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	$0.517245\pi$
$444$	−6.74094	+	11.6756i	−0.319911	+	0.554102i
$445$	−4.01089	+	6.94706i	−0.190134	+	0.329322i
$446$	2.13706	+	3.70150i	0.101193	+	0.175271i
$447$	−22.8310			−1.07987
$448$	1.80194	+	3.12105i	0.0851336	+	0.147456i
$449$	−10.2274	−	17.7143i	−0.482659	−	0.835990i	0.517143	−	0.855899i	$-0.326996\pi$
$449$	−10.2274	−	17.7143i	−0.482659	−	0.835990i	−0.999802	+	0.0199090i	$0.993662\pi$
$450$	−0.246980			−0.0116427
$451$	−4.53223	−	7.85005i	−0.213414	−	0.369644i
$452$	−3.50484	+	6.07057i	−0.164854	+	0.285536i
$453$	−4.38404	+	7.59339i	−0.205980	+	0.356768i
$454$	9.95407			0.467167
$455$		0			0
$456$	−0.643104			−0.0301161
$457$	−8.92154	+	15.4526i	−0.417332	+	0.722841i	−0.995670	−	0.0929568i	$-0.970368\pi$
$457$	−8.92154	+	15.4526i	−0.417332	+	0.722841i	0.578338	+	0.815797i	$0.303702\pi$
$458$	−11.5157	+	19.9458i	−0.538095	+	0.932007i
$459$	7.83513	+	13.5708i	0.365712	+	0.633432i
$460$	−6.49396			−0.302782
$461$	−1.76271	−	3.05310i	−0.0820975	−	0.142197i	0.822053	−	0.569411i	$-0.192829\pi$
$461$	−1.76271	−	3.05310i	−0.0820975	−	0.142197i	−0.904151	+	0.427214i	$0.859495\pi$
$462$	14.4330	+	24.9986i	0.671482	+	1.16304i
$463$	3.72587			0.173156			0.0865780	−	0.996245i	$-0.472407\pi$
$463$	3.72587			0.173156			0.0865780	+	0.996245i	$0.472407\pi$
$464$	1.44504	+	2.50289i	0.0670844	+	0.116194i
$465$	3.44504	−	5.96699i	0.159760	−	0.276712i
$466$	9.28501	−	16.0821i	0.430120	−	0.744989i
$467$	−12.8576			−0.594977			−0.297488	−	0.954725i	$-0.596149\pi$
$467$	−12.8576			−0.594977			−0.297488	+	0.954725i	$0.596149\pi$
$468$		0			0
$469$	−50.4456			−2.32936
$470$	5.85086	−	10.1340i	0.269880	−	0.467446i
$471$	−8.49396	+	14.7120i	−0.391381	+	0.677892i
$472$	−5.99880	−	10.3902i	−0.276117	−	0.478249i
$473$	44.5174			2.04691
$474$	5.29590	+	9.17276i	0.243249	+	0.421319i
$475$	0.178448	+	0.309081i	0.00818775	+	0.0141816i
$476$	11.3840			0.521787
$477$	1.52781	+	2.64625i	0.0699537	+	0.121163i
$478$	−9.47650	+	16.4138i	−0.433445	+	0.750749i
$479$	16.9976	−	29.4407i	0.776640	−	1.34518i	−0.157227	−	0.987562i	$-0.550256\pi$
$479$	16.9976	−	29.4407i	0.776640	−	1.34518i	0.933868	−	0.357618i	$-0.116411\pi$
$480$	1.80194			0.0822468
$481$		0			0
$482$	−22.7439			−1.03596
$483$	21.0858	−	36.5216i	0.959435	−	1.66179i
$484$	−4.37920	+	7.58499i	−0.199054	+	0.344772i
$485$	−1.97554	−	3.42174i	−0.0897047	−	0.155373i
$486$	−2.56033			−0.116139
$487$	−12.7409	−	22.0680i	−0.577347	−	0.999994i	−0.995782	−	0.0917478i	$-0.970755\pi$
$487$	−12.7409	−	22.0680i	−0.577347	−	0.999994i	0.418435	−	0.908247i	$-0.362579\pi$
$488$	−6.18598	−	10.7144i	−0.280026	−	0.485020i
$489$	−9.86831			−0.446261
$490$	2.99396	+	5.18569i	0.135253	+	0.234266i
$491$	−12.8889	+	22.3242i	−0.581667	+	1.00748i	0.413615	+	0.910452i	$0.364266\pi$
$491$	−12.8889	+	22.3242i	−0.581667	+	1.00748i	−0.995282	+	0.0970253i	$0.969067\pi$
$492$	1.83728	−	3.18226i	0.0828310	−	0.143468i
$493$	9.12929			0.411163
$494$		0			0
$495$	1.09783			0.0493440
$496$	−1.91185	+	3.31143i	−0.0858448	+	0.148688i
$497$	23.0858	−	39.9857i	1.03554	−	1.79360i
$498$	−4.21164	−	7.29477i	−0.188728	−	0.326886i
$499$	−21.6286			−0.968230			−0.484115	−	0.875004i	$-0.660858\pi$
$499$	−21.6286			−0.968230			−0.484115	+	0.875004i	$0.660858\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−2.42327	−	4.19723i	−0.108264	−	0.187518i
$502$	−14.5670			−0.650159
$503$	−13.3666	−	23.1516i	−0.595987	−	1.03228i	−0.993407	−	0.114642i	$-0.963428\pi$
$503$	−13.3666	−	23.1516i	−0.595987	−	1.03228i	0.397420	−	0.917637i	$-0.369906\pi$
$504$	−0.445042	+	0.770835i	−0.0198237	+	0.0343357i
$505$	−7.52111	+	13.0269i	−0.334685	+	0.579691i
$506$	28.8659			1.28325
$507$		0			0
$508$	−11.6582			−0.517248
$509$	−17.6407	+	30.5546i	−0.781911	+	1.35431i	0.148916	+	0.988850i	$0.452421\pi$
$509$	−17.6407	+	30.5546i	−0.781911	+	1.35431i	−0.930827	+	0.365459i	$0.880912\pi$
$510$	2.84601	−	4.92944i	0.126023	−	0.218279i
$511$	12.5526	+	21.7417i	0.555293	+	0.961795i
$512$	−1.00000			−0.0441942
$513$	0.885239	+	1.53328i	0.0390843	+	0.0676959i
$514$	1.00216	+	1.73578i	0.0442032	+	0.0765622i
$515$	7.82371			0.344754
$516$	9.02326	+	15.6287i	0.397227	+	0.688017i
$517$	−26.0073	+	45.0460i	−1.14380	+	1.98112i
$518$	13.4819	−	23.3513i	0.592360	−	1.02600i
$519$	−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	$0.411206\pi$
