LMFDB - Embedded newform 1690.2.e.p.191.1

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			191.1
Root			$-0.623490 + 1.07992i$ of defining polynomial
Character	$\chi$	$=$	1690.191
Dual form			1690.2.e.p.991.1

$q$-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} +(-0.623490 + 1.07992i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-0.623490 - 1.07992i) q^{6} +(1.24698 + 2.15983i) q^{7} +1.00000 q^{8} +(0.722521 + 1.25144i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.90097 - 5.02463i) q^{11} +1.24698 q^{12} -2.49396 q^{14} +(0.623490 - 1.07992i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.14795 - 3.72036i) q^{17} -1.44504 q^{18} +(2.02446 + 3.50647i) q^{19} +(0.500000 + 0.866025i) q^{20} -3.10992 q^{21} +(2.90097 + 5.02463i) q^{22} +(1.55496 - 2.69327i) q^{23} +(-0.623490 + 1.07992i) q^{24} +1.00000 q^{25} -5.54288 q^{27} +(1.24698 - 2.15983i) q^{28} +(2.80194 - 4.85310i) q^{29} +(0.623490 + 1.07992i) q^{30} +7.70171 q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.61745 + 6.26561i) q^{33} +4.29590 q^{34} +(-1.24698 - 2.15983i) q^{35} +(0.722521 - 1.25144i) q^{36} +(1.33513 - 2.31251i) q^{37} -4.04892 q^{38} -1.00000 q^{40} +(6.27144 - 10.8624i) q^{41} +(1.55496 - 2.69327i) q^{42} +(-3.49127 - 6.04706i) q^{43} -5.80194 q^{44} +(-0.722521 - 1.25144i) q^{45} +(1.55496 + 2.69327i) q^{46} +3.87800 q^{47} +(-0.623490 - 1.07992i) q^{48} +(0.390084 - 0.675645i) q^{49} +(-0.500000 + 0.866025i) q^{50} +5.35690 q^{51} -4.93362 q^{53} +(2.77144 - 4.80027i) q^{54} +(-2.90097 + 5.02463i) q^{55} +(1.24698 + 2.15983i) q^{56} -5.04892 q^{57} +(2.80194 + 4.85310i) q^{58} +(5.00753 + 8.67330i) q^{59} -1.24698 q^{60} +(2.46681 + 4.27264i) q^{61} +(-3.85086 + 6.66988i) q^{62} +(-1.80194 + 3.12105i) q^{63} +1.00000 q^{64} -7.23490 q^{66} +(-4.00753 + 6.94125i) q^{67} +(-2.14795 + 3.72036i) q^{68} +(1.93900 + 3.35845i) q^{69} +2.49396 q^{70} +(-2.74094 - 4.74745i) q^{71} +(0.722521 + 1.25144i) q^{72} -8.67456 q^{73} +(1.33513 + 2.31251i) q^{74} +(-0.623490 + 1.07992i) q^{75} +(2.02446 - 3.50647i) q^{76} +14.4698 q^{77} -1.82371 q^{79} +(0.500000 - 0.866025i) q^{80} +(1.28836 - 2.23151i) q^{81} +(6.27144 + 10.8624i) q^{82} +14.6407 q^{83} +(1.55496 + 2.69327i) q^{84} +(2.14795 + 3.72036i) q^{85} +6.98254 q^{86} +(3.49396 + 6.05171i) q^{87} +(2.90097 - 5.02463i) q^{88} +(-0.227365 + 0.393808i) q^{89} +1.44504 q^{90} -3.10992 q^{92} +(-4.80194 + 8.31720i) q^{93} +(-1.93900 + 3.35845i) q^{94} +(-2.02446 - 3.50647i) q^{95} +1.24698 q^{96} +(4.34601 + 7.52751i) q^{97} +(0.390084 + 0.675645i) q^{98} +8.38404 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
$3$	−0.623490	+	1.07992i	−0.359972	+	0.623490i	−0.987956	−	0.154737i	$-0.950547\pi$
$3$	−0.623490	+	1.07992i	−0.359972	+	0.623490i	0.627984	+	0.778226i	$0.283880\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.623490	−	1.07992i	−0.254539	−	0.440874i
$7$	1.24698	+	2.15983i	0.471314	+	0.816340i	0.999462	−	0.0328129i	$-0.0104465\pi$
$7$	1.24698	+	2.15983i	0.471314	+	0.816340i	−0.528148	+	0.849153i	$0.677113\pi$
$8$	1.00000			0.353553
$9$	0.722521	+	1.25144i	0.240840	+	0.417148i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	2.90097	−	5.02463i	0.874675	−	1.51498i	0.0175665	−	0.999846i	$-0.494408\pi$
$11$	2.90097	−	5.02463i	0.874675	−	1.51498i	0.857109	−	0.515136i	$-0.172259\pi$
$12$	1.24698			0.359972
$13$		0			0
$13$		0			0
$14$	−2.49396			−0.666539
$15$	0.623490	−	1.07992i	0.160984	−	0.278833i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.14795	−	3.72036i	−0.520954	−	0.902319i	−0.999703	−	0.0243671i	$-0.992243\pi$
$17$	−2.14795	−	3.72036i	−0.520954	−	0.902319i	0.478749	−	0.877952i	$-0.341090\pi$
$18$	−1.44504			−0.340600
$19$	2.02446	+	3.50647i	0.464443	+	0.804438i	0.999176	−	0.0405824i	$-0.0129213\pi$
$19$	2.02446	+	3.50647i	0.464443	+	0.804438i	−0.534734	+	0.845021i	$0.679588\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−3.10992			−0.678639
$22$	2.90097	+	5.02463i	0.618489	+	1.07125i
$23$	1.55496	−	2.69327i	0.324231	−	0.561585i	−0.657125	−	0.753781i	$-0.728228\pi$
$23$	1.55496	−	2.69327i	0.324231	−	0.561585i	0.981356	+	0.192196i	$0.0615611\pi$
$24$	−0.623490	+	1.07992i	−0.127269	+	0.220437i
$25$	1.00000			0.200000
$26$		0			0
$27$	−5.54288			−1.06673
$28$	1.24698	−	2.15983i	0.235657	−	0.408170i
$29$	2.80194	−	4.85310i	0.520307	−	0.901198i	−0.479414	−	0.877589i	$-0.659151\pi$
$29$	2.80194	−	4.85310i	0.520307	−	0.901198i	0.999721	−	0.0236092i	$-0.00751573\pi$
$30$	0.623490	+	1.07992i	0.113833	+	0.197165i
$31$	7.70171			1.38327			0.691634	−	0.722248i	$-0.256891\pi$
$31$	7.70171			1.38327			0.691634	+	0.722248i	$0.256891\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	3.61745	+	6.26561i	0.629717	+	1.09070i
$34$	4.29590			0.736740
$35$	−1.24698	−	2.15983i	−0.210778	−	0.365078i
$36$	0.722521	−	1.25144i	0.120420	−	0.208574i
$37$	1.33513	−	2.31251i	0.219493	−	0.380174i	−0.735160	−	0.677894i	$-0.762893\pi$
$37$	1.33513	−	2.31251i	0.219493	−	0.380174i	0.954653	+	0.297720i	$0.0962263\pi$
$38$	−4.04892			−0.656821
$39$		0			0
$40$	−1.00000			−0.158114
$41$	6.27144	−	10.8624i	0.979434	−	1.69643i	0.314984	−	0.949097i	$-0.398001\pi$
$41$	6.27144	−	10.8624i	0.979434	−	1.69643i	0.664450	−	0.747333i	$-0.268666\pi$
$42$	1.55496	−	2.69327i	0.239935	−	0.415580i
$43$	−3.49127	−	6.04706i	−0.532414	−	0.922168i	−0.999284	−	0.0378418i	$-0.987952\pi$
$43$	−3.49127	−	6.04706i	−0.532414	−	0.922168i	0.466870	−	0.884326i	$-0.345382\pi$
$44$	−5.80194			−0.874675
$45$	−0.722521	−	1.25144i	−0.107707	−	0.186554i
$46$	1.55496	+	2.69327i	0.229266	+	0.397100i
$47$	3.87800			0.565665			0.282832	−	0.959169i	$-0.408726\pi$
$47$	3.87800			0.565665			0.282832	+	0.959169i	$0.408726\pi$
$48$	−0.623490	−	1.07992i	−0.0899930	−	0.155872i
$49$	0.390084	−	0.675645i	0.0557262	−	0.0965207i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	5.35690			0.750115
$52$		0			0
$53$	−4.93362			−0.677685			−0.338843	−	0.940843i	$-0.610035\pi$
$53$	−4.93362			−0.677685			−0.338843	+	0.940843i	$0.610035\pi$
$54$	2.77144	−	4.80027i	0.377145	−	0.653234i
$55$	−2.90097	+	5.02463i	−0.391167	+	0.677520i
$56$	1.24698	+	2.15983i	0.166635	+	0.288620i
$57$	−5.04892			−0.668745
$58$	2.80194	+	4.85310i	0.367912	+	0.637243i
$59$	5.00753	+	8.67330i	0.651925	+	1.12917i	0.982655	+	0.185442i	$0.0593717\pi$
$59$	5.00753	+	8.67330i	0.651925	+	1.12917i	−0.330730	+	0.943725i	$0.607295\pi$
$60$	−1.24698			−0.160984
$61$	2.46681	+	4.27264i	0.315843	+	0.547056i	0.979616	−	0.200878i	$-0.0643794\pi$
$61$	2.46681	+	4.27264i	0.315843	+	0.547056i	−0.663773	+	0.747934i	$0.731046\pi$
$62$	−3.85086	+	6.66988i	−0.489059	+	0.847075i
$63$	−1.80194	+	3.12105i	−0.227023	+	0.393215i
$64$	1.00000			0.125000
$65$		0			0
$66$	−7.23490			−0.890554
$67$	−4.00753	+	6.94125i	−0.489598	+	0.848009i	−0.999928	−	0.0119698i	$-0.996190\pi$
$67$	−4.00753	+	6.94125i	−0.489598	+	0.848009i	0.510330	+	0.859978i	$0.329523\pi$
$68$	−2.14795	+	3.72036i	−0.260477	+	0.451159i
$69$	1.93900	+	3.35845i	0.233428	+	0.404310i
$70$	2.49396			0.298085
$71$	−2.74094	−	4.74745i	−0.325290	−	0.563418i	0.656281	−	0.754516i	$-0.272128\pi$
$71$	−2.74094	−	4.74745i	−0.325290	−	0.563418i	−0.981571	+	0.191098i	$0.938795\pi$
$72$	0.722521	+	1.25144i	0.0851499	+	0.147484i
$73$	−8.67456			−1.01528			−0.507640	−	0.861569i	$-0.669482\pi$
$73$	−8.67456			−1.01528			−0.507640	+	0.861569i	$0.669482\pi$
$74$	1.33513	+	2.31251i	0.155205	+	0.268823i
$75$	−0.623490	+	1.07992i	−0.0719944	+	0.124698i
$76$	2.02446	−	3.50647i	0.232221	−	0.402219i
$77$	14.4698			1.64899
$78$		0			0
$79$	−1.82371			−0.205183			−0.102592	−	0.994724i	$-0.532713\pi$
$79$	−1.82371			−0.205183			−0.102592	+	0.994724i	$0.532713\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	1.28836	−	2.23151i	0.143152	−	0.247946i
$82$	6.27144	+	10.8624i	0.692564	+	1.19956i
$83$	14.6407			1.60703			0.803513	−	0.595287i	$-0.202961\pi$
$83$	14.6407			1.60703			0.803513	+	0.595287i	$0.202961\pi$
