LMFDB - Embedded newform 43.2.e.b.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,2,Mod(4,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("43.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	43.e (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.343356728692$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			4.1
Root			$0.222521 - 0.974928i$ of defining polynomial
Character	$\chi$	$=$	43.4
Dual form			43.2.e.b.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.626980i) q^{2} +(-2.02446 - 2.53859i) q^{3} +(0.301938 + 1.32288i) q^{4} +(1.80194 + 0.867767i) q^{5} -2.60388 q^{6} -1.19806 q^{7} +(2.42543 + 1.16802i) q^{8} +(-1.67845 + 7.35376i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.626980i) q^{2} +(-2.02446 - 2.53859i) q^{3} +(0.301938 + 1.32288i) q^{4} +(1.80194 + 0.867767i) q^{5} -2.60388 q^{6} -1.19806 q^{7} +(2.42543 + 1.16802i) q^{8} +(-1.67845 + 7.35376i) q^{9} +(1.44504 - 0.695895i) q^{10} +(0.0745725 - 0.326723i) q^{11} +(2.74698 - 3.44460i) q^{12} +(-4.54892 - 2.19064i) q^{13} +(-0.599031 + 0.751161i) q^{14} +(-1.44504 - 6.33114i) q^{15} +(-0.500000 + 0.240787i) q^{16} +(1.44504 - 0.695895i) q^{17} +(3.77144 + 4.72923i) q^{18} +(-0.211636 - 0.927237i) q^{19} +(-0.603875 + 2.64575i) q^{20} +(2.42543 + 3.04139i) q^{21} +(-0.167563 - 0.210117i) q^{22} +(-0.791053 + 3.46583i) q^{23} +(-1.94504 - 8.52179i) q^{24} +(-0.623490 - 0.781831i) q^{25} +(-3.64795 + 1.75676i) q^{26} +(13.2899 - 6.40006i) q^{27} +(-0.361740 - 1.58489i) q^{28} +(3.02446 - 3.79255i) q^{29} +(-4.69202 - 2.25956i) q^{30} +(-2.83244 + 3.55176i) q^{31} +(-1.29709 + 5.68294i) q^{32} +(-0.980386 + 0.472129i) q^{33} +(0.286208 - 1.25396i) q^{34} +(-2.15883 - 1.03964i) q^{35} -10.2349 q^{36} +4.52111 q^{37} +(-0.687177 - 0.330927i) q^{38} +(3.64795 + 15.9827i) q^{39} +(3.35690 + 4.20941i) q^{40} +(3.60992 - 4.52669i) q^{41} +3.11960 q^{42} +(-2.57457 - 6.03089i) q^{43} +0.454731 q^{44} +(-9.40581 + 11.7945i) q^{45} +(1.77748 + 2.22889i) q^{46} +(0.222521 + 0.974928i) q^{47} +(1.62349 + 0.781831i) q^{48} -5.56465 q^{49} -0.801938 q^{50} +(-4.69202 - 2.25956i) q^{51} +(1.52446 - 6.67909i) q^{52} +(-2.40097 + 1.15625i) q^{53} +(2.63222 - 11.5325i) q^{54} +(0.417895 - 0.524023i) q^{55} +(-2.90581 - 1.39937i) q^{56} +(-1.92543 + 2.41441i) q^{57} +(-0.865625 - 3.79255i) q^{58} +(11.1773 - 5.38268i) q^{59} +(7.93900 - 3.82322i) q^{60} +(2.88740 + 3.62068i) q^{61} +(0.810667 + 3.55176i) q^{62} +(2.01089 - 8.81026i) q^{63} +(2.22252 + 2.78695i) q^{64} +(-6.29590 - 7.89481i) q^{65} +(-0.194177 + 0.850747i) q^{66} +(1.48039 + 6.48599i) q^{67} +(1.35690 + 1.70149i) q^{68} +(10.3998 - 5.00827i) q^{69} +(-1.73125 + 0.833726i) q^{70} +(0.149145 + 0.653447i) q^{71} +(-12.6603 + 15.8755i) q^{72} +(5.02446 + 2.41965i) q^{73} +(2.26055 - 2.83464i) q^{74} +(-0.722521 + 3.16557i) q^{75} +(1.16272 - 0.559936i) q^{76} +(-0.0893425 + 0.391435i) q^{77} +(11.8448 + 5.70416i) q^{78} +4.38404 q^{79} -1.10992 q^{80} +(-22.7642 - 10.9627i) q^{81} +(-1.03319 - 4.52669i) q^{82} +(-3.79440 - 4.75803i) q^{83} +(-3.29105 + 4.12685i) q^{84} +3.20775 q^{85} +(-5.06853 - 1.40124i) q^{86} -15.7506 q^{87} +(0.562491 - 0.705341i) q^{88} +(-8.71797 - 10.9320i) q^{89} +(2.69202 + 11.7945i) q^{90} +(5.44989 + 2.62453i) q^{91} -4.82371 q^{92} +14.7506 q^{93} +(0.722521 + 0.347948i) q^{94} +(0.423272 - 1.85447i) q^{95} +(17.0526 - 8.21208i) q^{96} +(-3.38189 + 14.8170i) q^{97} +(-2.78232 + 3.48892i) q^{98} +(2.27748 + 1.09678i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{3} - 7 q^{4} + 2 q^{5} + 2 q^{6} - 16 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^3 - 7 * q^4 + 2 * q^5 + 2 * q^6 - 16 * q^7 + q^8 - 6 * q^9	\( 6 q + 3 q^{2} - 3 q^{3} - 7 q^{4} + 2 q^{5} + 2 q^{6} - 16 q^{7} + q^{8} - 6 q^{9} + 8 q^{10} + 14 q^{11} + 7 q^{12} - 9 q^{13} - 8 q^{14} - 8 q^{15} - 3 q^{16} + 8 q^{17} + 4 q^{18} - 4 q^{19} + 14 q^{20} + q^{21} + q^{23} - 11 q^{24} + q^{25} - 8 q^{26} + 33 q^{27} + 28 q^{28} + 9 q^{29} - 18 q^{30} - 18 q^{31} - 21 q^{32} + 7 q^{33} + 18 q^{34} + 4 q^{35} - 14 q^{36} - 4 q^{37} - 16 q^{38} + 8 q^{39} + 12 q^{40} + 23 q^{41} - 24 q^{42} - 29 q^{43} - 42 q^{44} - 30 q^{45} + 11 q^{46} + q^{47} + 5 q^{48} + 10 q^{49} + 4 q^{50} - 18 q^{51} - 10 q^{53} + 27 q^{54} + 14 q^{55} + 9 q^{56} + 2 q^{57} - 13 q^{58} + 22 q^{59} + 28 q^{60} + 19 q^{61} + 12 q^{62} + 9 q^{63} + 13 q^{64} - 10 q^{65} + 28 q^{66} - 4 q^{67} + 17 q^{69} - 26 q^{70} + 28 q^{71} - 15 q^{72} + 21 q^{73} - 2 q^{74} - 4 q^{75} + 28 q^{76} - 49 q^{77} + 25 q^{78} + 6 q^{79} - 8 q^{80} - 58 q^{81} - 13 q^{82} - 39 q^{83} - 14 q^{84} - 16 q^{85} - 25 q^{86} - 22 q^{87} - 21 q^{88} + 11 q^{89} + 6 q^{90} + 10 q^{91} - 14 q^{92} + 16 q^{93} + 4 q^{94} + 8 q^{95} + 21 q^{96} - 19 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^3 - 7 * q^4 + 2 * q^5 + 2 * q^6 - 16 * q^7 + q^8 - 6 * q^9 + 8 * q^10 + 14 * q^11 + 7 * q^12 - 9 * q^13 - 8 * q^14 - 8 * q^15 - 3 * q^16 + 8 * q^17 + 4 * q^18 - 4 * q^19 + 14 * q^20 + q^21 + q^23 - 11 * q^24 + q^25 - 8 * q^26 + 33 * q^27 + 28 * q^28 + 9 * q^29 - 18 * q^30 - 18 * q^31 - 21 * q^32 + 7 * q^33 + 18 * q^34 + 4 * q^35 - 14 * q^36 - 4 * q^37 - 16 * q^38 + 8 * q^39 + 12 * q^40 + 23 * q^41 - 24 * q^42 - 29 * q^43 - 42 * q^44 - 30 * q^45 + 11 * q^46 + q^47 + 5 * q^48 + 10 * q^49 + 4 * q^50 - 18 * q^51 - 10 * q^53 + 27 * q^54 + 14 * q^55 + 9 * q^56 + 2 * q^57 - 13 * q^58 + 22 * q^59 + 28 * q^60 + 19 * q^61 + 12 * q^62 + 9 * q^63 + 13 * q^64 - 10 * q^65 + 28 * q^66 - 4 * q^67 + 17 * q^69 - 26 * q^70 + 28 * q^71 - 15 * q^72 + 21 * q^73 - 2 * q^74 - 4 * q^75 + 28 * q^76 - 49 * q^77 + 25 * q^78 + 6 * q^79 - 8 * q^80 - 58 * q^81 - 13 * q^82 - 39 * q^83 - 14 * q^84 - 16 * q^85 - 25 * q^86 - 22 * q^87 - 21 * q^88 + 11 * q^89 + 6 * q^90 + 10 * q^91 - 14 * q^92 + 16 * q^93 + 4 * q^94 + 8 * q^95 + 21 * q^96 - 19 * q^97 + 5 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{7}\right)$

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	−	0.626980i	0.353553	−	0.443342i	−0.572972	−	0.819575i	$-0.694209\pi$
$2$	0.500000	−	0.626980i	0.353553	−	0.443342i	0.926525	+	0.376233i	$0.122781\pi$
$3$	−2.02446	−	2.53859i	−1.16882	−	1.46566i	−0.856851	−	0.515564i	$-0.827582\pi$
$3$	−2.02446	−	2.53859i	−1.16882	−	1.46566i	−0.311971	−	0.950092i	$-0.600989\pi$
$4$	0.301938	+	1.32288i	0.150969	+	0.661438i
$5$	1.80194	+	0.867767i	0.805851	+	0.388077i	0.791003	−	0.611812i	$-0.209559\pi$
$5$	1.80194	+	0.867767i	0.805851	+	0.388077i	0.0148481	+	0.999890i	$0.495274\pi$
$6$	−2.60388			−1.06303
$7$	−1.19806			−0.452825			−0.226412	−	0.974032i	$-0.572700\pi$
$7$	−1.19806			−0.452825			−0.226412	+	0.974032i	$0.572700\pi$
$8$	2.42543	+	1.16802i	0.857518	+	0.412959i
$9$	−1.67845	+	7.35376i	−0.559483	+	2.45125i
$10$	1.44504	−	0.695895i	0.456962	−	0.220061i
$11$	0.0745725	−	0.326723i	0.0224844	−	0.0985108i	−0.962441	−	0.271492i	$-0.912483\pi$
$11$	0.0745725	−	0.326723i	0.0224844	−	0.0985108i	0.984925	+	0.172981i	$0.0553400\pi$
$12$	2.74698	−	3.44460i	0.792985	−	0.994371i
$13$	−4.54892	−	2.19064i	−1.26164	−	0.607575i	−0.321034	−	0.947068i	$-0.604030\pi$
$13$	−4.54892	−	2.19064i	−1.26164	−	0.607575i	−0.940609	+	0.339493i	$0.889745\pi$
$14$	−0.599031	+	0.751161i	−0.160098	+	0.200756i
$15$	−1.44504	−	6.33114i	−0.373108	−	1.63469i
$16$	−0.500000	+	0.240787i	−0.125000	+	0.0601968i
$17$	1.44504	−	0.695895i	0.350474	−	0.168779i	−0.250361	−	0.968153i	$-0.580549\pi$
$17$	1.44504	−	0.695895i	0.350474	−	0.168779i	0.600835	+	0.799373i	$0.294835\pi$
$18$	3.77144	+	4.72923i	0.888937	+	1.11469i
$19$	−0.211636	−	0.927237i	−0.0485526	−	0.212723i	0.944832	−	0.327554i	$-0.106224\pi$
$19$	−0.211636	−	0.927237i	−0.0485526	−	0.212723i	−0.993385	+	0.114831i	$0.963367\pi$
$20$	−0.603875	+	2.64575i	−0.135031	+	0.591608i
$21$	2.42543	+	3.04139i	0.529272	+	0.663686i
$22$	−0.167563	−	0.210117i	−0.0357245	−	0.0447971i
$23$	−0.791053	+	3.46583i	−0.164946	+	0.722675i	0.823021	+	0.568011i	$0.192287\pi$
$23$	−0.791053	+	3.46583i	−0.164946	+	0.722675i	−0.987967	+	0.154664i	$0.950570\pi$
$24$	−1.94504	−	8.52179i	−0.397030	−	1.73950i
$25$	−0.623490	−	0.781831i	−0.124698	−	0.156366i
$26$	−3.64795	+	1.75676i	−0.715422	+	0.344529i
$27$	13.2899	−	6.40006i	2.55763	−	1.23169i
$28$	−0.361740	−	1.58489i	−0.0683625	−	0.299516i
$29$	3.02446	−	3.79255i	0.561628	−	0.704259i	−0.417230	−	0.908801i	$-0.636999\pi$
$29$	3.02446	−	3.79255i	0.561628	−	0.704259i	0.978858	+	0.204542i	$0.0655705\pi$
$30$	−4.69202	−	2.25956i	−0.856642	−	0.412537i
$31$	−2.83244	+	3.55176i	−0.508721	+	0.637916i	−0.968172	−	0.250288i	$-0.919475\pi$
$31$	−2.83244	+	3.55176i	−0.508721	+	0.637916i	0.459451	+	0.888203i	$0.348046\pi$
$32$	−1.29709	+	5.68294i	−0.229296	+	1.00461i
$33$	−0.980386	+	0.472129i	−0.170663	+	0.0821871i
$34$	0.286208	−	1.25396i	0.0490843	−	0.215052i
$35$	−2.15883	−	1.03964i	−0.364909	−	0.175731i
$36$	−10.2349			−1.70582
$37$	4.52111			0.743265			0.371633	−	0.928380i	$-0.378798\pi$
$37$	4.52111			0.743265			0.371633	+	0.928380i	$0.378798\pi$
$38$	−0.687177	−	0.330927i	−0.111475	−	0.0536835i
$39$	3.64795	+	15.9827i	0.584139	+	2.55928i
$40$	3.35690	+	4.20941i	0.530772	+	0.665567i
$41$	3.60992	−	4.52669i	0.563774	−	0.706950i	−0.415476	−	0.909604i	$-0.636385\pi$
$41$	3.60992	−	4.52669i	0.563774	−	0.706950i	0.979251	+	0.202654i	$0.0649565\pi$
$42$	3.11960			0.481365
$43$	−2.57457	−	6.03089i	−0.392619	−	0.919701i
$43$	−2.57457	−	6.03089i	−0.392619	−	0.919701i
$44$	0.454731			0.0685532
$45$	−9.40581	+	11.7945i	−1.40214	+	1.75822i
$46$	1.77748	+	2.22889i	0.262075	+	0.328632i
$47$	0.222521	+	0.974928i	0.0324580	+	0.142208i	0.988561	−	0.150824i	$-0.0481928\pi$
$47$	0.222521	+	0.974928i	0.0324580	+	0.142208i	−0.956103	+	0.293032i	$0.905336\pi$
$48$	1.62349	+	0.781831i	0.234331	+	0.112848i
$49$	−5.56465			−0.794950
$50$	−0.801938			−0.113411
$51$	−4.69202	−	2.25956i	−0.657014	−	0.316401i
$52$	1.52446	−	6.67909i	0.211404	−	0.926223i
$53$	−2.40097	+	1.15625i	−0.329798	+	0.158823i	−0.591454	−	0.806339i	$-0.701446\pi$