$522$	−0.356896	+	0.618162i	−0.0156209	+	0.0270562i
$523$	−2.69471	+	4.66737i	−0.117831	+	0.204090i	−0.918908	−	0.394472i	$-0.870928\pi$
$523$	−2.69471	+	4.66737i	−0.117831	+	0.204090i	0.801077	+	0.598562i	$0.204261\pi$
$524$	0.672407	+	1.16464i	0.0293742	+	0.0508777i
$525$	6.49396			0.283420
$526$	2.20775	+	3.82394i	0.0962625	+	0.166732i
$527$	6.03923	+	10.4603i	0.263073	+	0.455656i
$528$	−8.00969			−0.348577
$529$	−9.58575	−	16.6030i	−0.416772	−	0.721870i
$530$	−6.18598	+	10.7144i	−0.268702	+	0.465405i
$531$	1.48158	−	2.56618i	0.0642952	−	0.111363i
$532$	1.28621			0.0557642
$533$		0			0
$534$	14.4547			0.625517
$535$	−4.65064	+	8.05514i	−0.201065	+	0.348254i
$536$	6.99880	−	12.1223i	0.302302	−	0.523603i
$537$	11.6969	+	20.2596i	0.504757	+	0.874265i
$538$	18.1521			0.782594
$539$	−13.3083	−	23.0506i	−0.573228	−	0.992860i
$540$	−2.48039	−	4.29615i	−0.106739	−	0.184877i
$541$	22.7332			0.977375			0.488688	−	0.872459i	$-0.337476\pi$
$541$	22.7332			0.977375			0.488688	+	0.872459i	$0.337476\pi$
$542$	−9.73556	−	16.8625i	−0.418178	−	0.724306i
$543$	20.4819	−	35.4757i	0.878961	−	1.52241i
$544$	−1.57942	+	2.73563i	−0.0677169	+	0.117289i
$545$	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	$0.260438\pi$
$548$	−3.90097	+	6.75668i	−0.166641	+	0.288631i
$549$	1.52781	−	2.64625i	0.0652054	−	0.112939i
$550$	2.22252	+	3.84952i	0.0947686	+	0.164144i
$551$	1.03146			0.0439416
$552$	5.85086	+	10.1340i	0.249029	+	0.431331i
$553$	−10.5918	−	18.3455i	−0.450409	−	0.780131i
$554$	18.3961			0.781576
$555$	−6.74094	−	11.6756i	−0.286137	−	0.495604i
$556$	−6.93631	+	12.0140i	−0.294165	+	0.509509i
$557$	−13.6082	+	23.5701i	−0.576597	+	0.998696i	0.419269	+	0.907862i	$0.362287\pi$
$557$	−13.6082	+	23.5701i	−0.576597	+	0.998696i	−0.995866	+	0.0908338i	$0.971047\pi$
$558$	−0.944378			−0.0399787
$559$		0			0
$560$	−3.60388			−0.152292
$561$	−12.6506	+	21.9115i	−0.534110	+	0.925106i
$562$	−7.97315	+	13.8099i	−0.336327	+	0.582535i
$563$	5.87800	+	10.1810i	0.247728	+	0.429078i	0.962895	−	0.269876i	$-0.0869827\pi$
$563$	5.87800	+	10.1810i	0.247728	+	0.429078i	−0.715167	+	0.698954i	$0.753649\pi$
$564$	−21.0858			−0.887870
$565$	−3.50484	−	6.07057i	−0.147450	−	0.255391i
$566$	−13.9955	−	24.2408i	−0.588273	−	1.01892i
$567$	34.8853			1.46504
$568$	6.40581	+	11.0952i	0.268782	+	0.465544i
$569$	9.63653	−	16.6910i	0.403984	−	0.699721i	−0.590218	−	0.807244i	$-0.700958\pi$
$569$	9.63653	−	16.6910i	0.403984	−	0.699721i	0.994203	+	0.107522i	$0.0342917\pi$
$570$	0.321552	−	0.556945i	0.0134683	−	0.0233278i
$571$	32.6329			1.36565			0.682823	−	0.730584i	$-0.260752\pi$
$571$	32.6329			1.36565			0.682823	+	0.730584i	$0.260752\pi$
$572$		0			0
$573$	−32.8310			−1.37153
$574$	−3.67456	+	6.36453i	−0.153373	+	0.265650i
$575$	3.24698	−	5.62393i	0.135408	−	0.234534i
$576$	−0.123490	−	0.213891i	−0.00514541	−	0.00891211i
$577$	−31.4534			−1.30942			−0.654711	−	0.755879i	$-0.727210\pi$
$577$	−31.4534			−1.30942			−0.654711	+	0.755879i	$0.727210\pi$
$578$	−3.51089	−	6.08103i	−0.146034	−	0.252938i
$579$	16.8916	+	29.2571i	0.701990	+	1.21588i
$580$	−2.89008			−0.120004
$581$	8.42327	+	14.5895i	0.349456	+	0.605276i
$582$	−3.55980	+	6.16576i	−0.147559	+	0.255579i
$583$	27.4969	−	47.6261i	1.13881	−	1.97247i
$584$	−6.96615			−0.288261
$585$		0			0
$586$	13.5603			0.560172
$587$	10.3808	−	17.9801i	0.428462	−	0.742119i	−0.568274	−	0.822839i	$-0.692389\pi$
$587$	10.3808	−	17.9801i	0.428462	−	0.742119i	0.996737	+	0.0807205i	$0.0257221\pi$
$588$	5.39493	−	9.34429i	0.222483	−	0.385352i
$589$	0.682333	+	1.18184i	0.0281150	+	0.0486967i
$590$	11.9976			0.493934
$591$	20.1957	+	34.9799i	0.830739	+	1.43888i
$592$	3.74094	+	6.47950i	0.153752	+	0.266306i
$593$	−31.9028			−1.31009			−0.655045	−	0.755590i	$-0.727350\pi$
$593$	−31.9028			−1.31009			−0.655045	+	0.755590i	$0.727350\pi$
$594$	11.0254	+	19.0966i	0.452378	+	0.783542i
$595$	−5.69202	+	9.85887i	−0.233350	+	0.404174i
$596$	−6.33513	+	10.9728i	−0.259497	+	0.449462i
$597$	−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	$0.552775\pi$
$600$	−0.900969	+	1.56052i	−0.0367819	+	0.0637081i
$601$	9.74847	−	16.8848i	0.397648	−	0.688747i	−0.595787	−	0.803143i	$-0.703160\pi$
$601$	9.74847	−	16.8848i	0.397648	−	0.688747i	0.993435	+	0.114395i	$0.0364930\pi$
$602$	−18.0465	−	31.2575i	−0.735521	−	1.27396i