$84$	1.55496	+	2.69327i	0.169660	+	0.293859i
$85$	2.14795	+	3.72036i	0.232978	+	0.403529i
$86$	6.98254			0.752947
$87$	3.49396	+	6.05171i	0.374592	+	0.648812i
$88$	2.90097	−	5.02463i	0.309244	−	0.535627i
$89$	−0.227365	+	0.393808i	−0.0241007	+	0.0417436i	−0.877824	−	0.478983i	$-0.841006\pi$
$89$	−0.227365	+	0.393808i	−0.0241007	+	0.0417436i	0.853724	+	0.520727i	$0.174339\pi$
$90$	1.44504			0.152321
$91$		0			0
$92$	−3.10992			−0.324231
$93$	−4.80194	+	8.31720i	−0.497938	+	0.862453i
$94$	−1.93900	+	3.35845i	−0.199993	+	0.346398i
$95$	−2.02446	−	3.50647i	−0.207705	−	0.359756i
$96$	1.24698			0.127269
$97$	4.34601	+	7.52751i	0.441271	+	0.764303i	0.997784	−	0.0665356i	$-0.0211946\pi$
$97$	4.34601	+	7.52751i	0.441271	+	0.764303i	−0.556514	+	0.830839i	$0.687861\pi$
$98$	0.390084	+	0.675645i	0.0394044	+	0.0682504i
$99$	8.38404			0.842628
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−7.87263	+	13.6358i	−0.783355	+	1.35681i	0.146621	+	0.989193i	$0.453160\pi$
$101$	−7.87263	+	13.6358i	−0.783355	+	1.35681i	−0.929977	+	0.367619i	$0.880173\pi$
$102$	−2.67845	+	4.63921i	−0.265206	+	0.459350i
$103$	−3.70171			−0.364740			−0.182370	−	0.983230i	$-0.558377\pi$
$103$	−3.70171			−0.364740			−0.182370	+	0.983230i	$0.558377\pi$
$104$		0			0
$105$	3.10992			0.303497
$106$	2.46681	−	4.27264i	0.239598	−	0.414996i
$107$	−7.54019	+	13.0600i	−0.728938	+	1.26256i	0.228395	+	0.973569i	$0.426652\pi$
$107$	−7.54019	+	13.0600i	−0.728938	+	1.26256i	−0.957333	+	0.288988i	$0.906681\pi$
$108$	2.77144	+	4.80027i	0.266682	+	0.461906i
$109$	17.4819			1.67446			0.837230	−	0.546851i	$-0.184173\pi$
$109$	17.4819			1.67446			0.837230	+	0.546851i	$0.184173\pi$
$110$	−2.90097	−	5.02463i	−0.276597	−	0.479079i
$111$	1.66487	+	2.88365i	0.158023	+	0.273704i
$112$	−2.49396			−0.235657
$113$	4.11745	+	7.13163i	0.387337	+	0.670887i	0.992090	−	0.125525i	$-0.0400617\pi$
$113$	4.11745	+	7.13163i	0.387337	+	0.670887i	−0.604753	+	0.796413i	$0.706728\pi$
$114$	2.52446	−	4.37249i	0.236437	−	0.409521i
$115$	−1.55496	+	2.69327i	−0.145001	+	0.251148i
$116$	−5.60388			−0.520307
$117$		0			0
$118$	−10.0151			−0.921962
$119$	5.35690	−	9.27842i	0.491066	−	0.850551i
$120$	0.623490	−	1.07992i	0.0569166	−	0.0985824i
$121$	−11.3312	−	19.6263i	−1.03011	−	1.78421i
$122$	−4.93362			−0.446669
$123$	7.82036	+	13.5453i	0.705138	+	1.22133i
$124$	−3.85086	−	6.66988i	−0.345817	−	0.598973i
$125$	−1.00000			−0.0894427
$126$	−1.80194	−	3.12105i	−0.160529	−	0.278045i
$127$	6.51573	−	11.2856i	0.578177	−	1.00143i	−0.417511	−	0.908672i	$-0.637097\pi$
$127$	6.51573	−	11.2856i	0.578177	−	1.00143i	0.995688	−	0.0927609i	$-0.0295692\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	8.70709			0.766616
$130$		0			0
$131$	9.82908			0.858771			0.429386	−	0.903121i	$-0.358730\pi$
$131$	9.82908			0.858771			0.429386	+	0.903121i	$0.358730\pi$
$132$	3.61745	−	6.26561i	0.314859	−	0.545351i
$133$	−5.04892	+	8.74498i	−0.437797	+	0.758286i
$134$	−4.00753	−	6.94125i	−0.346198	−	0.599633i
$135$	5.54288			0.477055
$136$	−2.14795	−	3.72036i	−0.184185	−	0.319018i
$137$	2.37651	+	4.11624i	0.203039	+	0.351674i	0.949506	−	0.313748i	$-0.101585\pi$
$137$	2.37651	+	4.11624i	0.203039	+	0.351674i	−0.746467	+	0.665422i	$0.768252\pi$
$138$	−3.87800			−0.330117
$139$	1.19687	+	2.07303i	0.101517	+	0.175832i	0.912310	−	0.409501i	$-0.134297\pi$
$139$	1.19687	+	2.07303i	0.101517	+	0.175832i	−0.810793	+	0.585333i	$0.800964\pi$
$140$	−1.24698	+	2.15983i	−0.105389	+	0.182539i
$141$	−2.41789	+	4.18792i	−0.203623	+	0.352686i
$142$	5.48188			0.460029
$143$		0			0
$144$	−1.44504			−0.120420
$145$	−2.80194	+	4.85310i	−0.232688	+	0.403028i
$146$	4.33728	−	7.51239i	0.358956	−	0.621730i
$147$	0.486426	+	0.842515i	0.0401198	+	0.0694895i
$148$	−2.67025			−0.219493
$149$	10.4058	+	18.0234i	0.852477	+	1.47653i	0.878966	+	0.476885i	$0.158234\pi$
$149$	10.4058	+	18.0234i	0.852477	+	1.47653i	−0.0264882	+	0.999649i	$0.508432\pi$
$150$	−0.623490	−	1.07992i	−0.0509077	−	0.0881748i
$151$	−5.95646			−0.484730			−0.242365	−	0.970185i	$-0.577923\pi$
$151$	−5.95646			−0.484730			−0.242365	+	0.970185i	$0.577923\pi$
$152$	2.02446	+	3.50647i	0.164205	+	0.284412i
$153$	3.10388	−	5.37607i	0.250933	−	0.434630i
$154$	−7.23490	+	12.5312i	−0.583005	+	1.00979i
$155$	−7.70171			−0.618616
$156$		0			0
$157$	8.19567			0.654086			0.327043	−	0.945010i	$-0.393948\pi$
$157$	8.19567			0.654086			0.327043	+	0.945010i	$0.393948\pi$
$158$	0.911854	−	1.57938i	0.0725432	−	0.125649i
$159$	3.07606	−	5.32790i	0.243948	−	0.422530i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	7.75600			0.611259
$162$	1.28836	+	2.23151i	0.101223	+	0.175324i
$163$	−8.44385	−	14.6252i	−0.661373	−	1.14553i	−0.980255	−	0.197737i	$-0.936641\pi$
$163$	−8.44385	−	14.6252i	−0.661373	−	1.14553i	0.318882	−	0.947794i	$-0.396693\pi$
$164$	−12.5429			−0.979434
$165$	−3.61745	−	6.26561i	−0.281618	−	0.487777i
$166$	−7.32036	+	12.6792i	−0.568170	+	0.984099i
$167$	9.82908	−	17.0245i	0.760597	−	1.31739i	−0.181946	−	0.983309i	$-0.558239\pi$
$167$	9.82908	−	17.0245i	0.760597	−	1.31739i	0.942543	−	0.334085i	$-0.108427\pi$
$168$	−3.10992			−0.239935
$169$		0			0
$170$	−4.29590			−0.329480
$171$	−2.92543	+	5.06699i	−0.223713	+	0.387482i
$172$	−3.49127	+	6.04706i	−0.266207	+	0.461084i
$173$	8.43296	+	14.6063i	0.641146	+	1.11050i	0.985177	+	0.171539i	$0.0548741\pi$
$173$	8.43296	+	14.6063i	0.641146	+	1.11050i	−0.344031	+	0.938958i	$0.611793\pi$
$174$	−6.98792			−0.529753
$175$	1.24698	+	2.15983i	0.0942628	+	0.163268i
$176$	2.90097	+	5.02463i	0.218669	+	0.378745i
$177$	−12.4886			−0.938699
$178$	−0.227365	−	0.393808i	−0.0170417	−	0.0295172i
$179$	2.99880	−	5.19408i	0.224141	−	0.388224i	−0.731920	−	0.681390i	$-0.761376\pi$
$179$	2.99880	−	5.19408i	0.224141	−	0.388224i	0.956061	+	0.293166i	$0.0947090\pi$
$180$	−0.722521	+	1.25144i	−0.0538535	+	0.0932771i
$181$	−16.5676			−1.23146			−0.615731	−	0.787956i	$-0.711139\pi$
$181$	−16.5676			−1.23146			−0.615731	+	0.787956i	$0.711139\pi$
$182$		0			0
$183$	−6.15213			−0.454778
$184$	1.55496	−	2.69327i	0.114633	−	0.198550i
$185$	−1.33513	+	2.31251i	−0.0981604	+	0.170019i
$186$	−4.80194	−	8.31720i	−0.352095	−	0.609847i
$187$	−24.9245			−1.82266
$188$	−1.93900	−	3.35845i	−0.141416	−	0.244940i
$189$	−6.91185	−	11.9717i	−0.502763	−	0.870812i
$190$	4.04892			0.293739
$191$	−6.39612	−	11.0784i	−0.462807	−	0.801606i	0.536292	−	0.844032i	$-0.319824\pi$
$191$	−6.39612	−	11.0784i	−0.462807	−	0.801606i	−0.999100	+	0.0424265i	$0.986491\pi$
$192$	−0.623490	+	1.07992i	−0.0449965	+	0.0779362i
$193$	−11.7925	+	20.4253i	−0.848846	+	1.47024i	0.0333930	+	0.999442i	$0.489369\pi$
$193$	−11.7925	+	20.4253i	−0.848846	+	1.47024i	−0.882239	+	0.470802i	$0.843965\pi$
$194$	−8.69202			−0.624051
$195$		0			0
$196$	−0.780167			−0.0557262
$197$	−0.987918	+	1.71112i	−0.0703863	+	0.121913i	−0.899071	−	0.437804i	$-0.855757\pi$
$197$	−0.987918	+	1.71112i	−0.0703863	+	0.121913i	0.828684	+	0.559716i	$0.189090\pi$
$198$	−4.19202	+	7.26079i	−0.297914	+	0.516002i
$199$	−0.417895	−	0.723815i	−0.0296238	−	0.0513099i	0.850833	−	0.525436i	$-0.176098\pi$
$199$	−0.417895	−	0.723815i	−0.0296238	−	0.0513099i	−0.880457	+	0.474126i	$0.842764\pi$
$200$	1.00000			0.0707107
$201$	−4.99731	−	8.65560i	−0.352483	−	0.610519i
$202$	−7.87263	−	13.6358i	−0.553916	−	0.959411i
$203$	13.9758			0.980911
$204$	−2.67845	−	4.63921i	−0.187529	−	0.324810i
$205$	−6.27144	+	10.8624i	−0.438016	+	0.758666i
$206$	1.85086	−	3.20578i	0.128955	−	0.223357i
$207$	4.49396			0.312352
$208$		0			0
$209$	23.4916			1.62495
$210$	−1.55496	+	2.69327i	−0.107302	+	0.185853i
$211$	−4.68114	+	8.10797i	−0.322263	+	0.558175i	−0.980955	−	0.194237i	$-0.937777\pi$
$211$	−4.68114	+	8.10797i	−0.322263	+	0.558175i	0.658692	+	0.752413i	$0.271110\pi$
$212$	2.46681	+	4.27264i	0.169421	+	0.293446i
$213$	6.83579			0.468381
$214$	−7.54019	−	13.0600i	−0.515437	−	0.892762i
$215$	3.49127	+	6.04706i	0.238103	+	0.412406i
$216$	−5.54288			−0.377145