$53$	−2.40097	+	1.15625i	−0.329798	+	0.158823i	0.261656	+	0.965161i	$0.415732\pi$
$54$	2.63222	−	11.5325i	0.358200	−	1.56938i
$55$	0.417895	−	0.524023i	0.0563489	−	0.0706593i
$56$	−2.90581	−	1.39937i	−0.388306	−	0.186998i
$57$	−1.92543	+	2.41441i	−0.255029	+	0.319796i
$58$	−0.865625	−	3.79255i	−0.113662	−	0.497986i
$59$	11.1773	−	5.38268i	1.45515	−	0.700765i	0.471673	−	0.881774i	$-0.343650\pi$
$59$	11.1773	−	5.38268i	1.45515	−	0.700765i	0.983482	+	0.181008i	$0.0579361\pi$
$60$	7.93900	−	3.82322i	1.02492	−	0.493576i
$61$	2.88740	+	3.62068i	0.369693	+	0.463580i	0.931528	−	0.363669i	$-0.118476\pi$
$61$	2.88740	+	3.62068i	0.369693	+	0.463580i	−0.561835	+	0.827249i	$0.689905\pi$
$62$	0.810667	+	3.55176i	0.102955	+	0.451074i
$63$	2.01089	−	8.81026i	0.253348	−	1.10999i
$64$	2.22252	+	2.78695i	0.277815	+	0.348369i
$65$	−6.29590	−	7.89481i	−0.780910	−	0.979230i
$66$	−0.194177	+	0.850747i	−0.0239016	+	0.104720i
$67$	1.48039	+	6.48599i	0.180858	+	0.792390i	0.981223	+	0.192877i	$0.0617819\pi$
$67$	1.48039	+	6.48599i	0.180858	+	0.792390i	−0.800365	+	0.599513i	$0.795361\pi$
$68$	1.35690	+	1.70149i	0.164548	+	0.206336i
$69$	10.3998	−	5.00827i	1.25199	−	0.602924i
$70$	−1.73125	+	0.833726i	−0.206924	+	0.0996493i
$71$	0.149145	+	0.653447i	0.0177002	+	0.0775498i	0.983007	−	0.183570i	$-0.0587654\pi$
$71$	0.149145	+	0.653447i	0.0177002	+	0.0775498i	−0.965306	+	0.261120i	$0.915908\pi$
$72$	−12.6603	+	15.8755i	−1.49203	+	1.87095i
$73$	5.02446	+	2.41965i	0.588068	+	0.283199i	0.704162	−	0.710039i	$-0.251323\pi$
$73$	5.02446	+	2.41965i	0.588068	+	0.283199i	−0.116093	+	0.993238i	$0.537037\pi$
$74$	2.26055	−	2.83464i	0.262784	−	0.329521i
$75$	−0.722521	+	3.16557i	−0.0834295	+	0.365529i
$76$	1.16272	−	0.559936i	0.133373	−	0.0642290i
$77$	−0.0893425	+	0.391435i	−0.0101815	+	0.0446081i
$78$	11.8448	+	5.70416i	1.34116	+	0.645869i
$79$	4.38404			0.493243			0.246622	−	0.969112i	$-0.420679\pi$
$79$	4.38404			0.493243			0.246622	+	0.969112i	$0.420679\pi$
$80$	−1.10992			−0.124092
$81$	−22.7642	−	10.9627i	−2.52936	−	1.21807i
$82$	−1.03319	−	4.52669i	−0.114097	−	0.499889i
$83$	−3.79440	−	4.75803i	−0.416490	−	0.522262i	0.528689	−	0.848816i	$-0.322684\pi$
$83$	−3.79440	−	4.75803i	−0.416490	−	0.522262i	−0.945179	+	0.326554i	$0.894113\pi$
$84$	−3.29105	+	4.12685i	−0.359083	+	0.450276i
$85$	3.20775			0.347929
$86$	−5.06853	−	1.40124i	−0.546554	−	0.151099i
$87$	−15.7506			−1.68864
$88$	0.562491	−	0.705341i	0.0599617	−	0.0751896i
$89$	−8.71797	−	10.9320i	−0.924103	−	1.15879i	−0.986992	−	0.160768i	$-0.948603\pi$
$89$	−8.71797	−	10.9320i	−0.924103	−	1.15879i	0.0628890	−	0.998021i	$-0.479969\pi$
$90$	2.69202	+	11.7945i	0.283764	+	1.24325i
$91$	5.44989	+	2.62453i	0.571303	+	0.275125i
$92$	−4.82371			−0.502906
$93$	14.7506			1.52957
$94$	0.722521	+	0.347948i	0.0745223	+	0.0358881i
$95$	0.423272	−	1.85447i	0.0434268	−	0.190265i
$96$	17.0526	−	8.21208i	1.74042	−	0.838142i
$97$	−3.38189	+	14.8170i	−0.343379	+	1.50444i	0.448512	+	0.893777i	$0.351954\pi$
$97$	−3.38189	+	14.8170i	−0.343379	+	1.50444i	−0.791891	+	0.610663i	$0.790903\pi$
$98$	−2.78232	+	3.48892i	−0.281057	+	0.352434i
$99$	2.27748	+	1.09678i	0.228895	+	0.110230i
$100$	0.846011	−	1.06086i	0.0846011	−	0.106086i
$101$	3.55765	+	15.5871i	0.353999	+	1.55097i	0.767852	+	0.640627i	$0.221326\pi$
$101$	3.55765	+	15.5871i	0.353999	+	1.55097i	−0.413853	+	0.910344i	$0.635817\pi$
$102$	−3.76271	+	1.81203i	−0.372564	+	0.179417i
$103$	−13.5918	+	6.54546i	−1.33924	+	0.644944i	−0.959907	−	0.280317i	$-0.909560\pi$
$103$	−13.5918	+	6.54546i	−1.33924	+	0.644944i	−0.379332	+	0.925261i	$0.623846\pi$
$104$	−8.47434	−	10.6265i	−0.830978	−	1.04201i
$105$	1.73125	+	7.58510i	0.168953	+	0.740230i
$106$	−0.475541	+	2.08348i	−0.0461887	+	0.202366i
$107$	2.29105	+	2.87289i	0.221484	+	0.277733i	0.880142	−	0.474710i	$-0.157447\pi$
$107$	2.29105	+	2.87289i	0.221484	+	0.277733i	−0.658658	+	0.752442i	$0.728876\pi$
$108$	12.4792	+	15.6484i	1.20081	+	1.50577i
$109$	1.25182	−	5.48460i	0.119903	−	0.525329i	−0.878926	−	0.476957i	$-0.841740\pi$
$109$	1.25182	−	5.48460i	0.119903	−	0.525329i	0.998829	−	0.0483719i	$-0.0154033\pi$
$110$	−0.119605	−	0.524023i	−0.0114039	−	0.0499637i
$111$	−9.15279	−	11.4772i	−0.868745	−	1.08937i
$112$	0.599031	−	0.288478i	0.0566031	−	0.0272586i
$113$	2.26659	−	1.09153i	0.213223	−	0.102683i	−0.324224	−	0.945980i	$-0.605103\pi$
$113$	2.26659	−	1.09153i	0.213223	−	0.102683i	0.537447	+	0.843298i	$0.319389\pi$
$114$	0.551073	+	2.41441i	0.0516127	+	0.226130i
$115$	−4.43296	+	5.55876i	−0.413376	+	0.518357i
$116$	5.93027	+	2.85587i	0.550612	+	0.265161i
$117$	23.7446	−	29.7748i	2.19519	−	2.75268i
$118$	2.21379	−	9.69926i	0.203796	−	0.892889i
$119$	−1.73125	+	0.833726i	−0.158703	+	0.0764275i
$120$	3.89008	−	17.0436i	0.355114	−	1.55586i
$121$	9.80947	+	4.72399i	0.891770	+	0.429454i
$122$	3.71379			0.336231
$123$	−18.7995			−1.69510
$124$	−5.55376	−	2.67455i	−0.498743	−	0.240182i
$125$	−2.67025	−	11.6991i	−0.238835	−	1.04640i
$126$	−4.51842	−	5.66592i	−0.402533	−	0.504760i