$603$	3.45712			0.140785
$604$	2.43296	+	4.21401i	0.0989957	+	0.171466i
$605$	−4.37920	−	7.58499i	−0.178040	−	0.308374i
$606$	27.1051			1.10107
$607$	17.9922	+	31.1635i	0.730282	+	1.26489i	0.956763	+	0.290870i	$0.0939447\pi$
$607$	17.9922	+	31.1635i	0.730282	+	1.26489i	−0.226480	+	0.974016i	$0.572722\pi$
$608$	−0.178448	+	0.309081i	−0.00723702	+	0.0125349i
$609$	9.38404	−	16.2536i	0.380261	−	0.658631i
$610$	12.3720			0.500926
$611$		0			0
$612$	−0.780167			−0.0315364
$613$	−9.08815	+	15.7411i	−0.367067	+	0.635778i	−0.989106	−	0.147208i	$-0.952971\pi$
$613$	−9.08815	+	15.7411i	−0.367067	+	0.635778i	0.622039	+	0.782986i	$0.286305\pi$
$614$	−7.57942	+	13.1279i	−0.305880	+	0.529800i
$615$	1.83728	+	3.18226i	0.0740863	+	0.128321i
$616$	16.0194			0.645439
$617$	−21.5266	−	37.2852i	−0.866629	−	1.50105i	−0.865421	−	0.501046i	$-0.832949\pi$
$617$	−21.5266	−	37.2852i	−0.866629	−	1.50105i	−0.00120820	−	0.999999i	$-0.500385\pi$
$618$	−7.04892	−	12.2091i	−0.283549	−	0.491121i
$619$	39.5120			1.58812			0.794061	−	0.607838i	$-0.207963\pi$
$619$	39.5120			1.58812			0.794061	+	0.607838i	$0.207963\pi$
$620$	−1.91185	−	3.31143i	−0.0767819	−	0.132990i
$621$	16.1075	−	27.8990i	0.646373	−	1.11955i
$622$	2.69202	−	4.66272i	0.107940	−	0.186958i
$623$	−28.9095			−1.15823
$624$		0			0
$625$	1.00000			0.0400000
$626$	−8.29321	+	14.3643i	−0.331463	+	0.574111i
$627$	−1.42931	+	2.47564i	−0.0570812	+	0.0988676i
$628$	4.71379	+	8.16453i	0.188101	+	0.325800i
$629$	23.6340			0.942350
$630$	−0.445042	−	0.770835i	−0.0177309	−	0.0307108i
$631$	−11.5308	−	19.9719i	−0.459034	−	0.795070i	0.539876	−	0.841744i	$-0.318471\pi$
$631$	−11.5308	−	19.9719i	−0.459034	−	0.795070i	−0.998910	+	0.0466746i	$0.985138\pi$
$632$	5.87800			0.233814
$633$	−4.98307	−	8.63094i	−0.198059	−	0.343049i
$634$	6.05429	−	10.4863i	0.240447	−	0.416466i
$635$	5.82908	−	10.0963i	0.231320	−	0.400658i
$636$	22.2935			0.883995
$637$		0			0
$638$	12.8465			0.508600
$639$	−1.58211	+	2.74029i	−0.0625871	+	0.108404i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−17.3523	−	30.0551i	−0.685377	−	1.18711i	−0.973318	−	0.229459i	$-0.926304\pi$
$641$	−17.3523	−	30.0551i	−0.685377	−	1.18711i	0.287942	−	0.957648i	$-0.407029\pi$
$642$	16.7603			0.661477
$643$	−17.1054	−	29.6274i	−0.674570	−	1.16839i	−0.976594	−	0.215089i	$-0.930996\pi$
$643$	−17.1054	−	29.6274i	−0.674570	−	1.16839i	0.302025	−	0.953300i	$-0.402338\pi$
$644$	−11.7017	−	20.2680i	−0.461112	−	0.798669i
$645$	−18.0465			−0.710581
$646$	0.563687	+	0.976335i	0.0221780	+	0.0384134i
$647$	−2.22952	+	3.86164i	−0.0876515	+	0.151817i	−0.906518	−	0.422167i	$-0.861270\pi$
$647$	−2.22952	+	3.86164i	−0.0876515	+	0.151817i	0.818866	+	0.573984i	$0.194603\pi$
$648$	−4.83997	+	8.38307i	−0.190132	+	0.329318i
$649$	−53.3299			−2.09338
$650$		0			0
$651$	24.8310			0.973204
$652$	−2.73825	+	4.74279i	−0.107238	+	0.185742i
$653$	−4.72348	+	8.18131i	−0.184844	+	0.320159i	−0.943524	−	0.331304i	$-0.892511\pi$
$653$	−4.72348	+	8.18131i	−0.184844	+	0.320159i	0.758680	+	0.651464i	$0.225845\pi$
$654$	−0.731250	−	1.26656i	−0.0285941	−	0.0495265i
$655$	−1.34481			−0.0525462
$656$	−1.01961	−	1.76602i	−0.0398093	−	0.0689516i
$657$	−0.860248	−	1.48999i	−0.0335615	−	0.0581302i
$658$	42.1715			1.64402
$659$	8.88889	+	15.3960i	0.346262	+	0.599743i	0.985582	−	0.169197i	$-0.0541175\pi$
$659$	8.88889	+	15.3960i	0.346262	+	0.599743i	−0.639320	+	0.768941i	$0.720784\pi$
$660$	4.00484	−	6.93659i	0.155888	−	0.270007i
$661$	−15.6407	+	27.0905i	−0.608353	+	1.05370i	0.383159	+	0.923683i	$0.374836\pi$
$661$	−15.6407	+	27.0905i	−0.608353	+	1.05370i	−0.991512	+	0.130016i	$0.958497\pi$
$662$	−14.6112			−0.567879
$663$		0			0
$664$	−4.67456			−0.181408
$665$	−0.643104	+	1.11389i	−0.0249385	+	0.0431948i
$666$	−0.923936	+	1.60030i	−0.0358018	+	0.0620105i
$667$	−9.38404	−	16.2536i	−0.363352	−	0.629343i
$668$	−2.68963			−0.104065
$669$	3.85086	+	6.66988i	0.148883	+	0.257872i
$670$	6.99880	+	12.1223i	0.270387	+	0.468325i
$671$	−54.9939			−2.12302
$672$	3.24698	+	5.62393i	0.125255	+	0.216948i
$673$	7.23072	−	12.5240i	0.278724	−	0.482764i	−0.692344	−	0.721567i	$-0.743422\pi$
$673$	7.23072	−	12.5240i	0.278724	−	0.482764i	0.971068	+	0.238804i	$0.0767553\pi$
$674$	−2.22976	+	3.86205i	−0.0858871	+	0.148761i
$675$	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	$0.375112\pi$
$678$	−6.31551	+	10.9388i	−0.242546	+	0.420102i