$217$	9.60388	+	16.6344i	0.651954	+	1.12922i
$218$	−8.74094	+	15.1398i	−0.592011	+	1.02539i
$219$	5.40850	−	9.36780i	0.365473	−	0.633017i
$220$	5.80194			0.391167
$221$		0			0
$222$	−3.32975			−0.223478
$223$	3.15883	−	5.47126i	0.211531	−	0.366383i	−0.740663	−	0.671877i	$-0.765488\pi$
$223$	3.15883	−	5.47126i	0.211531	−	0.366383i	0.952194	+	0.305494i	$0.0988217\pi$
$224$	1.24698	−	2.15983i	0.0833173	−	0.144310i
$225$	0.722521	+	1.25144i	0.0481681	+	0.0834295i
$226$	−8.23490			−0.547777
$227$	−2.44720	−	4.23867i	−0.162426	−	0.281330i	0.773312	−	0.634026i	$-0.218599\pi$
$227$	−2.44720	−	4.23867i	−0.162426	−	0.281330i	−0.935738	+	0.352695i	$0.885265\pi$
$228$	2.52446	+	4.37249i	0.167186	+	0.289575i
$229$	−0.689629			−0.0455719			−0.0227860	−	0.999740i	$-0.507254\pi$
$229$	−0.689629			−0.0455719			−0.0227860	+	0.999740i	$0.507254\pi$
$230$	−1.55496	−	2.69327i	−0.102531	−	0.177589i
$231$	−9.02177	+	15.6262i	−0.593589	+	1.02813i
$232$	2.80194	−	4.85310i	0.183956	−	0.318622i
$233$	14.1806			0.929002			0.464501	−	0.885573i	$-0.346234\pi$
$233$	14.1806			0.929002			0.464501	+	0.885573i	$0.346234\pi$
$234$		0			0
$235$	−3.87800			−0.252973
$236$	5.00753	−	8.67330i	0.325963	−	0.564584i
$237$	1.13706	−	1.96945i	0.0738602	−	0.127930i
$238$	5.35690	+	9.27842i	0.347236	+	0.601430i
$239$	−25.7754			−1.66727			−0.833635	−	0.552315i	$-0.813745\pi$
$239$	−25.7754			−1.66727			−0.833635	+	0.552315i	$0.813745\pi$
$240$	0.623490	+	1.07992i	0.0402461	+	0.0697083i
$241$	3.93362	+	6.81324i	0.253387	+	0.438879i	0.964456	−	0.264243i	$-0.0851221\pi$
$241$	3.93362	+	6.81324i	0.253387	+	0.438879i	−0.711069	+	0.703122i	$0.751789\pi$
$242$	22.6625			1.45680
$243$	−6.70775	−	11.6182i	−0.430302	−	0.745306i
$244$	2.46681	−	4.27264i	0.157921	−	0.273528i
$245$	−0.390084	+	0.675645i	−0.0249215	+	0.0431654i
$246$	−15.6407			−0.997215
$247$		0			0
$248$	7.70171			0.489059
$249$	−9.12833	+	15.8107i	−0.578485	+	1.00196i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−9.98911	−	17.3017i	−0.630507	−	1.09207i	−0.987448	−	0.157944i	$-0.949514\pi$
$251$	−9.98911	−	17.3017i	−0.630507	−	1.09207i	0.356941	−	0.934127i	$-0.383820\pi$
$252$	3.60388			0.227023
$253$	−9.02177	−	15.6262i	−0.567194	−	0.982409i
$254$	6.51573	+	11.2856i	0.408833	+	0.708120i
$255$	−5.35690			−0.335462
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.7262	−	22.0424i	0.793837	−	1.37497i	−0.129739	−	0.991548i	$-0.541414\pi$
$257$	12.7262	−	22.0424i	0.793837	−	1.37497i	0.923575	−	0.383417i	$-0.125253\pi$
$258$	−4.35354	+	7.54056i	−0.271040	+	0.469455i
$259$	6.65950			0.413801
$260$		0			0
$261$	8.09783			0.501243
$262$	−4.91454	+	8.51224i	−0.303621	+	0.525888i
$263$	9.98792	−	17.2996i	0.615881	−	1.06674i	−0.374348	−	0.927288i	$-0.622133\pi$
$263$	9.98792	−	17.2996i	0.615881	−	1.06674i	0.990229	−	0.139450i	$-0.0445333\pi$
$264$	3.61745	+	6.26561i	0.222639	+	0.385621i
$265$	4.93362			0.303070
$266$	−5.04892	−	8.74498i	−0.309569	−	0.536189i
$267$	−0.283520	−	0.491071i	−0.0173511	−	0.0300530i
$268$	8.01507			0.489598
$269$	8.07069	+	13.9788i	0.492079	+	0.852305i	0.999958	−	0.00912292i	$-0.00290396\pi$
$269$	8.07069	+	13.9788i	0.492079	+	0.852305i	−0.507880	+	0.861428i	$0.669571\pi$
$270$	−2.77144	+	4.80027i	−0.168664	+	0.292135i
$271$	7.55257	−	13.0814i	0.458786	−	0.794640i	−0.540111	−	0.841594i	$-0.681618\pi$
$271$	7.55257	−	13.0814i	0.458786	−	0.794640i	0.998897	+	0.0469534i	$0.0149512\pi$
$272$	4.29590			0.260477
$273$		0			0
$274$	−4.75302			−0.287140
$275$	2.90097	−	5.02463i	0.174935	−	0.302996i
$276$	1.93900	−	3.35845i	0.116714	−	0.202155i
$277$	12.2470	+	21.2124i	0.735850	+	1.27453i	0.954350	+	0.298692i	$0.0965503\pi$
$277$	12.2470	+	21.2124i	0.735850	+	1.27453i	−0.218500	+	0.975837i	$0.570116\pi$
$278$	−2.39373			−0.143566
$279$	5.56465	+	9.63825i	0.333147	+	0.577027i
$280$	−1.24698	−	2.15983i	−0.0745213	−	0.129075i
$281$	−23.3381			−1.39223			−0.696117	−	0.717928i	$-0.745091\pi$
$281$	−23.3381			−1.39223			−0.696117	+	0.717928i	$0.745091\pi$
$282$	−2.41789	−	4.18792i	−0.143984	−	0.249387i
$283$	5.71110	−	9.89192i	0.339490	−	0.588014i	−0.644847	−	0.764312i	$-0.723079\pi$
$283$	5.71110	−	9.89192i	0.339490	−	0.588014i	0.984337	+	0.176298i	$0.0564122\pi$
$284$	−2.74094	+	4.74745i	−0.162645	+	0.281709i
$285$	5.04892			0.299072
$286$		0			0
$287$	31.2814			1.84648
$288$	0.722521	−	1.25144i	0.0425750	−	0.0737420i
$289$	−0.727365	+	1.25983i	−0.0427862	+	0.0741079i
$290$	−2.80194	−	4.85310i	−0.164535	−	0.284984i
$291$	−10.8388			−0.635380
$292$	4.33728	+	7.51239i	0.253820	+	0.439629i
$293$	−12.2078	−	21.1444i	−0.713184	−	1.23527i	−0.963656	−	0.267148i	$-0.913919\pi$
$293$	−12.2078	−	21.1444i	−0.713184	−	1.23527i	0.250471	−	0.968124i	$-0.419414\pi$
$294$	−0.972853			−0.0567379
$295$	−5.00753	−	8.67330i	−0.291550	−	0.504979i
$296$	1.33513	−	2.31251i	0.0776026	−	0.134412i
$297$	−16.0797	+	27.8509i	−0.933040	+	1.61607i
$298$	−20.8116			−1.20559
$299$		0			0
$300$	1.24698			0.0719944
$301$	8.70709	−	15.0811i	0.501868	−	0.869261i
$302$	2.97823	−	5.15845i	0.171378	−	0.296835i
$303$	−9.81700	−	17.0035i	−0.563972	−	0.976828i
$304$	−4.04892			−0.232221
$305$	−2.46681	−	4.27264i	−0.141249	−	0.244651i
$306$	3.10388	+	5.37607i	0.177437	+	0.307329i
$307$	7.70410			0.439696			0.219848	−	0.975534i	$-0.429444\pi$
$307$	7.70410			0.439696			0.219848	+	0.975534i	$0.429444\pi$
$308$	−7.23490	−	12.5312i	−0.412247	−	0.714032i
$309$	2.30798	−	3.99754i	0.131296	−	0.227412i
$310$	3.85086	−	6.66988i	0.218714	−	0.378824i
$311$	4.71379			0.267295			0.133647	−	0.991029i	$-0.457331\pi$
$311$	4.71379			0.267295			0.133647	+	0.991029i	$0.457331\pi$
$312$		0			0
$313$	8.49157			0.479972			0.239986	−	0.970776i	$-0.422857\pi$
$313$	8.49157			0.479972			0.239986	+	0.970776i	$0.422857\pi$
$314$	−4.09783	+	7.09766i	−0.231254	+	0.400544i
$315$	1.80194	−	3.12105i	0.101528	−	0.175851i
$316$	0.911854	+	1.57938i	0.0512958	+	0.0888469i
$317$	−27.0508			−1.51933			−0.759663	−	0.650317i	$-0.774636\pi$
$317$	−27.0508			−1.51933			−0.759663	+	0.650317i	$0.774636\pi$
$318$	3.07606	+	5.32790i	0.172497	+	0.298774i
$319$	−16.2567	−	28.1574i	−0.910199	−	1.57651i
$320$	−1.00000			−0.0559017
$321$	−9.40246	−	16.2855i	−0.524794	−	0.908970i
$322$	−3.87800	+	6.71690i	−0.216113	+	0.374318i
$323$	8.69687	−	15.0634i	0.483907	−	0.838151i
$324$	−2.57673			−0.143152
$325$		0			0
$326$	16.8877			0.935323
$327$	−10.8998	+	18.8790i	−0.602759	+	1.04401i
$328$	6.27144	−	10.8624i	0.346282	−	0.599778i
$329$	4.83579	+	8.37583i	0.266606	+	0.461775i
$330$	7.23490			0.398268
$331$	−14.3720	−	24.8930i	−0.789954	−	1.36824i	−0.925994	−	0.377538i	$-0.876771\pi$
$331$	−14.3720	−	24.8930i	−0.789954	−	1.36824i	0.136040	−	0.990703i	$-0.456563\pi$
$332$	−7.32036	−	12.6792i	−0.401757	−	0.695863i
$333$	3.85862			0.211451
$334$	9.82908	+	17.0245i	0.537824	+	0.931538i
$335$	4.00753	−	6.94125i	0.218955	−	0.379241i
$336$	1.55496	−	2.69327i	0.0848299	−	0.146930i
$337$	−34.5972			−1.88463			−0.942314	−	0.334730i	$-0.891355\pi$
$337$	−34.5972			−1.88463			−0.942314	+	0.334730i	$0.891355\pi$
$338$		0			0
$339$	−10.2687			−0.557722
$340$	2.14795	−	3.72036i	0.116489	−	0.201765i
$341$	22.3424	−	38.6982i	1.20991	−	2.09563i
$342$	−2.92543	−	5.06699i	−0.158189	−	0.273991i
$343$	19.4034			1.04769
$344$	−3.49127	−	6.04706i	−0.188237	−	0.326036i
$345$	−1.93900	−	3.35845i	−0.104392	−	0.180813i
$346$	−16.8659			−0.906718
$347$	14.1521	+	24.5122i	0.759726	+	1.31588i	0.942990	+	0.332820i	$0.108000\pi$
$347$	14.1521	+	24.5122i	0.759726	+	1.31588i	−0.183264	+	0.983064i	$0.558666\pi$
$348$	3.49396	−	6.05171i	0.187296	−	0.324406i
$349$	8.41550	−	14.5761i	0.450471	−	0.780240i	−0.547944	−	0.836515i	$-0.684589\pi$
$349$	8.41550	−	14.5761i	0.450471	−	0.780240i	0.998415	+	0.0562757i	$0.0179226\pi$
$350$	−2.49396			−0.133308
$351$		0			0
$352$	−5.80194			−0.309244
$353$	−11.8714	+	20.5619i	−0.631852	+	1.09440i	0.355320	+	0.934745i	$0.384372\pi$
$353$	−11.8714	+	20.5619i	−0.631852	+	1.09440i	−0.987173	+	0.159656i	$0.948962\pi$