$127$	2.91454	−	3.65472i	0.258624	−	0.324304i	−0.635520	−	0.772085i	$-0.719214\pi$
$127$	2.91454	−	3.65472i	0.258624	−	0.324304i	0.894143	+	0.447781i	$0.147785\pi$
$128$	−8.79954			−0.777777
$129$	−10.0978	+	18.7451i	−0.889065	+	1.65041i
$130$	−8.09783			−0.710227
$131$	−2.74094	+	3.43703i	−0.239477	+	0.300295i	−0.887017	−	0.461737i	$-0.847226\pi$
$131$	−2.74094	+	3.43703i	−0.239477	+	0.300295i	0.647540	+	0.762031i	$0.275798\pi$
$132$	−0.920583	−	1.15437i	−0.0801265	−	0.100475i
$133$	0.253553	+	1.11089i	0.0219858	+	0.0963262i
$134$	4.80678	+	2.31482i	0.415243	+	0.199970i
$135$	29.5013			2.53906
$136$	4.31767			0.370237
$137$	−5.06853	−	2.44088i	−0.433034	−	0.208538i	0.204652	−	0.978835i	$-0.434394\pi$
$137$	−5.06853	−	2.44088i	−0.433034	−	0.208538i	−0.637686	+	0.770297i	$0.720108\pi$
$138$	2.05980	−	9.02458i	0.175342	−	0.768224i
$139$	−14.9046	+	7.17769i	−1.26419	+	0.608803i	−0.941281	−	0.337625i	$-0.890376\pi$
$139$	−14.9046	+	7.17769i	−1.26419	+	0.608803i	−0.322913	+	0.946429i	$0.604662\pi$
$140$	0.723480	−	3.16977i	0.0611453	−	0.267895i
$141$	2.02446	−	2.53859i	0.170490	−	0.213788i
$142$	0.484271	+	0.233212i	0.0406391	+	0.0195707i
$143$	−1.05496	+	1.32288i	−0.0882200	+	0.110624i
$144$	−0.931468	−	4.08103i	−0.0776224	−	0.340086i
$145$	8.74094	−	4.20941i	0.725895	−	0.349573i
$146$	4.02930	−	1.94041i	0.333467	−	0.160589i
$147$	11.2654	+	14.1264i	0.929154	+	1.16512i
$148$	1.36509	+	5.98086i	0.112210	+	0.491624i
$149$	−2.00484	+	8.78380i	−0.164243	+	0.719597i	0.823985	+	0.566611i	$0.191746\pi$
$149$	−2.00484	+	8.78380i	−0.164243	+	0.719597i	−0.988228	+	0.152985i	$0.951111\pi$
$150$	1.62349	+	2.03579i	0.132557	+	0.166222i
$151$	−1.80194	−	2.25956i	−0.146640	−	0.183880i	0.703087	−	0.711104i	$-0.251804\pi$
$151$	−1.80194	−	2.25956i	−0.146640	−	0.183880i	−0.849727	+	0.527224i	$0.823233\pi$
$152$	0.569728	−	2.49614i	0.0462111	−	0.202464i
$153$	2.69202	+	11.7945i	0.217637	+	0.953530i
$154$	0.200751	+	0.251733i	0.0161769	+	0.0202853i
$155$	−8.18598	+	3.94216i	−0.657514	+	0.316642i
$156$	−20.0417	+	9.65156i	−1.60462	+	0.772744i
$157$	−5.14310	−	22.5334i	−0.410464	−	1.79836i	−0.582005	−	0.813185i	$-0.697732\pi$
$157$	−5.14310	−	22.5334i	−0.410464	−	1.79836i	0.171541	−	0.985177i	$-0.445125\pi$
$158$	2.19202	−	2.74871i	0.174388	−	0.218675i
$159$	7.79590	+	3.75431i	0.618255	+	0.297736i
$160$	−7.26875	+	9.11472i	−0.574645	+	0.720582i
$161$	0.947730	−	4.15228i	0.0746916	−	0.327245i
$162$	−18.2555	+	8.79137i	−1.43429	+	0.690715i
$163$	2.79494	−	12.2454i	0.218916	−	0.959135i	−0.739364	−	0.673306i	$-0.764874\pi$
$163$	2.79494	−	12.2454i	0.218916	−	0.959135i	0.958280	−	0.285830i	$-0.0922691\pi$
$164$	7.07822	+	3.40869i	0.552716	+	0.266174i
$165$	−2.17629			−0.169424
$166$	−4.88040			−0.378792
$167$	20.0613	+	9.66101i	1.55239	+	0.747591i	0.996494	−	0.0836609i	$-0.0266613\pi$
$167$	20.0613	+	9.66101i	1.55239	+	0.747591i	0.555895	+	0.831252i	$0.312376\pi$
$168$	2.33028	+	10.2096i	0.179785	+	0.787690i
$169$	7.78836	+	9.76630i	0.599105	+	0.751254i
$170$	1.60388	−	2.01120i	0.123012	−	0.154252i
$171$	7.17390			0.548602
$172$	7.20075	−	5.22679i	0.549052	−	0.398539i
$173$	2.18598			0.166197			0.0830985	−	0.996541i	$-0.473518\pi$
$173$	2.18598			0.166197			0.0830985	+	0.996541i	$0.473518\pi$
$174$	−7.87531	+	9.87533i	−0.597026	+	0.748647i
$175$	0.746980	+	0.936683i	0.0564664	+	0.0708066i
$176$	0.0413846	+	0.181318i	0.00311948	+	0.0136673i
$177$	−36.2923	−	17.4775i	−2.72790	−	1.31369i
$178$	−11.2131			−0.840459
$179$	10.2174			0.763687			0.381844	−	0.924227i	$-0.375289\pi$
$179$	10.2174			0.763687			0.381844	+	0.924227i	$0.375289\pi$
$180$	−18.4426	−	8.88151i	−1.37463	−	0.661989i
$181$	2.95473	−	12.9455i	0.219623	−	0.962233i	−0.738134	−	0.674654i	$-0.764293\pi$
$181$	2.95473	−	12.9455i	0.219623	−	0.962233i	0.957757	−	0.287578i	$-0.0928502\pi$
$182$	4.37047	−	2.10471i	0.323961	−	0.156011i
$183$	3.34601	−	14.6598i	0.247344	−	1.08369i
$184$	−5.96681	+	7.48215i	−0.439879	+	0.551591i
$185$	8.14675	+	3.92327i	0.598961	+	0.288444i
$186$	7.37531	−	9.24835i	0.540784	−	0.678122i
$187$	−0.119605	−	0.524023i	−0.00874638	−	0.0383204i
$188$	−1.22252	+	0.588735i	−0.0891615	+	0.0429379i
$189$	−15.9221	+	7.66767i	−1.15816	+	0.557741i
$190$	−0.951083	−	1.19262i	−0.0689988	−	0.0865217i
$191$	4.76928	+	20.8956i	0.345093	+	1.51195i	0.788164	+	0.615465i	$0.211032\pi$
$191$	4.76928	+	20.8956i	0.345093	+	1.51195i	−0.443071	+	0.896487i	$0.646111\pi$
$192$	2.57553	−	11.2841i	0.185873	−	0.814363i
$193$	−5.45257	−	6.83731i	−0.392485	−	0.492161i	0.545853	−	0.837881i	$-0.316206\pi$
$193$	−5.45257	−	6.83731i	−0.392485	−	0.492161i	−0.938337	+	0.345721i	$0.887634\pi$
$194$	7.59903	+	9.52888i	0.545579	+	0.684134i
$195$	−7.29590	+	31.9654i	−0.522470	+	2.28909i
$196$	−1.68018	−	7.36134i	−0.120013	−	0.525810i
$197$	11.5571	+	14.4922i	0.823410	+	1.03252i	0.998846	+	0.0480329i	$0.0152952\pi$
$197$	11.5571	+	14.4922i	0.823410	+	1.03252i	−0.175435	+	0.984491i	$0.556133\pi$
$198$	1.82640	−	0.879546i	0.129796	−	0.0625066i