$679$	7.11960	−	12.3315i	0.273225	−	0.473240i
$680$	−1.57942	−	2.73563i	−0.0605679	−	0.104907i
$681$	17.9366			0.687332
$682$	8.49827	+	14.7194i	0.325416	+	0.563636i
$683$	20.1519	+	34.9041i	0.771091	+	1.33557i	0.936966	+	0.349421i	$0.113622\pi$
$683$	20.1519	+	34.9041i	0.771091	+	1.33557i	−0.165875	+	0.986147i	$0.553045\pi$
$684$	−0.0881460			−0.00337035
$685$	−3.90097	−	6.75668i	−0.149048	−	0.258159i
$686$	1.82371	−	3.15875i	0.0696295	−	0.120602i
$687$	−20.7506	+	35.9411i	−0.791686	+	1.37124i
$688$	10.0151			0.381821
$689$		0			0
$690$	−11.7017			−0.445476
$691$	−0.374117	+	0.647990i	−0.0142321	+	0.0246507i	−0.873054	−	0.487624i	$-0.837864\pi$
$691$	−0.374117	+	0.647990i	−0.0142321	+	0.0246507i	0.858822	+	0.512275i	$0.171197\pi$
$692$	−5.45473	+	9.44787i	−0.207358	+	0.359154i
$693$	1.97823	+	3.42639i	0.0751467	+	0.130158i
$694$	−28.5870			−1.08515
$695$	−6.93631	−	12.0140i	−0.263109	−	0.455719i
$696$	2.60388	+	4.51004i	0.0986996	+	0.170953i
$697$	−6.44158			−0.243992
$698$	−2.43967	−	4.22562i	−0.0923427	−	0.159942i
$699$	16.7310	−	28.9790i	0.632825	−	1.09609i
$700$	1.80194	−	3.12105i	0.0681068	−	0.117965i
$701$	−27.5555			−1.04076			−0.520379	−	0.853935i	$-0.674209\pi$
$701$	−27.5555			−1.04076			−0.520379	+	0.853935i	$0.674209\pi$
$702$		0			0
$703$	2.67025			0.100710
$704$	−2.22252	+	3.84952i	−0.0837644	+	0.145084i
$705$	10.5429	−	18.2608i	0.397068	−	0.687741i
$706$	−2.02984	−	3.51578i	−0.0763939	−	0.132318i
$707$	−54.2103			−2.03879
$708$	−10.8095	−	18.7226i	−0.406245	−	0.703637i
$709$	−3.54527	−	6.14059i	−0.133145	−	0.230615i	0.791742	−	0.610856i	$-0.209174\pi$
$709$	−3.54527	−	6.14059i	−0.133145	−	0.230615i	−0.924887	+	0.380241i	$0.875841\pi$
$710$	−12.8116			−0.480812
$711$	0.725873	+	1.25725i	0.0272224	+	0.0471505i
$712$	4.01089	−	6.94706i	0.150314	−	0.260352i
$713$	12.4155	−	21.5043i	0.464964	−	0.805342i
$714$	20.5133			0.767692
$715$		0			0
$716$	12.9825			0.485180
$717$	−17.0761	+	29.5766i	−0.637717	+	1.10456i
$718$	−2.56033	+	4.43463i	−0.0955509	+	0.165499i
$719$	5.35690	+	9.27842i	0.199779	+	0.346027i	0.948457	−	0.316907i	$-0.102644\pi$
$719$	5.35690	+	9.27842i	0.199779	+	0.346027i	−0.748678	+	0.662934i	$0.769311\pi$
$720$	0.246980			0.00920439
$721$	14.0978	+	24.4182i	0.525031	+	0.909380i
$722$	−9.43631	−	16.3442i	−0.351183	−	0.608267i
$723$	−40.9831			−1.52418
$724$	−11.3666	−	19.6875i	−0.422436	−	0.731680i
$725$	1.44504	−	2.50289i	0.0536675	−	0.0929548i
$726$	−7.89104	+	13.6677i	−0.292864	+	0.507255i
$727$	1.37329			0.0509325			0.0254662	−	0.999676i	$-0.491893\pi$
$727$	1.37329			0.0509325			0.0254662	+	0.999676i	$0.491893\pi$
$728$		0			0
$729$	24.4263			0.904676
$730$	3.48307	−	6.03286i	0.128914	−	0.223286i
$731$	15.8180	−	27.3975i	0.585048	−	1.01333i
$732$	−11.1468	−	19.3067i	−0.411996	−	0.713598i
$733$	−12.6160			−0.465981			−0.232991	−	0.972479i	$-0.574851\pi$
$733$	−12.6160			−0.465981			−0.232991	+	0.972479i	$0.574851\pi$
$734$	−4.64310	−	8.04209i	−0.171380	−	0.296839i
$735$	5.39493	+	9.34429i	0.198995	+	0.344669i
$736$	6.49396			0.239371
$737$	−31.1100	−	53.8841i	−1.14595	−	1.98484i
$738$	0.251824	−	0.436172i	0.00926977	−	0.0160557i
$739$	−18.5688	+	32.1622i	−0.683065	+	1.18310i	0.290975	+	0.956731i	$0.406020\pi$
$739$	−18.5688	+	32.1622i	−0.683065	+	1.18310i	−0.974041	+	0.226373i	$0.927313\pi$
$740$	−7.48188			−0.275039
$741$		0			0
$742$	−44.5870			−1.63684
$743$	−7.52648	+	13.0363i	−0.276120	+	0.478254i	−0.970417	−	0.241435i	$-0.922382\pi$
$743$	−7.52648	+	13.0363i	−0.276120	+	0.478254i	0.694297	+	0.719688i	$0.255715\pi$
$744$	−3.44504	+	5.96699i	−0.126301	+	0.218760i
$745$	−6.33513	−	10.9728i	−0.232101	−	0.402011i
$746$	7.30559			0.267476
$747$	−0.577261	−	0.999845i	−0.0211209	−	0.0365824i
$748$	7.02057	+	12.1600i	0.256698	+	0.444613i
$749$	−33.5206			−1.22482
$750$	−0.900969	−	1.56052i	−0.0328987	−	0.0569823i
$751$	11.1957	−	19.3915i	0.408536	−	0.707605i	−0.586190	−	0.810174i	$-0.699373\pi$
$751$	11.1957	−	19.3915i	0.408536	−	0.707605i	0.994726	+	0.102569i	$0.0327062\pi$
$752$	−5.85086	+	10.1340i	−0.213359	+	0.369548i
$753$	−26.2489			−0.956563
$754$		0			0
$755$	−4.86592			−0.177089
$756$	8.93900	−	15.4828i	0.325108	−	0.563104i
$757$	7.93661	−	13.7466i	0.288461	−	0.499629i	−0.684982	−	0.728560i	$-0.740190\pi$
$757$	7.93661	−	13.7466i	0.288461	−	0.499629i	0.973443	+	0.228931i	$0.0735231\pi$