$354$	6.24429	−	10.8154i	0.331880	−	0.574834i
$355$	2.74094	+	4.74745i	0.145474	+	0.251968i
$356$	0.454731			0.0241007
$357$	6.67994	+	11.5700i	0.353540	+	0.612349i
$358$	2.99880	+	5.19408i	0.158492	+	0.274516i
$359$	26.8310			1.41609			0.708043	−	0.706169i	$-0.249578\pi$
$359$	26.8310			1.41609			0.708043	+	0.706169i	$0.249578\pi$
$360$	−0.722521	−	1.25144i	−0.0380802	−	0.0659568i
$361$	1.30313	−	2.25709i	0.0685860	−	0.118794i
$362$	8.28382	−	14.3480i	0.435388	−	0.754114i
$363$	28.2597			1.48325
$364$		0			0
$365$	8.67456			0.454047
$366$	3.07606	−	5.32790i	0.160788	−	0.278494i
$367$	9.04892	−	15.6732i	0.472350	−	0.818134i	−0.527150	−	0.849772i	$-0.676739\pi$
$367$	9.04892	−	15.6732i	0.472350	−	0.818134i	0.999499	+	0.0316388i	$0.0100726\pi$
$368$	1.55496	+	2.69327i	0.0810578	+	0.140396i
$369$	18.1250			0.943549
$370$	−1.33513	−	2.31251i	−0.0694099	−	0.120221i
$371$	−6.15213	−	10.6558i	−0.319403	−	0.553222i
$372$	9.60388			0.497938
$373$	−7.18598	−	12.4465i	−0.372076	−	0.644454i	0.617809	−	0.786328i	$-0.288021\pi$
$373$	−7.18598	−	12.4465i	−0.372076	−	0.644454i	−0.989885	+	0.141874i	$0.954687\pi$
$374$	12.4623	−	21.5853i	0.644408	−	1.11615i
$375$	0.623490	−	1.07992i	0.0321969	−	0.0557666i
$376$	3.87800			0.199993
$377$		0			0
$378$	13.8237			0.711015
$379$	−13.0903	+	22.6731i	−0.672404	+	1.16464i	0.304817	+	0.952411i	$0.401405\pi$
$379$	−13.0903	+	22.6731i	−0.672404	+	1.16464i	−0.977221	+	0.212226i	$0.931929\pi$
$380$	−2.02446	+	3.50647i	−0.103853	+	0.179878i
$381$	8.12498	+	14.0729i	0.416255	+	0.720976i
$382$	12.7922			0.654508
$383$	5.67456	+	9.82863i	0.289957	+	0.502220i	0.973799	−	0.227410i	$-0.0730258\pi$
$383$	5.67456	+	9.82863i	0.289957	+	0.502220i	−0.683842	+	0.729630i	$0.739692\pi$
$384$	−0.623490	−	1.07992i	−0.0318173	−	0.0551092i
$385$	−14.4698			−0.737449
$386$	−11.7925	−	20.4253i	−0.600225	−	1.03962i
$387$	5.04503	−	8.73825i	0.256453	−	0.444190i
$388$	4.34601	−	7.52751i	0.220635	−	0.382151i
$389$	−12.8465			−0.651346			−0.325673	−	0.945483i	$-0.605591\pi$
$389$	−12.8465			−0.651346			−0.325673	+	0.945483i	$0.605591\pi$
$390$		0			0
$391$	−13.3599			−0.675638
$392$	0.390084	−	0.675645i	0.0197022	−	0.0341252i
$393$	−6.12833	+	10.6146i	−0.309134	+	0.535435i
$394$	−0.987918	−	1.71112i	−0.0497706	−	0.0862052i
$395$	1.82371			0.0917607
$396$	−4.19202	−	7.26079i	−0.210657	−	0.364869i
$397$	9.37196	+	16.2327i	0.470365	+	0.814697i	0.999426	−	0.0338877i	$-0.0107888\pi$
$397$	9.37196	+	16.2327i	0.470365	+	0.814697i	−0.529060	+	0.848584i	$0.677456\pi$
$398$	0.835790			0.0418943
$399$	−6.29590	−	10.9048i	−0.315189	−	0.545924i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	9.91066	−	17.1658i	0.494915	−	0.857217i	−0.505068	−	0.863079i	$-0.668533\pi$
$401$	9.91066	−	17.1658i	0.494915	−	0.857217i	0.999983	+	0.00586217i	$0.00186600\pi$
$402$	9.99462			0.498486
$403$		0			0
$404$	15.7453			0.783355
$405$	−1.28836	+	2.23151i	−0.0640193	+	0.110885i
$406$	−6.98792	+	12.1034i	−0.346805	+	0.600683i
$407$	−7.74632	−	13.4170i	−0.383971	−	0.665057i
$408$	5.35690			0.265206
$409$	−9.47434	−	16.4100i	−0.468476	−	0.811425i	0.530875	−	0.847450i	$-0.321863\pi$
$409$	−9.47434	−	16.4100i	−0.468476	−	0.811425i	−0.999351	+	0.0360258i	$0.988530\pi$
$410$	−6.27144	−	10.8624i	−0.309724	−	0.536458i
$411$	−5.92692			−0.292353
$412$	1.85086	+	3.20578i	0.0911851	+	0.157937i
$413$	−12.4886	+	21.6309i	−0.614523	+	1.06438i
$414$	−2.24698	+	3.89188i	−0.110433	+	0.191276i
$415$	−14.6407			−0.718684
$416$		0			0
$417$	−2.98493			−0.146173
$418$	−11.7458	+	20.3443i	−0.574505	+	0.995072i
$419$	−0.933624	+	1.61708i	−0.0456105	+	0.0789998i	−0.887929	−	0.459980i	$-0.847857\pi$
$419$	−0.933624	+	1.61708i	−0.0456105	+	0.0789998i	0.842319	+	0.538980i	$0.181190\pi$
$420$	−1.55496	−	2.69327i	−0.0758742	−	0.131418i
$421$	27.3250			1.33174			0.665869	−	0.746069i	$-0.268061\pi$
$421$	27.3250			1.33174			0.665869	+	0.746069i	$0.268061\pi$
$422$	−4.68114	−	8.10797i	−0.227874	−	0.394690i
$423$	2.80194	+	4.85310i	0.136235	+	0.235966i
$424$	−4.93362			−0.239598
$425$	−2.14795	−	3.72036i	−0.104191	−	0.180464i
$426$	−3.41789	+	5.91997i	−0.165598	+	0.286823i
$427$	−6.15213	+	10.6558i	−0.297722	+	0.515670i
$428$	15.0804			0.728938
$429$		0			0
$430$	−6.98254			−0.336728
$431$	0.780167	−	1.35129i	0.0375793	−	0.0650893i	−0.846624	−	0.532191i	$-0.821369\pi$
$431$	0.780167	−	1.35129i	0.0375793	−	0.0650893i	0.884203	+	0.467102i	$0.154702\pi$
$432$	2.77144	−	4.80027i	0.133341	−	0.230953i
$433$	12.0782	+	20.9201i	0.580442	+	1.00536i	0.995427	+	0.0955270i	$0.0304536\pi$
$433$	12.0782	+	20.9201i	0.580442	+	1.00536i	−0.414985	+	0.909828i	$0.636213\pi$
$434$	−19.2078			−0.922002
$435$	−3.49396	−	6.05171i	−0.167523	−	0.290158i
$436$	−8.74094	−	15.1398i	−0.418615	−	0.725063i
$437$	12.5918			0.602347
$438$	5.40850	+	9.36780i	0.258428	+	0.447611i
$439$	−10.6799	+	18.4982i	−0.509726	+	0.882871i	0.490211	+	0.871604i	$0.336920\pi$
$439$	−10.6799	+	18.4982i	−0.509726	+	0.882871i	−0.999937	+	0.0112669i	$0.996414\pi$
$440$	−2.90097	+	5.02463i	−0.138298	+	0.239540i
$441$	1.12737			0.0536845
$442$		0			0
$443$	−16.5351			−0.785607			−0.392803	−	0.919623i	$-0.628495\pi$
$443$	−16.5351			−0.785607			−0.392803	+	0.919623i	$0.628495\pi$
$444$	1.66487	−	2.88365i	0.0790114	−	0.136852i
$445$	0.227365	−	0.393808i	0.0107781	−	0.0186683i
$446$	3.15883	+	5.47126i	0.149575	+	0.259072i
$447$	−25.9517			−1.22747
$448$	1.24698	+	2.15983i	0.0589142	+	0.102042i
$449$	3.28352	+	5.68722i	0.154959	+	0.268397i	0.933044	−	0.359762i	$-0.117142\pi$
$449$	3.28352	+	5.68722i	0.154959	+	0.268397i	−0.778085	+	0.628159i	$0.783809\pi$
$450$	−1.44504			−0.0681199
$451$	−36.3865	−	63.0233i	−1.71337	−	2.96765i
$452$	4.11745	−	7.13163i	0.193669	−	0.335444i
$453$	3.71379	−	6.43248i	0.174489	−	0.302224i
$454$	4.89440			0.229705
$455$		0			0
$456$	−5.04892			−0.236437
$457$	−12.0858	+	20.9331i	−0.565348	+	0.979211i	0.431670	+	0.902032i	$0.357925\pi$
$457$	−12.0858	+	20.9331i	−0.565348	+	0.979211i	−0.997017	+	0.0771791i	$0.975409\pi$
$458$	0.344814	−	0.597236i	0.0161121	−	0.0279070i
$459$	11.9058	+	20.6215i	0.555716	+	0.962528i
$460$	3.10992			0.145001
$461$	−11.7899	−	20.4206i	−0.549108	−	0.951084i	−0.998336	−	0.0576662i	$-0.981634\pi$
$461$	−11.7899	−	20.4206i	−0.549108	−	0.951084i	0.449228	−	0.893417i	$-0.351699\pi$
$462$	−9.02177	−	15.6262i	−0.419731	−	0.726995i
$463$	−1.68233			−0.0781846			−0.0390923	−	0.999236i	$-0.512447\pi$
$463$	−1.68233			−0.0781846			−0.0390923	+	0.999236i	$0.512447\pi$
$464$	2.80194	+	4.85310i	0.130077	+	0.225299i
$465$	4.80194	−	8.31720i	0.222685	−	0.385701i
$466$	−7.09030	+	12.2808i	−0.328452	+	0.568895i
$467$	0.376273			0.0174118			0.00870592	−	0.999962i	$-0.497229\pi$
$467$	0.376273			0.0174118			0.00870592	+	0.999962i	$0.497229\pi$
$468$		0			0
$469$	−19.9892			−0.923018
$470$	1.93900	−	3.35845i	0.0894395	−	0.154914i
$471$	−5.10992	+	8.85063i	−0.235453	+	0.407816i
$472$	5.00753	+	8.67330i	0.230490	+	0.399221i
$473$	−40.5123			−1.86276
$474$	1.13706	+	1.96945i	0.0522270	+	0.0904599i
$475$	2.02446	+	3.50647i	0.0928885	+	0.160888i
$476$	−10.7138			−0.491066
$477$	−3.56465	−	6.17415i	−0.163214	−	0.282695i
$478$	12.8877	−	22.3221i	0.589469	−	1.02099i
$479$	5.01507	−	8.68635i	0.229144	−	0.396889i	−0.728411	−	0.685141i	$-0.759741\pi$
$479$	5.01507	−	8.68635i	0.229144	−	0.396889i	0.957555	+	0.288252i	$0.0930739\pi$
$480$	−1.24698			−0.0569166
$481$		0			0
$482$	−7.86725			−0.358343
$483$	−4.83579	+	8.37583i	−0.220036	+	0.381114i
$484$	−11.3312	+	19.6263i	−0.515056	+	0.892104i
$485$	−4.34601	−	7.52751i	−0.197342	−	0.341807i
$486$	13.4155			0.608540
$487$	7.66487	+	13.2760i	0.347329	+	0.601591i	0.985774	−	0.168076i	$-0.0537555\pi$
$487$	7.66487	+	13.2760i	0.347329	+	0.601591i	−0.638445	+	0.769667i	$0.720422\pi$
$488$	2.46681	+	4.27264i	0.111667	+	0.193414i
$489$	21.0586			0.952303
$490$	−0.390084	−	0.675645i	−0.0176222	−	0.0305225i