$199$	3.08211	−	1.48426i	0.218485	−	0.105217i	−0.321440	−	0.946930i	$-0.604167\pi$
$199$	3.08211	−	1.48426i	0.218485	−	0.105217i	0.539925	+	0.841713i	$0.318453\pi$
$200$	−0.599031	−	2.62453i	−0.0423579	−	0.185582i
$201$	13.4683	−	16.8887i	0.949981	−	1.19124i
$202$	11.5516	+	5.56296i	0.812768	+	0.391409i
$203$	−3.62349	+	4.54371i	−0.254319	+	0.318906i
$204$	1.57242	−	6.88921i	0.110091	−	0.482341i
$205$	10.4330	−	5.02425i	0.728670	−	0.350909i
$206$	−2.69202	+	11.7945i	−0.187562	+	0.821763i
$207$	−24.1591	−	11.6344i	−1.67918	−	0.808648i
$208$	2.80194			0.194279
$209$	−0.318732			−0.0220472
$210$	5.62133	+	2.70709i	0.387909	+	0.186807i
$211$	−1.98158	−	8.68188i	−0.136418	−	0.597685i	−0.996205	−	0.0870334i	$-0.972261\pi$
$211$	−1.98158	−	8.68188i	−0.136418	−	0.597685i	0.859788	−	0.510652i	$-0.170596\pi$
$212$	−2.25451	−	2.82707i	−0.154841	−	0.194164i
$213$	1.35690	−	1.70149i	0.0929730	−	0.116584i
$214$	2.94677			0.201437
$215$	0.594187	−	13.1014i	0.0405232	−	0.893509i
$216$	39.7090			2.70186
$217$	3.39344	−	4.25523i	0.230361	−	0.288864i
$218$	−2.81282	−	3.52717i	−0.190508	−	0.238890i
$219$	−4.02930	−	17.6535i	−0.272275	−	1.19292i
$220$	0.819396	+	0.394600i	0.0552437	+	0.0266040i
$221$	−8.09783			−0.544719
$222$	−11.7724			−0.790112
$223$	4.40581	+	2.12173i	0.295035	+	0.142081i	0.575546	−	0.817769i	$-0.304790\pi$
$223$	4.40581	+	2.12173i	0.295035	+	0.142081i	−0.280511	+	0.959851i	$0.590504\pi$
$224$	1.55400	−	6.80851i	0.103831	−	0.454913i
$225$	6.79590	−	3.27273i	0.453060	−	0.218182i
$226$	0.448927	−	1.96688i	0.0298622	−	0.130835i
$227$	−2.58964	+	3.24730i	−0.171880	+	0.215531i	−0.860309	−	0.509773i	$-0.829729\pi$
$227$	−2.58964	+	3.24730i	−0.171880	+	0.215531i	0.688429	+	0.725304i	$0.258301\pi$
$228$	−3.77532	−	1.81810i	−0.250027	−	0.120407i
$229$	−12.1881	+	15.2834i	−0.805415	+	1.00996i	0.194165	+	0.980969i	$0.437800\pi$
$229$	−12.1881	+	15.2834i	−0.805415	+	1.00996i	−0.999580	+	0.0289892i	$0.990771\pi$
$230$	1.26875	+	5.55876i	0.0836589	+	0.366534i
$231$	1.17456	−	0.565640i	0.0772806	−	0.0372164i
$232$	11.7654	−	5.66592i	0.772436	−	0.371986i
$233$	−4.83728	−	6.06576i	−0.316901	−	0.397381i	0.597713	−	0.801710i	$-0.296076\pi$
$233$	−4.83728	−	6.06576i	−0.316901	−	0.397381i	−0.914613	+	0.404329i	$0.867505\pi$
$234$	−6.79590	−	29.7748i	−0.444262	−	1.94644i
$235$	−0.445042	+	1.94986i	−0.0290313	+	0.127195i
$236$	10.4955	+	13.1609i	0.683196	+	0.856700i
$237$	−8.87531	−	11.1293i	−0.576514	−	0.722925i
$238$	−0.342895	+	1.50232i	−0.0222266	+	0.0973811i
$239$	−3.48254	−	15.2580i	−0.225267	−	0.986959i	−0.953444	−	0.301570i	$-0.902489\pi$
$239$	−3.48254	−	15.2580i	−0.225267	−	0.986959i	0.728177	−	0.685389i	$-0.240368\pi$
$240$	2.24698	+	2.81762i	0.145042	+	0.181877i
$241$	8.63975	−	4.16069i	0.556535	−	0.268013i	−0.134403	−	0.990927i	$-0.542912\pi$
$241$	8.63975	−	4.16069i	0.556535	−	0.268013i	0.690939	+	0.722913i	$0.257197\pi$
$242$	7.86658	−	3.78835i	0.505683	−	0.243524i
$243$	8.40850	+	36.8401i	0.539406	+	2.36329i
$244$	−3.91789	+	4.91288i	−0.250818	+	0.314515i
$245$	−10.0271	−	4.82882i	−0.640611	−	0.308502i
$246$	−9.39977	+	11.7869i	−0.599308	+	0.751508i
$247$	−1.06853	+	4.68154i	−0.0679890	+	0.297879i
$248$	−11.0184	+	5.30619i	−0.699670	+	0.336943i
$249$	−4.39708	+	19.2649i	−0.278654	+	1.22086i
$250$	−8.67025	−	4.17537i	−0.548355	−	0.264074i
$251$	−13.1317			−0.828865			−0.414432	−	0.910080i	$-0.636020\pi$
$251$	−13.1317			−0.828865			−0.414432	+	0.910080i	$0.636020\pi$
$252$	12.2620			0.772436
$253$	1.07338	+	0.516911i	0.0674826	+	0.0324979i
$254$	−0.834166	−	3.65472i	−0.0523402	−	0.229318i
$255$	−6.49396	−	8.14317i	−0.406668	−	0.509945i
$256$	−8.84481	+	11.0910i	−0.552801	+	0.693190i
$257$	−17.8213			−1.11166			−0.555832	−	0.831295i	$-0.687600\pi$
$257$	−17.8213			−1.11166			−0.555832	+	0.831295i	$0.687600\pi$
$258$	6.70387	+	15.7037i	0.417364	+	0.977668i
$259$	−5.41657			−0.336569
$260$	8.54288	−	10.7124i	0.529807	−	0.664357i
$261$	22.8131	+	28.6067i	1.41210	+	1.77071i
$262$	0.784479	+	3.43703i	0.0484653	+	0.212340i
$263$	28.7848	+	13.8620i	1.77495	+	0.854769i	0.962291	+	0.272023i	$0.0876926\pi$
$263$	28.7848	+	13.8620i	1.77495	+	0.854769i	0.812654	+	0.582746i	$0.198022\pi$
$264$	−2.92931			−0.180287
$265$	−5.32975			−0.327404
$266$	0.823281	+	0.396471i	0.0504786	+	0.0243092i
$267$	−10.1027	+	44.2627i	−0.618274	+	2.70884i
$268$	−8.13318	+	3.91673i	−0.496813	+	0.239253i
$269$	0.189866	−	0.831855i	0.0115763	−	0.0507191i	−0.968810	−	0.247805i	$-0.920291\pi$
$269$	0.189866	−	0.831855i	0.0115763	−	0.0507191i	0.980386	+	0.197086i	$0.0631478\pi$
$270$	14.7506	−	18.4967i	0.897695	−	1.12567i
$271$	−2.05280	−	0.988577i	−0.124699	−	0.0600518i	0.370494	−	0.928835i	$-0.379188\pi$
$271$	−2.05280	−	0.988577i	−0.124699	−	0.0600518i	−0.495193	+	0.868783i	$0.664903\pi$
$272$	−0.554958	+	0.695895i	−0.0336493	+	0.0421949i
$273$	−4.37047	−	19.1483i	−0.264513	−	1.15891i
$274$	−4.06465	+	1.95743i	−0.245554	+	0.118253i
$275$	−0.301938	+	0.145406i	−0.0182075	+	0.00876828i