$758$	−15.2850	−	26.4744i	−0.555177	−	0.961594i
$759$	52.0146			1.88801
$760$	−0.178448	−	0.309081i	−0.00647299	−	0.0112115i
$761$	19.2841	+	33.4011i	0.699048	+	1.21079i	0.968797	+	0.247857i	$0.0797262\pi$
$761$	19.2841	+	33.4011i	0.699048	+	1.21079i	−0.269748	+	0.962931i	$0.586940\pi$
$762$	−21.0073			−0.761014
$763$	1.46250	+	2.53312i	0.0529461	+	0.0917053i
$764$	−9.10992	+	15.7788i	−0.329585	+	0.570858i
$765$	0.390084	−	0.675645i	0.0141035	−	0.0244280i
$766$	−7.93230			−0.286606
$767$		0			0
$768$	−1.80194			−0.0650218
$769$	24.5160	−	42.4630i	0.884070	−	1.53125i	0.0372951	−	0.999304i	$-0.488126\pi$
$769$	24.5160	−	42.4630i	0.884070	−	1.53125i	0.846775	−	0.531951i	$-0.178541\pi$
$770$	−8.00969	+	13.8732i	−0.288649	+	0.499955i
$771$	1.80582	+	3.12778i	0.0650351	+	0.112644i
$772$	18.7482			0.674764
$773$	5.94438	+	10.2960i	0.213804	+	0.370320i	0.952902	−	0.303278i	$-0.0980811\pi$
$773$	5.94438	+	10.2960i	0.213804	+	0.370320i	−0.739098	+	0.673598i	$0.764748\pi$
$774$	1.23676	+	2.14213i	0.0444544	+	0.0769972i
$775$	3.82371			0.137352
$776$	1.97554	+	3.42174i	0.0709178	+	0.122833i
$777$	24.2935	−	42.0776i	0.871525	−	1.50952i
$778$	0.679940	−	1.17769i	0.0243770	−	0.0422222i
$779$	−0.727792			−0.0260759
$780$		0			0
$781$	56.9482			2.03777
$782$	10.2567	−	17.7651i	0.366778	−	0.635278i
$783$	7.16852	−	12.4162i	0.256182	−	0.443720i
$784$	−2.99396	−	5.18569i	−0.106927	−	0.185203i
$785$	−9.42758			−0.336485
$786$	1.21164	+	2.09861i	0.0432176	+	0.0748551i
$787$	1.62833	+	2.82036i	0.0580438	+	0.100535i	0.893587	−	0.448890i	$-0.148180\pi$
$787$	1.62833	+	2.82036i	0.0580438	+	0.100535i	−0.835543	+	0.549424i	$0.814847\pi$
$788$	22.4155			0.798519
$789$	3.97823	+	6.89050i	0.141629	+	0.245308i
$790$	−2.93900	+	5.09050i	−0.104565	+	0.181112i
$791$	12.6310	−	21.8776i	0.449107	−	0.777877i
$792$	−1.09783			−0.0390099
$793$		0			0
$794$	24.6112			0.873418
$795$	−11.1468	+	19.3067i	−0.395335	+	0.684740i
$796$	−8.54288	+	14.7967i	−0.302794	+	0.524455i
$797$	−18.4765	−	32.0022i	−0.654471	−	1.13358i	−0.982026	−	0.188745i	$-0.939558\pi$
$797$	−18.4765	−	32.0022i	−0.654471	−	1.13358i	0.327555	−	0.944832i	$-0.393775\pi$
$798$	2.31767			0.0820445
$799$	18.4819	+	32.0116i	0.653842	+	1.13249i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	1.98121			0.0700027
$802$	2.44773	+	4.23959i	0.0864324	+	0.149705i
$803$	−15.4824	+	26.8163i	−0.546362	+	0.946327i
$804$	12.6114	−	21.8436i	0.444770	−	0.770364i
$805$	23.4034			0.824862
$806$		0			0
$807$	32.7090			1.15141
$808$	7.52111	−	13.0269i	0.264592	−	0.458286i
$809$	2.08599	−	3.61304i	0.0733395	−	0.127028i	−0.827023	−	0.562167i	$-0.809968\pi$
$809$	2.08599	−	3.61304i	0.0733395	−	0.127028i	0.900363	+	0.435140i	$0.143301\pi$
$810$	−4.83997	−	8.38307i	−0.170059	−	0.294551i
$811$	17.0696			0.599396			0.299698	−	0.954034i	$-0.403114\pi$
$811$	17.0696			0.599396			0.299698	+	0.954034i	$0.403114\pi$
$812$	−5.20775	−	9.02009i	−0.182756	−	0.316543i
$813$	−17.5429	−	30.3852i	−0.615256	−	1.06565i
$814$	33.2573			1.16567
$815$	−2.73825	−	4.74279i	−0.0959167	−	0.166133i
$816$	−2.84601	+	4.92944i	−0.0996303	+	0.172565i
$817$	1.78717	−	3.09547i	0.0625251	−	0.108297i
$818$	4.37435			0.152946
$819$		0			0
$820$	2.03923			0.0712130
$821$	−18.9148	+	32.7615i	−0.660132	+	1.14338i	0.320448	+	0.947266i	$0.396167\pi$
$821$	−18.9148	+	32.7615i	−0.660132	+	1.14338i	−0.980581	+	0.196117i	$0.937167\pi$
$822$	−7.02930	+	12.1751i	−0.245175	+	0.424656i
$823$	−20.5362	−	35.5697i	−0.715846	−	1.23988i	−0.962632	−	0.270812i	$-0.912708\pi$
$823$	−20.5362	−	35.5697i	−0.715846	−	1.23988i	0.246786	−	0.969070i	$-0.420625\pi$
$824$	−7.82371			−0.272552
$825$	4.00484	+	6.93659i	0.139431	+	0.241501i
$826$	21.6189	+	37.4451i	0.752219	+	1.30288i
$827$	26.9855			0.938379			0.469189	−	0.883098i	$-0.344546\pi$
$827$	26.9855			0.938379			0.469189	+	0.883098i	$0.344546\pi$
$828$	0.801938	+	1.38900i	0.0278693	+	0.0482710i
$829$	6.08277	−	10.5357i	0.211263	−	0.365919i	−0.740847	−	0.671674i	$-0.765576\pi$
$829$	6.08277	−	10.5357i	0.211263	−	0.365919i	0.952110	+	0.305755i	$0.0989089\pi$
$830$	2.33728	−	4.04829i	0.0811282	−	0.140518i
$831$	33.1487			1.14991
$832$		0			0
$833$	−18.9148			−0.655360
$834$	−12.4988	+	21.6486i	−0.432798	+	0.749628i
$835$	1.34481	−	2.32929i	0.0465392	−	0.0806083i
$836$	0.793209	+	1.37388i	0.0274337	+	0.0475165i