$491$	−4.59634	+	7.96110i	−0.207430	+	0.359279i	−0.950904	−	0.309485i	$-0.899843\pi$
$491$	−4.59634	+	7.96110i	−0.207430	+	0.359279i	0.743474	+	0.668765i	$0.233177\pi$
$492$	7.82036	−	13.5453i	0.352569	−	0.610667i
$493$	−24.0737			−1.08422
$494$		0			0
$495$	−8.38404			−0.376835
$496$	−3.85086	+	6.66988i	−0.172908	+	0.299486i
$497$	6.83579	−	11.8399i	0.306627	−	0.531094i
$498$	−9.12833	−	15.8107i	−0.409050	−	0.708496i
$499$	−2.74632			−0.122942			−0.0614710	−	0.998109i	$-0.519579\pi$
$499$	−2.74632			−0.122942			−0.0614710	+	0.998109i	$0.519579\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	12.2567	+	21.2292i	0.547588	+	0.948449i
$502$	19.9782			0.891672
$503$	6.28382	+	10.8839i	0.280181	+	0.485289i	0.971429	−	0.237329i	$-0.0762720\pi$
$503$	6.28382	+	10.8839i	0.280181	+	0.485289i	−0.691248	+	0.722618i	$0.742939\pi$
$504$	−1.80194	+	3.12105i	−0.0802647	+	0.139023i
$505$	7.87263	−	13.6358i	0.350327	−	0.606785i
$506$	18.0435			0.802133
$507$		0			0
$508$	−13.0315			−0.578177
$509$	0.0338518	−	0.0586331i	0.00150046	−	0.00259887i	−0.865274	−	0.501299i	$-0.832856\pi$
$509$	0.0338518	−	0.0586331i	0.00150046	−	0.00259887i	0.866775	+	0.498700i	$0.166189\pi$
$510$	2.67845	−	4.63921i	0.118604	−	0.205428i
$511$	−10.8170	−	18.7356i	−0.478516	−	0.828814i
$512$	1.00000			0.0441942
$513$	−11.2213	−	19.4359i	−0.495434	−	0.858116i
$514$	12.7262	+	22.0424i	0.561327	+	0.972247i
$515$	3.70171			0.163117
$516$	−4.35354	−	7.54056i	−0.191654	−	0.331955i
$517$	11.2500	−	19.4855i	0.494773	−	0.856972i
$518$	−3.32975	+	5.76729i	−0.146301	+	0.253400i
$519$	−21.0315			−0.923179
$520$		0			0
$521$	8.18060			0.358399			0.179199	−	0.983813i	$-0.442649\pi$
$521$	8.18060			0.358399			0.179199	+	0.983813i	$0.442649\pi$
$522$	−4.04892	+	7.01293i	−0.177216	+	0.306948i
$523$	−8.46562	+	14.6629i	−0.370176	+	0.641163i	−0.989592	−	0.143900i	$-0.954036\pi$
$523$	−8.46562	+	14.6629i	−0.370176	+	0.641163i	0.619417	+	0.785062i	$0.287369\pi$
$524$	−4.91454	−	8.51224i	−0.214693	−	0.371859i
$525$	−3.10992			−0.135728
$526$	9.98792	+	17.2996i	0.435494	+	0.754298i
$527$	−16.5429	−	28.6531i	−0.720619	−	1.24815i
$528$	−7.23490			−0.314859
$529$	6.66421	+	11.5428i	0.289748	+	0.501859i
$530$	−2.46681	+	4.27264i	−0.107151	+	0.185592i
$531$	−7.23609	+	12.5333i	−0.314020	+	0.543898i
$532$	10.0978			0.437797
$533$		0			0
$534$	0.567040			0.0245382
$535$	7.54019	−	13.0600i	0.325991	−	0.564633i
$536$	−4.00753	+	6.94125i	−0.173099	+	0.299816i
$537$	3.73945	+	6.47691i	0.161369	+	0.279499i
$538$	−16.1414			−0.695904
$539$	−2.26324	−	3.92005i	−0.0974847	−	0.168848i
$540$	−2.77144	−	4.80027i	−0.119264	−	0.206571i
$541$	16.5676			0.712298			0.356149	−	0.934429i	$-0.384090\pi$
$541$	16.5676			0.712298			0.356149	+	0.934429i	$0.384090\pi$
$542$	7.55257	+	13.0814i	0.324410	+	0.561895i
$543$	10.3297	−	17.8916i	0.443292	−	0.767804i
$544$	−2.14795	+	3.72036i	−0.0920925	+	0.159509i
$545$	−17.4819			−0.748841
$546$		0			0
$547$	−3.57540			−0.152873			−0.0764365	−	0.997074i	$-0.524354\pi$
$547$	−3.57540			−0.152873			−0.0764365	+	0.997074i	$0.524354\pi$
$548$	2.37651	−	4.11624i	0.101519	−	0.175837i
$549$	−3.56465	+	6.17415i	−0.152135	+	0.263506i
$550$	2.90097	+	5.02463i	0.123698	+	0.214251i
$551$	22.6896			0.966611
$552$	1.93900	+	3.35845i	0.0825294	+	0.142945i
$553$	−2.27413	−	3.93890i	−0.0967057	−	0.167499i
$554$	−24.4940			−1.04065
$555$	−1.66487	−	2.88365i	−0.0706700	−	0.122404i
$556$	1.19687	−	2.07303i	0.0507584	−	0.0879162i
$557$	−19.9463	+	34.5480i	−0.845152	+	1.46385i	0.0403377	+	0.999186i	$0.487157\pi$
$557$	−19.9463	+	34.5480i	−0.845152	+	1.46385i	−0.885489	+	0.464660i	$0.846177\pi$
$558$	−11.1293			−0.471141
$559$		0			0
$560$	2.49396			0.105389
$561$	15.5402	−	26.9164i	0.656107	−	1.13641i
$562$	11.6691	−	20.2114i	0.492229	−	0.852566i
$563$	1.82371	+	3.15875i	0.0768601	+	0.133126i	0.901894	−	0.431958i	$-0.142177\pi$
$563$	1.82371	+	3.15875i	0.0768601	+	0.133126i	−0.825034	+	0.565084i	$0.808844\pi$
$564$	4.83579			0.203623
$565$	−4.11745	−	7.13163i	−0.173222	−	0.300030i
$566$	5.71110	+	9.89192i	0.240056	+	0.415788i
$567$	6.42626			0.269877
$568$	−2.74094	−	4.74745i	−0.115007	−	0.199198i
$569$	−9.17606	+	15.8934i	−0.384680	+	0.666286i	−0.991725	−	0.128382i	$-0.959022\pi$
$569$	−9.17606	+	15.8934i	−0.384680	+	0.666286i	0.607045	+	0.794668i	$0.292355\pi$
$570$	−2.52446	+	4.37249i	−0.105738	+	0.183143i
$571$	−19.1987			−0.803439			−0.401719	−	0.915763i	$-0.631587\pi$
$571$	−19.1987			−0.803439			−0.401719	+	0.915763i	$0.631587\pi$
$572$		0			0
$573$	15.9517			0.666391
$574$	−15.6407	+	27.0905i	−0.652831	+	1.13074i
$575$	1.55496	−	2.69327i	0.0648462	−	0.112317i
$576$	0.722521	+	1.25144i	0.0301050	+	0.0521435i
$577$	35.2218			1.46630			0.733150	−	0.680067i	$-0.238049\pi$
$577$	35.2218			1.46630			0.733150	+	0.680067i	$0.238049\pi$
$578$	−0.727365	−	1.25983i	−0.0302544	−	0.0524022i
$579$	−14.7051	−	25.4699i	−0.611122	−	1.05849i
$580$	5.60388			0.232688
$581$	18.2567	+	31.6215i	0.757414	+	1.31188i
$582$	5.41939	−	9.38665i	0.224641	−	0.389089i
$583$	−14.3123	+	24.7896i	−0.592755	+	1.02668i
$584$	−8.67456			−0.358956
$585$		0			0
$586$	24.4155			1.00860
$587$	16.2298	−	28.1109i	0.669876	−	1.16026i	−0.308062	−	0.951366i	$-0.599680\pi$
$587$	16.2298	−	28.1109i	0.669876	−	1.16026i	0.977938	−	0.208893i	$-0.0669862\pi$
$588$	0.486426	−	0.842515i	0.0200599	−	0.0347447i
$589$	15.5918	+	27.0058i	0.642449	+	1.11275i
$590$	10.0151			0.412314
$591$	−1.23191	−	2.13374i	−0.0506742	−	0.0877702i
$592$	1.33513	+	2.31251i	0.0548733	+	0.0950434i
$593$	9.57135			0.393048			0.196524	−	0.980499i	$-0.437035\pi$
$593$	9.57135			0.393048			0.196524	+	0.980499i	$0.437035\pi$
$594$	−16.0797	−	27.8509i	−0.659759	−	1.14274i
$595$	−5.35690	+	9.27842i	−0.219611	+	0.380378i
$596$	10.4058	−	18.0234i	0.426239	−	0.738267i
$597$	1.04221			0.0426549
$598$		0			0
$599$	−29.0858			−1.18841			−0.594206	−	0.804313i	$-0.702534\pi$
$599$	−29.0858			−1.18841			−0.594206	+	0.804313i	$0.702534\pi$
$600$	−0.623490	+	1.07992i	−0.0254539	+	0.0440874i
$601$	3.15615	−	5.46660i	0.128742	−	0.222987i	−0.794448	−	0.607333i	$-0.792239\pi$
$601$	3.15615	−	5.46660i	0.128742	−	0.222987i	0.923189	+	0.384345i	$0.125573\pi$
$602$	8.70709	+	15.0811i	0.354874	+	0.614660i
$603$	−11.5821			−0.471660
$604$	2.97823	+	5.15845i	0.121182	+	0.209894i
$605$	11.3312	+	19.6263i	0.460680	+	0.797922i
$606$	19.6340			0.797577
$607$	−16.2325	−	28.1155i	−0.658857	−	1.14117i	−0.980912	−	0.194453i	$-0.937707\pi$
$607$	−16.2325	−	28.1155i	−0.658857	−	1.14117i	0.322055	−	0.946721i	$-0.395626\pi$
$608$	2.02446	−	3.50647i	0.0821026	−	0.142206i
$609$	−8.71379	+	15.0927i	−0.353101	+	0.611588i
$610$	4.93362			0.199757
$611$		0			0
$612$	−6.20775			−0.250933
$613$	14.8509	−	25.7224i	0.599820	−	1.03892i	−0.393027	−	0.919527i	$-0.628572\pi$
$613$	14.8509	−	25.7224i	0.599820	−	1.03892i	0.992847	−	0.119392i	$-0.0380946\pi$
$614$	−3.85205	+	6.67195i	−0.155456	+	0.269258i
$615$	−7.82036	−	13.5453i	−0.315347	−	0.546197i
$616$	14.4698			0.583005
$617$	5.42782	+	9.40126i	0.218516	+	0.378481i	0.954354	−	0.298676i	$-0.0965451\pi$
$617$	5.42782	+	9.40126i	0.218516	+	0.378481i	−0.735839	+	0.677157i	$0.763212\pi$
$618$	2.30798	+	3.99754i	0.0928405	+	0.160804i
$619$	−23.2948			−0.936298			−0.468149	−	0.883649i	$-0.655079\pi$
$619$	−23.2948			−0.936298			−0.468149	+	0.883649i	$0.655079\pi$
$620$	3.85086	+	6.66988i	0.154654	+	0.267869i
$621$	−8.61894	+	14.9284i	−0.345866	+	0.599058i
$622$	−2.35690	+	4.08226i	−0.0945029	+	0.163684i
$623$	−1.13408			−0.0454359
$624$		0			0
$625$	1.00000			0.0400000
$626$	−4.24578	+	7.35391i	−0.169696	+	0.293921i
$627$	−14.6468	+	25.3689i	−0.584935	+	1.01314i
$628$	−4.09783	−	7.09766i	−0.163521	−	0.283227i
$629$	−11.4711			−0.457384
$630$	1.80194	+	3.12105i	0.0717909	+	0.124346i
$631$	−3.36227	−	5.82363i	−0.133850	−	0.231835i	0.791308	−	0.611418i	$-0.209401\pi$
$631$	−3.36227	−	5.82363i	−0.133850	−	0.231835i	−0.925158	+	0.379583i	$0.876067\pi$