$276$	9.76540	+	12.2454i	0.587808	+	0.737088i
$277$	−0.773831	−	3.39038i	−0.0464950	−	0.203708i	0.946345	−	0.323157i	$-0.104744\pi$
$277$	−0.773831	−	3.39038i	−0.0464950	−	0.203708i	−0.992840	+	0.119449i	$0.961887\pi$
$278$	−2.95204	+	12.9337i	−0.177052	+	0.775714i
$279$	−21.3647	−	26.7905i	−1.27907	−	1.60391i
$280$	−4.02177	−	5.04314i	−0.240347	−	0.301385i
$281$	4.02811	−	17.6483i	0.240297	−	1.05281i	−0.700451	−	0.713701i	$-0.747018\pi$
$281$	4.02811	−	17.6483i	0.240297	−	1.05281i	0.940747	−	0.339108i	$-0.110125\pi$
$282$	−0.579417	−	2.53859i	−0.0345038	−	0.151171i
$283$	−14.8802	−	18.6591i	−0.884534	−	1.10917i	−0.993353	−	0.115108i	$-0.963278\pi$
$283$	−14.8802	−	18.6591i	−0.884534	−	1.10917i	0.108819	−	0.994062i	$-0.465293\pi$
$284$	−0.819396	+	0.394600i	−0.0486222	+	0.0234152i
$285$	−5.56465	+	2.67979i	−0.329621	+	0.158737i
$286$	0.301938	+	1.32288i	0.0178540	+	0.0782233i
$287$	−4.32490	+	5.42326i	−0.255291	+	0.320125i
$288$	−39.6139	−	19.0770i	−2.33427	−	1.12412i
$289$	−8.99545	+	11.2799i	−0.529144	+	0.663526i
$290$	1.73125	−	7.58510i	0.101663	−	0.445413i
$291$	44.4608	−	21.4112i	2.60634	−	1.25515i
$292$	−1.68382	+	7.37732i	−0.0985384	+	0.431725i
$293$	−24.7787	−	11.9328i	−1.44759	−	0.697122i	−0.465414	−	0.885093i	$-0.654095\pi$
$293$	−24.7787	−	11.9328i	−1.44759	−	0.697122i	−0.982175	+	0.187971i	$0.939809\pi$
$294$	14.4896			0.845053
$295$	24.8116			1.44459
$296$	10.9656	+	5.28076i	0.637363	+	0.306938i
$297$	−1.09999	−	4.81937i	−0.0638279	−	0.279648i
$298$	4.50484	+	5.64890i	0.260959	+	0.327232i
$299$	11.1908	−	14.0329i	0.647182	−	0.811541i
$300$	−4.40581			−0.254370
$301$	3.08450	+	7.22538i	0.177788	+	0.416464i
$302$	−2.31767			−0.133367
$303$	32.3669	−	40.5868i	1.85943	−	2.33165i
$304$	0.329085	+	0.412659i	0.0188743	+	0.0236676i
$305$	2.06100	+	9.02983i	0.118012	+	0.517046i
$306$	8.74094	+	4.20941i	0.499686	+	0.240636i
$307$	−20.2838			−1.15766			−0.578829	−	0.815449i	$-0.696490\pi$
$307$	−20.2838			−1.15766			−0.578829	+	0.815449i	$0.696490\pi$
$308$	−0.544796			−0.0310426
$309$	44.1323	+	21.2530i	2.51060	+	1.20904i
$310$	−1.62133	+	7.10353i	−0.0920856	+	0.403453i
$311$	5.15010	−	2.48016i	0.292036	−	0.140637i	−0.282130	−	0.959376i	$-0.591041\pi$
$311$	5.15010	−	2.48016i	0.292036	−	0.140637i	0.574165	+	0.818739i	$0.305327\pi$
$312$	−9.82036	+	43.0258i	−0.555968	+	2.43586i
$313$	−15.1746	+	19.0283i	−0.857717	+	1.07554i	0.138647	+	0.990342i	$0.455725\pi$
$313$	−15.1746	+	19.0283i	−0.857717	+	1.07554i	−0.996364	+	0.0852012i	$0.972847\pi$
$314$	−16.6996	−	8.04208i	−0.942410	−	0.453841i
$315$	11.2687	−	14.1306i	0.634922	−	0.796167i
$316$	1.32371	+	5.79954i	0.0744644	+	0.326250i
$317$	−13.6555	+	6.57613i	−0.766968	+	0.369352i	−0.776103	−	0.630606i	$-0.782806\pi$
$317$	−13.6555	+	6.57613i	−0.766968	+	0.369352i	0.00913503	+	0.999958i	$0.497092\pi$
$318$	6.25182	−	3.01072i	0.350585	−	0.168833i
$319$	−1.01357	−	1.27098i	−0.0567492	−	0.0711613i
$320$	1.58642	+	6.95055i	0.0886834	+	0.388547i
$321$	2.65495	−	11.6321i	0.148185	−	0.649240i
$322$	−2.12953	−	2.67035i	−0.118674	−	0.148813i
$323$	−0.951083	−	1.19262i	−0.0529197	−	0.0663591i
$324$	7.62887	−	33.4242i	0.423826	−	1.85690i
$325$	1.12349	+	4.92233i	0.0623200	+	0.273042i
$326$	−6.28017	−	7.87508i	−0.347826	−	0.436160i
$327$	−16.4574	+	7.92548i	−0.910097	+	0.438280i
$328$	14.0429	−	6.76269i	0.775388	−	0.373407i
$329$	−0.266594	−	1.16802i	−0.0146978	−	0.0643953i
$330$	−1.08815	+	1.36449i	−0.0599005	+	0.0751128i
$331$	−20.8898	−	10.0600i	−1.14821	−	0.552949i	−0.239714	−	0.970843i	$-0.577054\pi$
$331$	−20.8898	−	10.0600i	−1.14821	−	0.552949i	−0.908495	+	0.417895i	$0.862768\pi$
$332$	5.14861	−	6.45616i	0.282567	−	0.354328i
$333$	−7.58844	+	33.2471i	−0.415844	+	1.82193i
$334$	16.0879	−	7.74753i	0.880291	−	0.423926i
$335$	−2.96077	+	12.9720i	−0.161764	+	0.708735i
$336$	−1.94504	−	0.936683i	−0.106111	−	0.0511002i
$337$	21.4644			1.16924			0.584621	−	0.811307i	$-0.301243\pi$
$337$	21.4644			1.16924			0.584621	+	0.811307i	$0.301243\pi$
$338$	10.0175			0.544878
$339$	−7.35958	−	3.54419i	−0.399718	−	0.192494i
$340$	0.968541	+	4.24346i	0.0525265	+	0.230134i
$341$	0.949222	+	1.19029i	0.0514033	+	0.0644577i
$342$	3.58695	−	4.49789i	0.193960	−	0.243218i
$343$	15.0532			0.812798
$344$	0.799782	−	17.6346i	0.0431213	−	0.950796i
$345$	23.0858			1.24290
$346$	1.09299	−	1.37057i	0.0587595	−	0.0736821i
$347$	−15.9717	−	20.0278i	−0.857403	−	1.07515i	−0.996393	−	0.0848561i	$-0.972957\pi$
$347$	−15.9717	−	20.0278i	−0.857403	−	1.07515i	0.138990	−	0.990294i	$-0.455614\pi$
$348$	−4.75571	−	20.8361i	−0.254933	−	1.11693i
$349$	8.72132	+	4.19997i	0.466842	+	0.224819i	0.652490	−	0.757797i	$-0.273724\pi$
$349$	8.72132	+	4.19997i	0.466842	+	0.224819i	−0.185649	+	0.982616i	$0.559439\pi$
$350$	0.960771			0.0513554
$351$	−74.4747			−3.97517
$352$	1.76002	+	0.847581i	0.0938094	+	0.0451762i
$353$	0.0924579	−	0.405084i	0.00492104	−	0.0215605i	−0.972408	−	0.233288i	$-0.925052\pi$
$353$	0.0924579	−	0.405084i	0.00492104	−	0.0215605i	0.977329	+	0.211727i	$0.0679088\pi$