$837$	18.9685			0.655649
$838$	8.37196	+	14.5007i	0.289205	+	0.500917i
$839$	−0.933624	−	1.61708i	−0.0322323	−	0.0558280i	0.849459	−	0.527654i	$-0.176928\pi$
$839$	−0.933624	−	1.61708i	−0.0322323	−	0.0558280i	−0.881692	+	0.471826i	$0.843595\pi$
$840$	−6.49396			−0.224063
$841$	10.3237	+	17.8812i	0.355990	+	0.616593i
$842$	0.241603	−	0.418468i	0.00832618	−	0.0144214i
$843$	−14.3671	+	24.8846i	−0.494830	+	0.857070i
$844$	−5.53079			−0.190378
$845$		0			0
$846$	−2.89008			−0.0993631
$847$	15.7821	−	27.3354i	0.542279	−	0.939255i
$848$	6.18598	−	10.7144i	0.212427	−	0.367935i
$849$	−25.2189	−	43.6805i	−0.865511	−	1.49911i
$850$	3.15883			0.108347
$851$	−24.2935	−	42.0776i	−0.832771	−	1.44240i
$852$	11.5429	+	19.9928i	0.395452	+	0.684944i
$853$	27.7453			0.949979			0.474990	−	0.879991i	$-0.342452\pi$
$853$	27.7453			0.949979			0.474990	+	0.879991i	$0.342452\pi$
$854$	22.2935	+	38.6135i	0.762868	+	1.32133i
$855$	0.0440730	−	0.0763367i	0.00150726	−	0.00261066i
$856$	4.65064	−	8.05514i	0.158955	−	0.275319i
$857$	−24.2553			−0.828547			−0.414273	−	0.910153i	$-0.635964\pi$
$857$	−24.2553			−0.828547			−0.414273	+	0.910153i	$0.635964\pi$
$858$		0			0
$859$	26.1089			0.890823			0.445411	−	0.895326i	$-0.353057\pi$
$859$	26.1089			0.890823			0.445411	+	0.895326i	$0.353057\pi$
$860$	−5.00753	+	8.67330i	−0.170755	+	0.295757i
$861$	−6.62133	+	11.4685i	−0.225654	+	0.390845i
$862$	−5.98792	−	10.3714i	−0.203949	−	0.353251i
$863$	39.5905			1.34768			0.673838	−	0.738880i	$-0.264645\pi$
$863$	39.5905			1.34768			0.673838	+	0.738880i	$0.264645\pi$
$864$	2.48039	+	4.29615i	0.0843844	+	0.146158i
$865$	−5.45473	−	9.44787i	−0.185466	−	0.321237i
$866$	4.15452			0.141176
$867$	−6.32640	−	10.9576i	−0.214856	−	0.372141i
$868$	6.89008	−	11.9340i	0.233865	−	0.405066i
$869$	13.0640	−	22.6275i	0.443165	−	0.767585i
$870$	−5.20775			−0.176559
$871$		0			0
$872$	−0.811626			−0.0274851
$873$	−0.487918	+	0.845099i	−0.0165135	+	0.0286023i
$874$	1.15883	−	2.00716i	0.0391981	−	0.0678932i
$875$	1.80194	+	3.12105i	0.0609166	+	0.105511i
$876$	−12.5526			−0.424112
$877$	20.2543	+	35.0814i	0.683938	+	1.18462i	0.973769	+	0.227538i	$0.0730676\pi$
$877$	20.2543	+	35.0814i	0.683938	+	1.18462i	−0.289831	+	0.957078i	$0.593599\pi$
$878$	−6.25667	−	10.8369i	−0.211152	−	0.365727i
$879$	24.4349			0.824168
$880$	−2.22252	−	3.84952i	−0.0749212	−	0.129767i
$881$	18.1876	−	31.5019i	0.612756	−	1.06132i	−0.378018	−	0.925798i	$-0.623394\pi$
$881$	18.1876	−	31.5019i	0.612756	−	1.06132i	0.990774	−	0.135526i	$-0.0432725\pi$
$882$	0.739447	−	1.28076i	0.0248985	−	0.0431254i
$883$	6.51275			0.219171			0.109586	−	0.993977i	$-0.465048\pi$
$883$	6.51275			0.219171			0.109586	+	0.993977i	$0.465048\pi$
$884$		0			0
$885$	21.6189			0.726713
$886$	−1.13975	+	1.97411i	−0.0382907	+	0.0663215i
$887$	−1.65817	+	2.87203i	−0.0556759	+	0.0964335i	−0.892520	−	0.451008i	$-0.851065\pi$
$887$	−1.65817	+	2.87203i	−0.0556759	+	0.0964335i	0.836844	+	0.547441i	$0.184398\pi$
$888$	6.74094	+	11.6756i	0.226211	+	0.391809i
$889$	42.0146			1.40912
$890$	4.01089	+	6.94706i	0.134445	+	0.232866i
$891$	21.5139	+	37.2631i	0.720742	+	1.24836i
$892$	4.27413			0.143108
$893$	2.08815	+	3.61677i	0.0698771	+	0.121031i
$894$	−11.4155	+	19.7722i	−0.381791	+	0.661282i
$895$	−6.49127	+	11.2432i	−0.216979	+	0.375819i
$896$	3.60388			0.120397
$897$		0			0
$898$	−20.4547			−0.682583
$899$	5.52542	−	9.57030i	0.184283	−	0.319188i
$900$	−0.123490	+	0.213891i	−0.00411633	+	0.00712969i
$901$	−19.5405	−	33.8451i	−0.650988	−	1.12754i
$902$	−9.06446			−0.301813
$903$	−32.5187	−	56.3241i	−1.08216	−	1.87435i
$904$	3.50484	+	6.07057i	0.116569	+	0.201904i
$905$	22.7332			0.755676
$906$	4.38404	+	7.59339i	0.145650	+	0.252273i
$907$	24.1824	−	41.8851i	0.802963	−	1.39077i	−0.114694	−	0.993401i	$-0.536589\pi$
$907$	24.1824	−	41.8851i	0.802963	−	1.39077i	0.917658	−	0.397372i	$-0.130078\pi$
$908$	4.97703	−	8.62047i	0.165169	−	0.286080i
$909$	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	$0.597837\pi$
$912$	−0.321552	+	0.556945i	−0.0106477	+	0.0184423i
$913$	−10.3893	+	17.9948i	−0.343836	+	0.595542i
$914$	8.92154	+	15.4526i	0.295098	+	0.511125i
$915$	22.2935			0.737001
$916$	11.5157	+	19.9458i	0.380490	+	0.659029i
$917$	−2.42327	−	4.19723i	−0.0800235	−	0.138605i
$918$	15.6703			0.517195
$919$	−11.0804	−	19.1918i	−0.365508	−	0.633078i	0.623350	−	0.781943i	$-0.285771\pi$