$632$	−1.82371			−0.0725432
$633$	−5.83728	−	10.1105i	−0.232011	−	0.401855i
$634$	13.5254	−	23.4267i	0.537163	−	0.930394i
$635$	−6.51573	+	11.2856i	−0.258569	+	0.447854i
$636$	−6.15213			−0.243948
$637$		0			0
$638$	32.5133			1.28722
$639$	3.96077	−	6.86026i	0.156686	−	0.271388i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−4.66219	−	8.07514i	−0.184145	−	0.318949i	0.759143	−	0.650924i	$-0.225618\pi$
$641$	−4.66219	−	8.07514i	−0.184145	−	0.318949i	−0.943288	+	0.331975i	$0.892285\pi$
$642$	18.8049			0.742171
$643$	6.10723	+	10.5780i	0.240846	+	0.417157i	0.960955	−	0.276703i	$-0.0892419\pi$
$643$	6.10723	+	10.5780i	0.240846	+	0.417157i	−0.720110	+	0.693860i	$0.755909\pi$
$644$	−3.87800	−	6.71690i	−0.152815	−	0.264683i
$645$	−8.70709			−0.342841
$646$	8.69687	+	15.0634i	0.342174	+	0.592662i
$647$	18.4426	−	31.9436i	0.725055	−	1.25583i	−0.233896	−	0.972262i	$-0.575147\pi$
$647$	18.4426	−	31.9436i	0.725055	−	1.25583i	0.958951	−	0.283571i	$-0.0915192\pi$
$648$	1.28836	−	2.23151i	0.0506117	−	0.0876621i
$649$	58.1068			2.28089
$650$		0			0
$651$	−23.9517			−0.938740
$652$	−8.44385	+	14.6252i	−0.330687	+	0.572766i
$653$	19.3327	−	33.4853i	0.756548	−	1.31038i	−0.188053	−	0.982159i	$-0.560218\pi$
$653$	19.3327	−	33.4853i	0.756548	−	1.31038i	0.944601	−	0.328221i	$-0.106449\pi$
$654$	−10.8998	−	18.8790i	−0.426215	−	0.738226i
$655$	−9.82908			−0.384054
$656$	6.27144	+	10.8624i	0.244859	+	0.424107i
$657$	−6.26755	−	10.8557i	−0.244521	−	0.423522i
$658$	−9.67158			−0.377037
$659$	0.596343	+	1.03290i	0.0232302	+	0.0402359i	0.877407	−	0.479747i	$-0.159272\pi$
$659$	0.596343	+	1.03290i	0.0232302	+	0.0402359i	−0.854177	+	0.519983i	$0.825938\pi$
$660$	−3.61745	+	6.26561i	−0.140809	+	0.243888i
$661$	−1.96615	+	3.40547i	−0.0764743	+	0.132457i	−0.901726	−	0.432307i	$-0.857700\pi$
$661$	−1.96615	+	3.40547i	−0.0764743	+	0.132457i	0.825252	+	0.564764i	$0.191033\pi$
$662$	28.7439			1.11716
$663$		0			0
$664$	14.6407			0.568170
$665$	5.04892	−	8.74498i	0.195789	−	0.339116i
$666$	−1.92931	+	3.34167i	−0.0747593	+	0.129487i
$667$	−8.71379	−	15.0927i	−0.337399	−	0.584393i
$668$	−19.6582			−0.760597
$669$	3.93900	+	6.82255i	0.152291	+	0.263775i
$670$	4.00753	+	6.94125i	0.154824	+	0.268164i
$671$	28.6246			1.10504
$672$	1.55496	+	2.69327i	0.0599838	+	0.103895i
$673$	−2.43512	+	4.21775i	−0.0938668	+	0.162582i	−0.909135	−	0.416501i	$-0.863256\pi$
$673$	−2.43512	+	4.21775i	−0.0938668	+	0.162582i	0.815268	+	0.579083i	$0.196589\pi$
$674$	17.2986	−	29.9620i	0.666317	−	1.15409i
$675$	−5.54288			−0.213345
$676$		0			0
$677$	−14.6461			−0.562895			−0.281447	−	0.959577i	$-0.590815\pi$
$677$	−14.6461			−0.562895			−0.281447	+	0.959577i	$0.590815\pi$
$678$	5.13437	−	8.89300i	0.197184	−	0.341534i
$679$	−10.8388	+	18.7733i	−0.415954	+	0.720453i
$680$	2.14795	+	3.72036i	0.0823701	+	0.142669i
$681$	6.10321			0.233876
$682$	22.3424	+	38.6982i	0.855536	+	1.48183i
$683$	17.5999	+	30.4839i	0.673440	+	1.16643i	0.976922	+	0.213595i	$0.0685173\pi$
$683$	17.5999	+	30.4839i	0.673440	+	1.16643i	−0.303482	+	0.952837i	$0.598149\pi$
$684$	5.85086			0.223713
$685$	−2.37651	−	4.11624i	−0.0908018	−	0.157273i
$686$	−9.70171	+	16.8039i	−0.370413	+	0.641574i
$687$	0.429976	−	0.744741i	0.0164046	−	0.0284136i
$688$	6.98254			0.266207
$689$		0			0
$690$	3.87800			0.147633
$691$	−20.7925	+	36.0137i	−0.790986	+	1.37003i	0.134372	+	0.990931i	$0.457098\pi$
$691$	−20.7925	+	36.0137i	−0.790986	+	1.37003i	−0.925357	+	0.379096i	$0.876235\pi$
$692$	8.43296	−	14.6063i	0.320573	−	0.555249i
$693$	10.4547	+	18.1081i	0.397142	+	0.687871i
$694$	−28.3043			−1.07441
$695$	−1.19687	−	2.07303i	−0.0453997	−	0.0786346i
$696$	3.49396	+	6.05171i	0.132438	+	0.229390i
$697$	−53.8829			−2.04096
$698$	8.41550	+	14.5761i	0.318531	+	0.551713i
$699$	−8.84146	+	15.3139i	−0.334415	+	0.579223i
$700$	1.24698	−	2.15983i	0.0471314	−	0.0816340i
$701$	5.61463			0.212062			0.106031	−	0.994363i	$-0.466186\pi$
$701$	5.61463			0.212062			0.106031	+	0.994363i	$0.466186\pi$
$702$		0			0
$703$	10.8116			0.407768
$704$	2.90097	−	5.02463i	0.109334	−	0.189373i
$705$	2.41789	−	4.18792i	0.0910632	−	0.157726i
$706$	−11.8714	−	20.5619i	−0.446787	−	0.773858i
$707$	−39.2680			−1.47683
$708$	6.24429	+	10.8154i	0.234675	+	0.406469i
$709$	17.4330	+	30.1948i	0.654709	+	1.13399i	0.981967	+	0.189054i	$0.0605420\pi$
$709$	17.4330	+	30.1948i	0.654709	+	1.13399i	−0.327258	+	0.944935i	$0.606125\pi$
$710$	−5.48188			−0.205731
$711$	−1.31767	−	2.28227i	−0.0494164	−	0.0855917i
$712$	−0.227365	+	0.393808i	−0.00852087	+	0.0147586i
$713$	11.9758	−	20.7428i	0.448499	−	0.776822i
$714$	−13.3599			−0.499981
$715$		0			0
$716$	−5.99761			−0.224141
$717$	16.0707	−	27.8352i	0.600171	−	1.03953i
$718$	−13.4155	+	23.2363i	−0.500662	+	0.867172i
$719$	0.951083	+	1.64732i	0.0354694	+	0.0614348i	0.883215	−	0.468968i	$-0.155374\pi$
$719$	0.951083	+	1.64732i	0.0354694	+	0.0614348i	−0.847746	+	0.530403i	$0.822041\pi$
$720$	1.44504			0.0538535
$721$	−4.61596	−	7.99507i	−0.171907	−	0.297752i
$722$	1.30313	+	2.25709i	0.0484976	+	0.0840004i
$723$	−9.81030			−0.364849
$724$	8.28382	+	14.3480i	0.307866	+	0.533239i
$725$	2.80194	−	4.85310i	0.104061	−	0.180240i
$726$	−14.1298	+	24.4736i	−0.524407	+	0.908300i
$727$	−23.7211			−0.879766			−0.439883	−	0.898055i	$-0.644980\pi$
$727$	−23.7211			−0.879766			−0.439883	+	0.898055i	$0.644980\pi$
$728$		0			0
$729$	24.4590			0.905890
$730$	−4.33728	+	7.51239i	−0.160530	+	0.278046i
$731$	−14.9981	+	25.9775i	−0.554726	+	0.960814i
$732$	3.07606	+	5.32790i	0.113695	+	0.196925i
$733$	13.2862			0.490737			0.245369	−	0.969430i	$-0.421091\pi$
$733$	13.2862			0.490737			0.245369	+	0.969430i	$0.421091\pi$
$734$	9.04892	+	15.6732i	0.334002	+	0.578508i
$735$	−0.486426	−	0.842515i	−0.0179421	−	0.0310766i
$736$	−3.10992			−0.114633
$737$	23.2515	+	40.2727i	0.856478	+	1.48346i
$738$	−9.06249	+	15.6967i	−0.333595	+	0.577803i
$739$	3.17307	−	5.49592i	0.116723	−	0.202171i	−0.801744	−	0.597668i	$-0.796094\pi$
$739$	3.17307	−	5.49592i	0.116723	−	0.202171i	0.918467	+	0.395497i	$0.129428\pi$
$740$	2.67025			0.0981604
$741$		0			0
$742$	12.3043			0.451704
$743$	20.0901	−	34.7970i	0.737033	−	1.27658i	−0.216793	−	0.976218i	$-0.569560\pi$
$743$	20.0901	−	34.7970i	0.737033	−	1.27658i	0.953826	−	0.300361i	$-0.0971071\pi$
$744$	−4.80194	+	8.31720i	−0.176048	+	0.304923i
$745$	−10.4058	−	18.0234i	−0.381239	−	0.660326i
$746$	14.3720			0.526195
$747$	10.5782	+	18.3220i	0.387037	+	0.670367i
$748$	12.4623	+	21.5853i	0.455665	+	0.789236i
$749$	−37.6098			−1.37423
$750$	0.623490	+	1.07992i	0.0227666	+	0.0394330i
$751$	−7.76809	+	13.4547i	−0.283461	+	0.490970i	−0.972235	−	0.234007i	$-0.924816\pi$
$751$	−7.76809	+	13.4547i	−0.283461	+	0.490970i	0.688773	+	0.724977i	$0.258149\pi$
$752$	−1.93900	+	3.35845i	−0.0707081	+	0.122470i
$753$	24.9124			0.907860
$754$		0			0
$755$	5.95646			0.216778
$756$	−6.91185	+	11.9717i	−0.251382	+	0.435406i
$757$	−16.1032	+	27.8916i	−0.585281	+	1.01374i	0.409559	+	0.912284i	$0.365683\pi$
$757$	−16.1032	+	27.8916i	−0.585281	+	1.01374i	−0.994840	+	0.101453i	$0.967651\pi$
$758$	−13.0903	−	22.6731i	−0.475461	−	0.823523i
$759$	22.4999			0.816696
$760$	−2.02446	−	3.50647i	−0.0734348	−	0.127193i
$761$	9.82358	+	17.0149i	0.356104	+	0.616791i	0.987306	−	0.158828i	$-0.0507714\pi$
$761$	9.82358	+	17.0149i	0.356104	+	0.616791i	−0.631202	+	0.775619i	$0.717438\pi$
$762$	−16.2500			−0.588674
$763$	21.7995	+	37.7579i	0.789197	+	1.36693i
$764$	−6.39612	+	11.0784i	−0.231404	+	0.400803i
$765$	−3.10388	+	5.37607i	−0.112221	+	0.194372i
$766$	−11.3491			−0.410061
$767$		0			0
$768$	1.24698			0.0449965
$769$	3.25116	−	5.63117i	0.117240	−	0.203065i	−0.801433	−	0.598084i	$-0.795929\pi$
$769$	3.25116	−	5.63117i	0.117240	−	0.203065i	0.918673	+	0.395019i	$0.129262\pi$
$770$	7.23490	−	12.5312i	0.260728	−	0.451593i
$771$	15.8693	+	27.4864i	0.571518	+	0.989898i
$772$	23.5851			0.848846
$773$	−16.1293	−	27.9368i	−0.580130	−	1.00482i	−0.995463	−	0.0951458i	$-0.969668\pi$