$354$	−29.1042	+	14.0158i	−1.54687	+	0.744933i
$355$	−0.298290	+	1.30689i	−0.0158316	+	0.0693627i
$356$	11.8294	−	14.8336i	0.626956	−	0.786178i
$357$	5.62133	+	2.70709i	0.297513	+	0.143274i
$358$	5.10872	−	6.40613i	0.270004	−	0.338575i
$359$	1.58964	+	6.96466i	0.0838979	+	0.367581i	0.999396	−	0.0347408i	$-0.0110606\pi$
$359$	1.58964	+	6.96466i	0.0838979	+	0.367581i	−0.915498	+	0.402321i	$0.868203\pi$
$360$	−36.5894	+	17.6205i	−1.92843	+	0.928683i
$361$	16.3034	−	7.85132i	0.858075	−	0.413227i
$362$	−6.63922	−	8.32532i	−0.348950	−	0.437569i
$363$	−7.86658	−	34.4658i	−0.412889	−	1.80898i
$364$	−1.82640	+	8.00197i	−0.0957292	+	0.419417i
$365$	6.95407	+	8.72012i	0.363992	+	0.456432i
$366$	−7.51842	−	9.42780i	−0.392994	−	0.492799i
$367$	−1.78113	+	7.80363i	−0.0929741	+	0.407346i	−0.999903	−	0.0139379i	$-0.995563\pi$
$367$	−1.78113	+	7.80363i	−0.0929741	+	0.407346i	0.906929	+	0.421284i	$0.138420\pi$
$368$	−0.439001	−	1.92339i	−0.0228845	−	0.100264i
$369$	27.2292	+	34.1443i	1.41749	+	1.77748i
$370$	6.53319	−	3.14622i	0.339644	−	0.163564i
$371$	2.87651	−	1.38525i	0.149341	−	0.0719188i
$372$	4.45377	+	19.5132i	0.230917	+	1.01171i
$373$	12.2823	−	15.4015i	0.635955	−	0.797462i	−0.354536	−	0.935042i	$-0.615361\pi$
$373$	12.2823	−	15.4015i	0.635955	−	0.797462i	0.990491	+	0.137581i	$0.0439326\pi$
$374$	−0.388355	−	0.187022i	−0.0200813	−	0.00967067i
$375$	−24.2935	+	30.4631i	−1.25451	+	1.57311i
$376$	−0.599031	+	2.62453i	−0.0308927	+	0.135350i
$377$	−22.0661	+	10.6265i	−1.13646	+	0.547292i
$378$	−3.15356	+	13.8167i	−0.162202	+	0.710652i
$379$	11.8204	+	5.69238i	0.607171	+	0.292398i	0.712096	−	0.702082i	$-0.247746\pi$
$379$	11.8204	+	5.69238i	0.607171	+	0.292398i	−0.104925	+	0.994480i	$0.533460\pi$
$380$	2.58104			0.132405
$381$	−15.1782			−0.777603
$382$	15.4858	+	7.45755i	0.792321	+	0.381561i
$383$	1.34266	+	5.88257i	0.0686066	+	0.300585i	0.997577	−	0.0695683i	$-0.0221622\pi$
$383$	1.34266	+	5.88257i	0.0686066	+	0.300585i	−0.928971	+	0.370154i	$0.879305\pi$
$384$	17.8143	+	22.3384i	0.909083	+	1.13995i
$385$	−0.500664	+	0.627813i	−0.0255162	+	0.0319963i
$386$	−7.01315			−0.356960
$387$	48.6710	−	8.81026i	2.47408	−	0.447851i
$388$	−20.6222			−1.04693
$389$	−0.502688	+	0.630351i	−0.0254873	+	0.0319601i	−0.794412	−	0.607380i	$-0.792221\pi$
$389$	−0.502688	+	0.630351i	−0.0254873	+	0.0319601i	0.768924	+	0.639340i	$0.220792\pi$
$390$	16.3937	+	20.5571i	0.830129	+	1.04095i
$391$	1.26875	+	5.55876i	0.0641634	+	0.281118i
$392$	−13.4966	−	6.49964i	−0.681684	−	0.328282i
$393$	14.2741			0.720034
$394$	14.8649			0.748881
$395$	7.89977	+	3.80433i	0.397481	+	0.191417i
$396$	−0.763242	+	3.34398i	−0.0383543	+	0.168041i
$397$	−8.36927	+	4.03043i	−0.420042	+	0.202281i	−0.631952	−	0.775008i	$-0.717746\pi$
$397$	−8.36927	+	4.03043i	−0.420042	+	0.202281i	0.211910	+	0.977289i	$0.432032\pi$
$398$	0.610449	−	2.67455i	0.0305990	−	0.134063i
$399$	2.30678	−	2.89261i	0.115484	−	0.144812i
$400$	0.500000	+	0.240787i	0.0250000	+	0.0120394i
$401$	−17.0553	+	21.3866i	−0.851699	+	1.06800i	0.145208	+	0.989401i	$0.453615\pi$
$401$	−17.0553	+	21.3866i	−0.851699	+	1.06800i	−0.996907	+	0.0785953i	$0.974957\pi$
$402$	−3.85474	−	16.8887i	−0.192257	−	0.842333i
$403$	20.6652	−	9.95182i	1.02941	−	0.495736i
$404$	−19.5456	+	9.41265i	−0.972428	+	0.468297i
$405$	−31.5066	−	39.5081i	−1.56558	−	1.96317i
$406$	1.03707	+	4.54371i	0.0514691	+	0.225501i
$407$	0.337150	−	1.47715i	0.0167119	−	0.0732196i
$408$	−8.74094	−	10.9608i	−0.432741	−	0.542640i
$409$	−2.29440	−	2.87709i	−0.113451	−	0.142263i	0.721863	−	0.692036i	$-0.243286\pi$
$409$	−2.29440	−	2.87709i	−0.113451	−	0.142263i	−0.835314	+	0.549772i	$0.814714\pi$
$410$	2.06638	−	9.05338i	0.102051	−	0.447115i
$411$	4.06465	+	17.8084i	0.200494	+	0.878423i
$412$	−12.7627	−	16.0039i	−0.628774	−	0.788457i
$413$	−13.3910	+	6.44879i	−0.658930	+	0.317324i
$414$	−19.3741	+	9.33008i	−0.952186	+	0.458549i
$415$	−2.70841	−	11.8663i	−0.132951	−	0.582496i
$416$	18.3497	−	23.0097i	0.899666	−	1.12815i
$417$	48.3950	+	23.3058i	2.36991	+	1.14129i
$418$	−0.159366	+	0.199839i	−0.00779485	+	0.00977443i
$419$	5.62833	−	24.6593i	0.274962	−	1.20469i	−0.629113	−	0.777314i	$-0.716582\pi$
$419$	5.62833	−	24.6593i	0.274962	−	1.20469i	0.904075	−	0.427374i	$-0.140561\pi$
$420$	−9.51142	+	4.58046i	−0.464110	+	0.223503i
$421$	−3.82813	+	16.7721i	−0.186571	+	0.817423i	0.791835	+	0.610735i	$0.209126\pi$
$421$	−3.82813	+	16.7721i	−0.186571	+	0.817423i	−0.978407	+	0.206688i	$0.933731\pi$
$422$	−6.43416	−	3.09853i	−0.313210	−	0.150834i
$423$	−7.54288			−0.366747
$424$	−7.17390			−0.348395
$425$	−1.44504	−	0.695895i	−0.0700948	−	0.0337559i
$426$	−0.388355	−	1.70149i	−0.0188159	−	0.0824376i
$427$	−3.45928	−	4.33780i	−0.167406	−	0.209921i
$428$	−3.10872	+	3.89821i	−0.150266	+	0.188427i
$429$	5.49396			0.265251
$430$	−7.91723	−	6.92325i	−0.381803	−	0.333869i
$431$	3.73364			0.179843			0.0899216	−	0.995949i	$-0.471338\pi$
$431$	3.73364			0.179843			0.0899216	+	0.995949i	$0.471338\pi$