$919$	−11.0804	−	19.1918i	−0.365508	−	0.633078i	−0.988858	+	0.148865i	$0.952438\pi$
$920$	−3.24698	+	5.62393i	−0.107050	+	0.185416i
$921$	−13.6576	+	23.6557i	−0.450034	+	0.779483i
$922$	−3.52542			−0.116103
$923$		0			0
$924$	28.8659			0.949619
$925$	3.74094	−	6.47950i	0.123001	−	0.213045i
$926$	1.86294	−	3.22670i	0.0612199	−	0.106036i
$927$	−0.966148	−	1.67342i	−0.0317325	−	0.0549622i
$928$	2.89008			0.0948716
$929$	−3.96399	−	6.86584i	−0.130054	−	0.225261i	0.793643	−	0.608384i	$-0.208182\pi$
$929$	−3.96399	−	6.86584i	−0.130054	−	0.225261i	−0.923697	+	0.383123i	$0.874849\pi$
$930$	−3.44504	−	5.96699i	−0.112967	−	0.195665i
$931$	−2.13706			−0.0700394
$932$	−9.28501	−	16.0821i	−0.304141	−	0.526787i
$933$	4.85086	−	8.40193i	0.158810	−	0.275067i
$934$	−6.42878	+	11.1350i	−0.210356	+	0.364347i
$935$	−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	$0.347766\pi$
$938$	−25.2228	+	43.6872i	−0.823554	+	1.42644i
$939$	−14.9438	+	25.8835i	−0.487674	+	0.844676i
$940$	−5.85086	−	10.1340i	−0.190834	−	0.330534i
$941$	−31.4228			−1.02435			−0.512177	−	0.858880i	$-0.671161\pi$
$941$	−31.4228			−1.02435			−0.512177	+	0.858880i	$0.671161\pi$
$942$	8.49396	+	14.7120i	0.276748	+	0.479342i
$943$	6.62133	+	11.4685i	0.215620	+	0.373465i
$944$	−11.9976			−0.390489
$945$	8.93900	+	15.4828i	0.290786	+	0.503656i
$946$	22.2587	−	38.5532i	0.723693	−	1.25347i
$947$	3.98039	−	6.89423i	0.129345	−	0.224032i	−0.794078	−	0.607816i	$-0.792046\pi$
$947$	3.98039	−	6.89423i	0.129345	−	0.224032i	0.923423	+	0.383784i	$0.125379\pi$
$948$	10.5918			0.344005
$949$		0			0
$950$	0.356896			0.0115792
$951$	10.9095	−	18.8957i	0.353764	−	0.612736i
$952$	5.69202	−	9.85887i	0.184479	−	0.319528i
$953$	3.45257	+	5.98003i	0.111840	+	0.193712i	0.916512	−	0.400007i	$-0.130992\pi$
$953$	3.45257	+	5.98003i	0.111840	+	0.193712i	−0.804672	+	0.593719i	$0.797659\pi$
$954$	3.05562			0.0989294
$955$	−9.10992	−	15.7788i	−0.294790	−	0.510591i
$956$	9.47650	+	16.4138i	0.306492	+	0.530860i
$957$	23.1487			0.748290
$958$	−16.9976	−	29.4407i	−0.549168	−	0.951186i
$959$	14.0586	−	24.3502i	0.453976	−	0.786310i
$960$	0.900969	−	1.56052i	0.0290786	−	0.0503657i
$961$	−16.3793			−0.528363
$962$		0			0
$963$	2.29722			0.0740270
$964$	−11.3720	+	19.6968i	−0.366266	+	0.634392i
$965$	−9.37412	+	16.2364i	−0.301764	+	0.522670i
$966$	−21.0858	−	36.5216i	−0.678423	−	1.17506i
$967$	31.3297			1.00750			0.503748	−	0.863850i	$-0.331954\pi$
$967$	31.3297			1.00750			0.503748	+	0.863850i	$0.331954\pi$
$968$	4.37920	+	7.58499i	0.140753	+	0.243791i
$969$	1.01573	+	1.75930i	0.0326299	+	0.0565167i
$970$	−3.95108			−0.126862
$971$	2.45257	+	4.24798i	0.0787069	+	0.136324i	0.902692	−	0.430287i	$-0.141588\pi$
$971$	2.45257	+	4.24798i	0.0787069	+	0.136324i	−0.823985	+	0.566611i	$0.808254\pi$
$972$	−1.28017	+	2.21732i	−0.0410614	+	0.0711204i
$973$	24.9976	−	43.2971i	0.801386	−	1.38804i
$974$	−25.4819			−0.816492
$975$		0			0
$976$	−12.3720			−0.396017
$977$	−6.75816	+	11.7055i	−0.216213	+	0.374491i	−0.953647	−	0.300927i	$-0.902704\pi$
$977$	−6.75816	+	11.7055i	−0.216213	+	0.374491i	0.737434	+	0.675419i	$0.236037\pi$
$978$	−4.93416	+	8.54621i	−0.157777	+	0.273278i
$979$	−17.8286	−	30.8800i	−0.569803	−	0.986928i
$980$	5.98792			0.191277
$981$	−0.100228	−	0.173599i	−0.00320002	−	0.00554260i
$982$	12.8889	+	22.3242i	0.411301	+	0.712394i
$983$	31.7453			1.01252			0.506258	−	0.862382i	$-0.331028\pi$
$983$	31.7453			1.01252			0.506258	+	0.862382i	$0.331028\pi$
$984$	−1.83728	−	3.18226i	−0.0585704	−	0.101447i
$985$	−11.2078	+	19.4124i	−0.357109	+	0.618530i
$986$	4.56465	−	7.90620i	0.145368	−	0.251785i
$987$	75.9904			2.41880
$988$		0			0
$989$	−65.0374			−2.06807
$990$	0.548917	−	0.950753i	0.0174457	−	0.0302169i
$991$	−6.80492	+	11.7865i	−0.216165	+	0.374410i	−0.953632	−	0.300974i	$-0.902688\pi$
$991$	−6.80492	+	11.7865i	−0.216165	+	0.374410i	0.737467	+	0.675383i	$0.236022\pi$
$992$	1.91185	+	3.31143i	0.0607014	+	0.105138i
$993$	−26.3284			−0.835507
$994$	−23.0858	−	39.9857i	−0.732236	−	1.26827i
$995$	−8.54288	−	14.7967i	−0.270827	−	0.469087i
$996$	−8.42327			−0.266902
$997$	19.7060	+	34.1318i	0.624096	+	1.08097i	0.988715	+	0.149809i	$0.0478659\pi$
$997$	19.7060	+	34.1318i	0.624096	+	1.08097i	−0.364619	+	0.931157i	$0.618801\pi$
$998$	−10.8143	+	18.7309i	−0.342321	+	0.592918i