$773$	−16.1293	−	27.9368i	−0.580130	−	1.00482i	0.415333	−	0.909669i	$-0.363665\pi$
$774$	5.04503	+	8.73825i	0.181340	+	0.314090i
$775$	7.70171			0.276654
$776$	4.34601	+	7.52751i	0.156013	+	0.270222i
$777$	−4.15213	+	7.19170i	−0.148957	+	0.258001i
$778$	6.42327	−	11.1254i	0.230285	−	0.398866i
$779$	50.7851			1.81956
$780$		0			0
$781$	−31.8055			−1.13809
$782$	6.67994	−	11.5700i	0.238874	−	0.413742i
$783$	−15.5308	+	26.9001i	−0.555025	+	0.961332i
$784$	0.390084	+	0.675645i	0.0139316	+	0.0241302i
$785$	−8.19567			−0.292516
$786$	−6.12833	−	10.6146i	−0.218590	−	0.378610i
$787$	6.83997	+	11.8472i	0.243819	+	0.422306i	0.961799	−	0.273757i	$-0.0882665\pi$
$787$	6.83997	+	11.8472i	0.243819	+	0.422306i	−0.717980	+	0.696064i	$0.754933\pi$
$788$	1.97584			0.0703863
$789$	12.4547	+	21.5722i	0.443400	+	0.767992i
$790$	−0.911854	+	1.57938i	−0.0324423	+	0.0561917i
$791$	−10.2687	+	17.7860i	−0.365115	+	0.632397i
$792$	8.38404			0.297914
$793$		0			0
$794$	−18.7439			−0.665197
$795$	−3.07606	+	5.32790i	−0.109097	+	0.188961i
$796$	−0.417895	+	0.723815i	−0.0148119	+	0.0256549i
$797$	3.88769	+	6.73368i	0.137709	+	0.238519i	0.926629	−	0.375977i	$-0.122693\pi$
$797$	3.88769	+	6.73368i	0.137709	+	0.238519i	−0.788920	+	0.614496i	$0.789359\pi$
$798$	12.5918			0.445745
$799$	−8.32975	−	14.4275i	−0.294685	−	0.510410i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−0.657105			−0.0232177
$802$	9.91066	+	17.1658i	0.349957	+	0.606144i
$803$	−25.1646	+	43.5864i	−0.888041	+	1.53813i
$804$	−4.99731	+	8.65560i	−0.176242	+	0.305259i
$805$	−7.75600			−0.273363
$806$		0			0
$807$	−20.1280			−0.708538
$808$	−7.87263	+	13.6358i	−0.276958	+	0.479705i
$809$	21.5770	−	37.3725i	0.758608	−	1.31395i	−0.184953	−	0.982747i	$-0.559213\pi$
$809$	21.5770	−	37.3725i	0.758608	−	1.31395i	0.943561	−	0.331200i	$-0.107453\pi$
$810$	−1.28836	−	2.23151i	−0.0452685	−	0.0784073i
$811$	35.8165			1.25769			0.628844	−	0.777531i	$-0.283528\pi$
$811$	35.8165			1.25769			0.628844	+	0.777531i	$0.283528\pi$
$812$	−6.98792	−	12.1034i	−0.245228	−	0.424747i
$813$	9.41789	+	16.3123i	0.330300	+	0.572096i
$814$	15.4926			0.543016
$815$	8.44385	+	14.6252i	0.295775	+	0.512297i
$816$	−2.67845	+	4.63921i	−0.0937644	+	0.162405i
$817$	14.1359	−	24.4840i	0.494551	−	0.856588i
$818$	18.9487			0.662525
$819$		0			0
$820$	12.5429			0.438016
$821$	3.35152	−	5.80500i	0.116969	−	0.202596i	−0.801596	−	0.597866i	$-0.796016\pi$
$821$	3.35152	−	5.80500i	0.116969	−	0.202596i	0.918565	+	0.395270i	$0.129349\pi$
$822$	2.96346	−	5.13286i	0.103363	−	0.179029i
$823$	−17.8552	−	30.9261i	−0.622392	−	1.07801i	−0.989039	−	0.147654i	$-0.952828\pi$
$823$	−17.8552	−	30.9261i	−0.622392	−	1.07801i	0.366647	−	0.930360i	$-0.380506\pi$
$824$	−3.70171			−0.128955
$825$	3.61745	+	6.26561i	0.125943	+	0.218140i
$826$	−12.4886	−	21.6309i	−0.434533	−	0.752634i
$827$	1.79523			0.0624264			0.0312132	−	0.999513i	$-0.490063\pi$
$827$	1.79523			0.0624264			0.0312132	+	0.999513i	$0.490063\pi$
$828$	−2.24698	−	3.89188i	−0.0780879	−	0.135252i
$829$	−0.366585	+	0.634943i	−0.0127320	+	0.0220525i	−0.872321	−	0.488933i	$-0.837386\pi$
$829$	−0.366585	+	0.634943i	−0.0127320	+	0.0220525i	0.859589	+	0.510986i	$0.170720\pi$
$830$	7.32036	−	12.6792i	0.254093	−	0.440102i
$831$	−30.5435			−1.05954
$832$		0			0
$833$	−3.35152			−0.116123
$834$	1.49247	−	2.58503i	0.0516799	−	0.0895122i
$835$	−9.82908	+	17.0245i	−0.340150	+	0.589156i
$836$	−11.7458	−	20.3443i	−0.406236	−	0.703622i
$837$	−42.6896			−1.47557
$838$	−0.933624	−	1.61708i	−0.0322515	−	0.0558613i
$839$	−13.3056	−	23.0460i	−0.459360	−	0.795635i	0.539567	−	0.841942i	$-0.318588\pi$
$839$	−13.3056	−	23.0460i	−0.459360	−	0.795635i	−0.998927	+	0.0463079i	$0.985254\pi$
$840$	3.10992			0.107302
$841$	−1.20171	−	2.08142i	−0.0414383	−	0.0717732i
$842$	−13.6625	+	23.6641i	−0.470840	+	0.815519i
$843$	14.5511	−	25.2032i	0.501166	−	0.868044i
$844$	9.36227			0.322263
$845$		0			0
$846$	−5.60388			−0.192665
$847$	28.2597	−	48.9472i	0.971013	−	1.68184i
$848$	2.46681	−	4.27264i	0.0847107	−	0.146723i
$849$	7.12163	+	12.3350i	0.244414	+	0.423337i
$850$	4.29590			0.147348
$851$	−4.15213	−	7.19170i	−0.142333	−	0.246528i
$852$	−3.41789	−	5.91997i	−0.117095	−	0.202815i
$853$	4.78746			0.163920			0.0819598	−	0.996636i	$-0.473882\pi$
$853$	4.78746			0.163920			0.0819598	+	0.996636i	$0.473882\pi$
$854$	−6.15213	−	10.6558i	−0.210522	−	0.364634i
$855$	2.92543	−	5.06699i	0.100048	−	0.173287i
$856$	−7.54019	+	13.0600i	−0.257718	+	0.446381i
$857$	−24.9748			−0.853122			−0.426561	−	0.904459i	$-0.640275\pi$
$857$	−24.9748			−0.853122			−0.426561	+	0.904459i	$0.640275\pi$
$858$		0			0
$859$	−16.2737			−0.555250			−0.277625	−	0.960690i	$-0.589547\pi$
$859$	−16.2737			−0.555250			−0.277625	+	0.960690i	$0.589547\pi$
$860$	3.49127	−	6.04706i	0.119051	−	0.206203i
$861$	−19.5036	+	33.7813i	−0.664683	+	1.15126i
$862$	0.780167	+	1.35129i	0.0265726	+	0.0460251i
$863$	−44.3806			−1.51073			−0.755366	−	0.655303i	$-0.772541\pi$
$863$	−44.3806			−1.51073			−0.755366	+	0.655303i	$0.772541\pi$
$864$	2.77144	+	4.80027i	0.0942862	+	0.163309i
$865$	−8.43296	−	14.6063i	−0.286729	−	0.496630i
$866$	−24.1564			−0.820869
$867$	−0.907010	−	1.57099i	−0.0308037	−	0.0533535i
$868$	9.60388	−	16.6344i	0.325977	−	0.564608i
$869$	−5.29052	+	9.16345i	−0.179469	+	0.310849i
$870$	6.98792			0.236913
$871$		0			0
$872$	17.4819			0.592011
$873$	−6.28017	+	10.8776i	−0.212551	+	0.368150i
$874$	−6.29590	+	10.9048i	−0.212962	+	0.368861i
$875$	−1.24698	−	2.15983i	−0.0421556	−	0.0730156i
$876$	−10.8170			−0.365473
$877$	18.6950	+	32.3807i	0.631285	+	1.09342i	0.987289	+	0.158934i	$0.0508057\pi$
$877$	18.6950	+	32.3807i	0.631285	+	1.09342i	−0.356004	+	0.934485i	$0.615861\pi$
$878$	−10.6799	−	18.4982i	−0.360431	−	0.624284i
$879$	30.4456			1.02691
$880$	−2.90097	−	5.02463i	−0.0977916	−	0.169380i
$881$	−19.0942	+	33.0722i	−0.643301	+	1.11423i	0.341390	+	0.939922i	$0.389102\pi$
$881$	−19.0942	+	33.0722i	−0.643301	+	1.11423i	−0.984691	+	0.174309i	$0.944231\pi$
$882$	−0.563687	+	0.976335i	−0.0189803	+	0.0328749i
$883$	4.45281			0.149849			0.0749245	−	0.997189i	$-0.476128\pi$
$883$	4.45281			0.149849			0.0749245	+	0.997189i	$0.476128\pi$
$884$		0			0
$885$	12.4886			0.419799
$886$	8.26755	−	14.3198i	0.277754	−	0.481084i
$887$	−3.03146	+	5.25064i	−0.101786	+	0.176299i	−0.912421	−	0.409254i	$-0.865789\pi$
$887$	−3.03146	+	5.25064i	−0.101786	+	0.176299i	0.810634	+	0.585553i	$0.199123\pi$
$888$	1.66487	+	2.88365i	0.0558695	+	0.0967689i
$889$	32.4999			1.09001
$890$	0.227365	+	0.393808i	0.00762130	+	0.0132005i
$891$	−7.47501	−	12.9471i	−0.250422	−	0.433744i
$892$	−6.31767			−0.211531
$893$	7.85086	+	13.5981i	0.262719	+	0.455042i
$894$	12.9758	−	22.4748i	0.433977	−	0.751670i
$895$	−2.99880	+	5.19408i	−0.100239	+	0.173619i
$896$	−2.49396			−0.0833173
$897$		0			0
$898$	−6.56704			−0.219145
$899$	21.5797	−	37.3772i	0.719724	−	1.24660i
$900$	0.722521	−	1.25144i	0.0240840	−	0.0417148i
$901$	10.5972	+	18.3548i	0.353043	+	0.611488i
$902$	72.7730			2.42308
$903$	10.8576	+	18.8058i	0.361317	+	0.625819i
$904$	4.11745	+	7.13163i	0.136944	+	0.237195i
$905$	16.5676			0.550727
$906$	3.71379	+	6.43248i	0.123382	+	0.213705i
$907$	−12.5558	+	21.7473i	−0.416908	+	0.722106i	−0.995627	−	0.0934214i	$-0.970220\pi$
$907$	−12.5558	+	21.7473i	−0.416908	+	0.722106i	0.578719	+	0.815527i	$0.303553\pi$
$908$	−2.44720	+	4.23867i	−0.0812131	+	0.140665i
$909$	−22.7525			−0.754654
$910$		0			0
$911$	4.11721			0.136409			0.0682047	−	0.997671i	$-0.478273\pi$
$911$	4.11721			0.136409			0.0682047	+	0.997671i	$0.478273\pi$
$912$	2.52446	−	4.37249i	0.0835932	−	0.144788i
$913$	42.4722	−	73.5641i	1.40563	−	2.43462i
$914$	−12.0858	−	20.9331i	−0.399761	−	0.692407i
$915$	6.15213			0.203383
$916$	0.344814	+	0.597236i	0.0113930	+	0.0197332i
$917$	12.2567	+	21.2292i	0.404751	+	0.701049i
$918$	−23.8116			−0.785901
$919$	17.3817	+	30.1059i	0.573368	+	0.993102i	0.996217	+	0.0869019i	$0.0276967\pi$