$999$	18.5579	−	32.1433i	0.587147	−	1.01697i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.a.p.1.1	✓	3	13.9	even	3
1690.2.a.r.1.1	yes	3	13.4	even	6
1690.2.d.i.1351.1		6	13.7	odd	12
1690.2.d.i.1351.4		6	13.6	odd	12
1690.2.e.p.191.3		6	13.12	even	2
1690.2.e.p.991.3		6	13.10	even	6
1690.2.e.r.191.3		6	1.1	even	1	trivial
1690.2.e.r.991.3		6	13.3	even	3	inner
1690.2.l.m.361.3		12	13.11	odd	12
1690.2.l.m.361.6		12	13.2	odd	12
1690.2.l.m.1161.3		12	13.5	odd	4
1690.2.l.m.1161.6		12	13.8	odd	4
8450.2.a.bv.1.3		3	65.4	even	6
8450.2.a.cg.1.3		3	65.9	even	6

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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.900969 - 1.56052i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.900969 - 1.56052i) q^{6} +(1.80194 + 3.12105i) q^{7} -1.00000 q^{8} +(-0.123490 - 0.213891i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.22252 + 3.84952i) q^{11} -1.80194 q^{12} +3.60388 q^{14} +(0.900969 - 1.56052i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.57942 + 2.73563i) q^{17} -0.246980 q^{18} +(0.178448 + 0.309081i) q^{19} +(-0.500000 - 0.866025i) q^{20} +6.49396 q^{21} +(2.22252 + 3.84952i) q^{22} +(3.24698 - 5.62393i) q^{23} +(-0.900969 + 1.56052i) q^{24} +1.00000 q^{25} +4.96077 q^{27} +(1.80194 - 3.12105i) q^{28} +(1.44504 - 2.50289i) q^{29} +(-0.900969 - 1.56052i) q^{30} +3.82371 q^{31} +(0.500000 + 0.866025i) q^{32} +(4.00484 + 6.93659i) q^{33} +3.15883 q^{34} +(1.80194 + 3.12105i) q^{35} +(-0.123490 + 0.213891i) q^{36} +(3.74094 - 6.47950i) q^{37} +0.356896 q^{38} -1.00000 q^{40} +(-1.01961 + 1.76602i) q^{41} +(3.24698 - 5.62393i) q^{42} +(-5.00753 - 8.67330i) q^{43} +4.44504 q^{44} +(-0.123490 - 0.213891i) q^{45} +(-3.24698 - 5.62393i) q^{46} +11.7017 q^{47} +(0.900969 + 1.56052i) q^{48} +(-2.99396 + 5.18569i) q^{49} +(0.500000 - 0.866025i) q^{50} +5.69202 q^{51} -12.3720 q^{53} +(2.48039 - 4.29615i) q^{54} +(-2.22252 + 3.84952i) q^{55} +(-1.80194 - 3.12105i) q^{56} +0.643104 q^{57} +(-1.44504 - 2.50289i) q^{58} +(5.99880 + 10.3902i) q^{59} -1.80194 q^{60} +(6.18598 + 10.7144i) q^{61} +(1.91185 - 3.31143i) q^{62} +(0.445042 - 0.770835i) q^{63} +1.00000 q^{64} +8.00969 q^{66} +(-6.99880 + 12.1223i) q^{67} +(1.57942 - 2.73563i) q^{68} +(-5.85086 - 10.1340i) q^{69} +3.60388 q^{70} +(-6.40581 - 11.0952i) q^{71} +(0.123490 + 0.213891i) q^{72} +6.96615 q^{73} +(-3.74094 - 6.47950i) q^{74} +(0.900969 - 1.56052i) q^{75} +(0.178448 - 0.309081i) q^{76} -16.0194 q^{77} -5.87800 q^{79} +(-0.500000 + 0.866025i) q^{80} +(4.83997 - 8.38307i) q^{81} +(1.01961 + 1.76602i) q^{82} +4.67456 q^{83} +(-3.24698 - 5.62393i) q^{84} +(1.57942 + 2.73563i) q^{85} -10.0151 q^{86} +(-2.60388 - 4.51004i) q^{87} +(2.22252 - 3.84952i) q^{88} +(-4.01089 + 6.94706i) q^{89} -0.246980 q^{90} -6.49396 q^{92} +(3.44504 - 5.96699i) q^{93} +(5.85086 - 10.1340i) q^{94} +(0.178448 + 0.309081i) q^{95} +1.80194 q^{96} +(-1.97554 - 3.42174i) q^{97} +(2.99396 + 5.18569i) q^{98} +1.09783 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + q^{3} - 3 q^{4} + 6 q^{5} - q^{6} + 2 q^{7} - 6 q^{8} + 4 q^{9} + 3 q^{10} - 13 q^{11} - 2 q^{12} + 4 q^{14} + q^{15} - 3 q^{16} + q^{17} + 8 q^{18} - 3 q^{19} - 3 q^{20} + 20 q^{21}+ \cdots - 30 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + q^3 - 3 * q^4 + 6 * q^5 - q^6 + 2 * q^7 - 6 * q^8 + 4 * q^9 + 3 * q^10 - 13 * q^11 - 2 * q^12 + 4 * q^14 + q^15 - 3 * q^16 + q^17 + 8 * q^18 - 3 * q^19 - 3 * q^20 + 20 * q^21 + 13 * q^22 + 10 * q^23 - q^24 + 6 * q^25 + 4 * q^27 + 2 * q^28 + 8 * q^29 - q^30 + 8 * q^31 + 3 * q^32 + 2 * q^33 + 2 * q^34 + 2 * q^35 + 4 * q^36 - 6 * q^37 - 6 * q^38 - 6 * q^40 - 19 * q^41 + 10 * q^42 - 5 * q^43 + 26 * q^44 + 4 * q^45 - 10 * q^46 + 16 * q^47 + q^48 + q^49 + 3 * q^50 + 24 * q^51 - 16 * q^53 + 2 * q^54 - 13 * q^55 - 2 * q^56 + 12 * q^57 - 8 * q^58 - 5 * q^59 - 2 * q^60 + 8 * q^61 + 4 * q^62 + 2 * q^63 + 6 * q^64 + 4 * q^66 - q^67 + q^68 - 8 * q^69 + 4 * q^70 - 12 * q^71 - 4 * q^72 + 10 * q^73 + 6 * q^74 + q^75 - 3 * q^76 - 8 * q^77 + 4 * q^79 - 3 * q^80 + 5 * q^81 + 19 * q^82 - 14 * q^83 - 10 * q^84 + q^85 - 10 * q^86 + 2 * q^87 + 13 * q^88 - 21 * q^89 + 8 * q^90 - 20 * q^92 + 20 * q^93 + 8 * q^94 - 3 * q^95 + 2 * q^96 - 21 * q^97 - q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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