$919$	17.3817	+	30.1059i	0.573368	+	0.993102i	−0.422849	+	0.906200i	$0.638970\pi$
$920$	−1.55496	+	2.69327i	−0.0512655	+	0.0887944i
$921$	−4.80343	+	8.31978i	−0.158278	+	0.274146i
$922$	23.5797			0.776556
$923$		0			0
$924$	18.0435			0.593589
$925$	1.33513	−	2.31251i	0.0438987	−	0.0760347i
$926$	0.841166	−	1.45694i	0.0276424	−	0.0478781i
$927$	−2.67456	−	4.63248i	−0.0878442	−	0.152151i
$928$	−5.60388			−0.183956
$929$	19.4007	+	33.6031i	0.636517	+	1.10248i	0.986191	+	0.165609i	$0.0529590\pi$
$929$	19.4007	+	33.6031i	0.636517	+	1.10248i	−0.349674	+	0.936871i	$0.613708\pi$
$930$	4.80194	+	8.31720i	0.157462	+	0.272732i
$931$	3.15883			0.103527
$932$	−7.09030	−	12.2808i	−0.232251	−	0.402270i
$933$	−2.93900	+	5.09050i	−0.0962186	+	0.166655i
$934$	−0.188137	+	0.325862i	−0.00615602	+	0.0106625i
$935$	24.9245			0.815119
$936$		0			0
$937$	−31.7808			−1.03823			−0.519116	−	0.854704i	$-0.673739\pi$
$937$	−31.7808			−1.03823			−0.519116	+	0.854704i	$0.673739\pi$
$938$	9.99462	−	17.3112i	0.326336	−	0.565231i
$939$	−5.29440	+	9.17018i	−0.172776	+	0.299257i
$940$	1.93900	+	3.35845i	0.0632432	+	0.109541i
$941$	−30.2258			−0.985333			−0.492666	−	0.870218i	$-0.663978\pi$
$941$	−30.2258			−0.985333			−0.492666	+	0.870218i	$0.663978\pi$
$942$	−5.10992	−	8.85063i	−0.166490	−	0.288369i
$943$	−19.5036	−	33.7813i	−0.635126	−	1.10007i
$944$	−10.0151			−0.325963
$945$	6.91185	+	11.9717i	0.224843	+	0.389439i
$946$	20.2561	−	35.0847i	0.658584	−	1.14070i
$947$	1.27144	−	2.20220i	0.0413162	−	0.0715617i	−0.844628	−	0.535354i	$-0.820178\pi$
$947$	1.27144	−	2.20220i	0.0413162	−	0.0715617i	0.885944	+	0.463792i	$0.153512\pi$
$948$	−2.27413			−0.0738602
$949$		0			0
$950$	−4.04892			−0.131364
$951$	16.8659	−	29.2126i	0.546915	−	0.947284i
$952$	5.35690	−	9.27842i	0.173618	−	0.300715i
$953$	3.29321	+	5.70400i	0.106677	+	0.184771i	0.914422	−	0.404761i	$-0.132645\pi$
$953$	3.29321	+	5.70400i	0.106677	+	0.184771i	−0.807745	+	0.589532i	$0.799312\pi$
$954$	7.12929			0.230819
$955$	6.39612	+	11.0784i	0.206974	+	0.358489i
$956$	12.8877	+	22.3221i	0.416818	+	0.721949i
$957$	40.5435			1.31058
$958$	5.01507	+	8.68635i	0.162029	+	0.280643i
$959$	−5.92692	+	10.2657i	−0.191390	+	0.331498i
$960$	0.623490	−	1.07992i	0.0201230	−	0.0348541i
$961$	28.3163			0.913430
$962$		0			0
$963$	−21.7918			−0.702230
$964$	3.93362	−	6.81324i	0.126694	−	0.219440i
$965$	11.7925	−	20.4253i	0.379615	−	0.657513i
$966$	−4.83579	−	8.37583i	−0.155589	−	0.269488i
$967$	−23.1884			−0.745688			−0.372844	−	0.927894i	$-0.621617\pi$
$967$	−23.1884			−0.745688			−0.372844	+	0.927894i	$0.621617\pi$
$968$	−11.3312	−	19.6263i	−0.364200	−	0.630813i
$969$	10.8448	+	18.7838i	0.348386	+	0.603422i
$970$	8.69202			0.279084
$971$	2.29321	+	3.97195i	0.0735926	+	0.127466i	0.900473	−	0.434911i	$-0.143220\pi$
$971$	2.29321	+	3.97195i	0.0735926	+	0.127466i	−0.826881	+	0.562377i	$0.809887\pi$
$972$	−6.70775	+	11.6182i	−0.215151	+	0.372653i
$973$	−2.98493	+	5.17006i	−0.0956926	+	0.165744i
$974$	−15.3297			−0.491197
$975$		0			0
$976$	−4.93362			−0.157921
$977$	−15.0788	+	26.1172i	−0.482412	+	0.835562i	−0.999796	−	0.0201911i	$-0.993573\pi$
$977$	−15.0788	+	26.1172i	−0.482412	+	0.835562i	0.517384	+	0.855753i	$0.326906\pi$
$978$	−10.5293	+	18.2373i	−0.336690	+	0.583164i
$979$	1.31916	+	2.28485i	0.0421605	+	0.0730241i
$980$	0.780167			0.0249215
$981$	12.6310	+	21.8776i	0.403278	+	0.698497i
$982$	−4.59634	−	7.96110i	−0.146675	−	0.254049i
$983$	0.787463			0.0251162			0.0125581	−	0.999921i	$-0.496003\pi$
$983$	0.787463			0.0251162			0.0125581	+	0.999921i	$0.496003\pi$
$984$	7.82036	+	13.5453i	0.249304	+	0.431807i
$985$	0.987918	−	1.71112i	0.0314777	−	0.0545210i
$986$	12.0368	−	20.8484i	0.383331	−	0.663949i
$987$	−12.0603			−0.383882
$988$		0			0
$989$	−21.7151			−0.690501
$990$	4.19202	−	7.26079i	0.133231	−	0.230763i
$991$	6.04461	−	10.4696i	0.192013	−	0.332577i	−0.753904	−	0.656984i	$-0.771832\pi$
$991$	6.04461	−	10.4696i	0.192013	−	0.332577i	0.945917	+	0.324408i	$0.105165\pi$
$992$	−3.85086	−	6.66988i	−0.122265	−	0.211769i
$993$	35.8431			1.13745
$994$	6.83579	+	11.8399i	0.216818	+	0.375540i
$995$	0.417895	+	0.723815i	0.0132482	+	0.0229465i
$996$	18.2567			0.578485
$997$	−23.3303	−	40.4093i	−0.738879	−	1.27978i	−0.953000	−	0.302969i	$-0.902022\pi$
$997$	−23.3303	−	40.4093i	−0.738879	−	1.27978i	0.214121	−	0.976807i	$-0.431311\pi$
$998$	1.37316	−	2.37838i	0.0434666	−	0.0752863i
$999$	−7.40044	+	12.8179i	−0.234139	+	0.405541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.e.p.191.1		6
13.2	odd	12		1690.2.l.m.361.1		12
13.3	even	3	inner	1690.2.e.p.991.1		6
13.4	even	6		1690.2.a.p.1.3	✓	3
13.5	odd	4		1690.2.l.m.1161.4		12
13.6	odd	12		1690.2.d.i.1351.3		6
13.7	odd	12		1690.2.d.i.1351.6		6
13.8	odd	4		1690.2.l.m.1161.1		12
13.9	even	3		1690.2.a.r.1.3	yes	3
13.10	even	6		1690.2.e.r.991.1		6
13.11	odd	12		1690.2.l.m.361.4		12
13.12	even	2		1690.2.e.r.191.1		6
65.4	even	6		8450.2.a.cg.1.1		3
65.9	even	6		8450.2.a.bv.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.a.p.1.3	✓	3	13.4	even	6
1690.2.a.r.1.3	yes	3	13.9	even	3
1690.2.d.i.1351.3		6	13.6	odd	12
1690.2.d.i.1351.6		6	13.7	odd	12
1690.2.e.p.191.1		6	1.1	even	1	trivial
1690.2.e.p.991.1		6	13.3	even	3	inner
1690.2.e.r.191.1		6	13.12	even	2
1690.2.e.r.991.1		6	13.10	even	6
1690.2.l.m.361.1		12	13.2	odd	12
1690.2.l.m.361.4		12	13.11	odd	12
1690.2.l.m.1161.1		12	13.8	odd	4
1690.2.l.m.1161.4		12	13.5	odd	4
8450.2.a.bv.1.1		3	65.9	even	6
8450.2.a.cg.1.1		3	65.4	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} +(-0.623490 + 1.07992i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-0.623490 - 1.07992i) q^{6} +(1.24698 + 2.15983i) q^{7} +1.00000 q^{8} +(0.722521 + 1.25144i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.90097 - 5.02463i) q^{11} +1.24698 q^{12} -2.49396 q^{14} +(0.623490 - 1.07992i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.14795 - 3.72036i) q^{17} -1.44504 q^{18} +(2.02446 + 3.50647i) q^{19} +(0.500000 + 0.866025i) q^{20} -3.10992 q^{21} +(2.90097 + 5.02463i) q^{22} +(1.55496 - 2.69327i) q^{23} +(-0.623490 + 1.07992i) q^{24} +1.00000 q^{25} -5.54288 q^{27} +(1.24698 - 2.15983i) q^{28} +(2.80194 - 4.85310i) q^{29} +(0.623490 + 1.07992i) q^{30} +7.70171 q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.61745 + 6.26561i) q^{33} +4.29590 q^{34} +(-1.24698 - 2.15983i) q^{35} +(0.722521 - 1.25144i) q^{36} +(1.33513 - 2.31251i) q^{37} -4.04892 q^{38} -1.00000 q^{40} +(6.27144 - 10.8624i) q^{41} +(1.55496 - 2.69327i) q^{42} +(-3.49127 - 6.04706i) q^{43} -5.80194 q^{44} +(-0.722521 - 1.25144i) q^{45} +(1.55496 + 2.69327i) q^{46} +3.87800 q^{47} +(-0.623490 - 1.07992i) q^{48} +(0.390084 - 0.675645i) q^{49} +(-0.500000 + 0.866025i) q^{50} +5.35690 q^{51} -4.93362 q^{53} +(2.77144 - 4.80027i) q^{54} +(-2.90097 + 5.02463i) q^{55} +(1.24698 + 2.15983i) q^{56} -5.04892 q^{57} +(2.80194 + 4.85310i) q^{58} +(5.00753 + 8.67330i) q^{59} -1.24698 q^{60} +(2.46681 + 4.27264i) q^{61} +(-3.85086 + 6.66988i) q^{62} +(-1.80194 + 3.12105i) q^{63} +1.00000 q^{64} -7.23490 q^{66} +(-4.00753 + 6.94125i) q^{67} +(-2.14795 + 3.72036i) q^{68} +(1.93900 + 3.35845i) q^{69} +2.49396 q^{70} +(-2.74094 - 4.74745i) q^{71} +(0.722521 + 1.25144i) q^{72} -8.67456 q^{73} +(1.33513 + 2.31251i) q^{74} +(-0.623490 + 1.07992i) q^{75} +(2.02446 - 3.50647i) q^{76} +14.4698 q^{77} -1.82371 q^{79} +(0.500000 - 0.866025i) q^{80} +(1.28836 - 2.23151i) q^{81} +(6.27144 + 10.8624i) q^{82} +14.6407 q^{83} +(1.55496 + 2.69327i) q^{84} +(2.14795 + 3.72036i) q^{85} +6.98254 q^{86} +(3.49396 + 6.05171i) q^{87} +(2.90097 - 5.02463i) q^{88} +(-0.227365 + 0.393808i) q^{89} +1.44504 q^{90} -3.10992 q^{92} +(-4.80194 + 8.31720i) q^{93} +(-1.93900 + 3.35845i) q^{94} +(-2.02446 - 3.50647i) q^{95} +1.24698 q^{96} +(4.34601 + 7.52751i) q^{97} +(0.390084 + 0.675645i) q^{98} +8.38404 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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