$432$	−5.10388	+	6.40006i	−0.245560	+	0.307923i
$433$	13.3877	+	16.7876i	0.643371	+	0.806762i	0.991420	−	0.130714i	$-0.0417271\pi$
$433$	13.3877	+	16.7876i	0.643371	+	0.806762i	−0.348049	+	0.937476i	$0.613156\pi$
$434$	−0.971229	−	4.25523i	−0.0466205	−	0.204258i
$435$	−28.3817	−	13.6679i	−1.36080	−	0.655325i
$436$	7.63342			0.365574
$437$	3.38106			0.161738
$438$	−13.0831	−	6.30047i	−0.625133	−	0.301048i
$439$	2.93458	−	12.8573i	0.140060	−	0.613643i	−0.855359	−	0.518036i	$-0.826663\pi$
$439$	2.93458	−	12.8573i	0.140060	−	0.613643i	0.995419	−	0.0956075i	$-0.0304794\pi$
$440$	1.62565	−	0.782870i	0.0774996	−	0.0373218i
$441$	9.33997	−	40.9211i	0.444760	−	1.94862i
$442$	−4.04892	+	5.07718i	−0.192587	+	0.241497i
$443$	25.4148	+	12.2391i	1.20750	+	0.581499i	0.925803	−	0.378006i	$-0.123390\pi$
$443$	25.4148	+	12.2391i	1.20750	+	0.581499i	0.281692	+	0.959505i	$0.409104\pi$
$444$	12.4194	−	15.5734i	0.589398	−	0.739082i
$445$	−6.22282	−	27.2639i	−0.294990	−	1.29243i
$446$	3.53319	−	1.70149i	0.167301	−	0.0805681i
$447$	26.3572	−	12.6930i	1.24665	−	0.600356i
$448$	−2.66272	−	3.33894i	−0.125802	−	0.157750i
$449$	−5.38955	−	23.6132i	−0.254349	−	1.11437i	−0.927191	−	0.374589i	$-0.877784\pi$
$449$	−5.38955	−	23.6132i	−0.254349	−	1.11437i	0.672843	−	0.739786i	$-0.265073\pi$
$450$	1.34601	−	5.89726i	0.0634516	−	0.277999i
$451$	−1.20978	−	1.51701i	−0.0569661	−	0.0714332i
$452$	2.12833	+	2.66885i	0.100108	+	0.125532i
$453$	−2.08815	+	9.14877i	−0.0981097	+	0.429846i
$454$	0.741176	+	3.24730i	0.0347851	+	0.152403i
$455$	7.54288	+	9.45847i	0.353616	+	0.443420i
$456$	−7.49007	+	3.60703i	−0.350755	+	0.168915i
$457$	−21.1250	+	10.1733i	−0.988185	+	0.475885i	−0.856913	−	0.515462i	$-0.827620\pi$
$457$	−21.1250	+	10.1733i	−0.988185	+	0.475885i	−0.131272	+	0.991346i	$0.541906\pi$
$458$	3.48835	+	15.2834i	0.163000	+	0.714148i
$459$	14.7506	−	18.4967i	0.688500	−	0.863352i
$460$	−8.69202	−	4.18586i	−0.405268	−	0.195167i
$461$	−10.3626	+	12.9942i	−0.482633	+	0.605203i	−0.962214	−	0.272295i	$-0.912217\pi$
$461$	−10.3626	+	12.9942i	−0.482633	+	0.605203i	0.479581	+	0.877498i	$0.340789\pi$
$462$	0.232637	−	1.01925i	0.0108232	−	0.0474197i
$463$	5.18114	−	2.49510i	0.240788	−	0.115957i	−0.309599	−	0.950867i	$-0.600195\pi$
$463$	5.18114	−	2.49510i	0.240788	−	0.115957i	0.550386	+	0.834910i	$0.314480\pi$
$464$	−0.599031	+	2.62453i	−0.0278093	+	0.121841i
$465$	26.5797	+	12.8001i	1.23260	+	0.593591i
$466$	−6.22175			−0.288217
$467$	23.4547			1.08536			0.542678	−	0.839941i	$-0.317410\pi$
$467$	23.4547			1.08536			0.542678	+	0.839941i	$0.317410\pi$
$468$	46.5577	+	22.4210i	2.15213	+	1.03641i
$469$	−1.77359	−	7.77062i	−0.0818970	−	0.358814i
$470$	1.00000	+	1.25396i	0.0461266	+	0.0578409i
$471$	−46.7911	+	58.6742i	−2.15602	+	2.70356i
$472$	33.3967			1.53721
$473$	−2.16242	+	0.391435i	−0.0994283	+	0.0179982i
$474$	−11.4155			−0.524331
$475$	−0.592990	+	0.743586i	−0.0272083	+	0.0341181i
$476$	−1.62565	−	2.03850i	−0.0745114	−	0.0934343i
$477$	−4.47285	−	19.5968i	−0.204798	−	0.897278i
$478$	−11.3077	−	5.44552i	−0.517204	−	0.249072i
$479$	26.7278			1.22122			0.610612	−	0.791930i	$-0.290924\pi$
$479$	26.7278			1.22122			0.610612	+	0.791930i	$0.290924\pi$
$480$	37.8538			1.72778
$481$	−20.5661	−	9.90413i	−0.937735	−	0.451589i
$482$	1.71121	−	7.49730i	0.0779434	−	0.341492i
$483$	−12.4596	+	6.00022i	−0.566930	+	0.273019i
$484$	−3.28740	+	14.4031i	−0.149427	+	0.654685i
$485$	−18.9517	+	23.7646i	−0.860551	+	1.07910i
$486$	27.3022	+	13.1481i	1.23845	+	0.596408i
$487$	−6.25116	+	7.83871i	−0.283267	+	0.355206i	−0.903025	−	0.429587i	$-0.858659\pi$
$487$	−6.25116	+	7.83871i	−0.283267	+	0.355206i	0.619758	+	0.784793i	$0.287231\pi$
$488$	2.77413	+	12.1542i	0.125579	+	0.550197i
$489$	−36.7443	+	17.6951i	−1.66164	+	0.800202i
$490$	−8.04115	+	3.87241i	−0.363262	+	0.174938i
$491$	−13.1114	−	16.4412i	−0.591710	−	0.741980i	0.392351	−	0.919816i	$-0.371662\pi$
$491$	−13.1114	−	16.4412i	−0.591710	−	0.741980i	−0.984060	+	0.177835i	$0.943091\pi$
$492$	−5.67629	−	24.8695i	−0.255907	−	1.12120i
$493$	1.73125	−	7.58510i	0.0779716	−	0.341616i
$494$	2.40097	+	3.01072i	0.108025	+	0.135459i
$495$	3.15213	+	3.95264i	0.141678	+	0.177658i
$496$	0.560999	−	2.45790i	0.0251896	−	0.110363i
$497$	−0.178685	−	0.782870i	−0.00801511	−	0.0351165i
$498$	9.88016	+	12.3893i	0.442740	+	0.555179i
$499$	−27.8279	+	13.4012i	−1.24575	+	0.599920i	−0.936369	−	0.351019i	$-0.885835\pi$
$499$	−27.8279	+	13.4012i	−1.24575	+	0.599920i	−0.309379	+	0.950939i	$0.600121\pi$
$500$	14.6703	−	7.06482i	0.656074	−	0.315948i
$501$	−16.0879	−	70.4857i	−0.718755	−	3.14907i
$502$	−6.56584	+	8.23331i	−0.293048	+	0.367470i
$503$	27.8751	+	13.4239i	1.24289	+	0.598543i	0.935596	−	0.353072i	$-0.114863\pi$
$503$	27.8751	+	13.4239i	1.24289	+	0.598543i	0.307292	+	0.951615i	$0.400577\pi$
$504$	15.1679	−	19.0199i	0.675630	−	0.847213i
$505$	−7.11529	+	31.1741i	−0.316626	+	1.38723i
$506$	0.860781	−	0.414530i	0.0382664	−	0.0184281i
$507$	9.02542	−	39.5429i	0.400833	−	1.75616i
$508$	5.71475	+	2.75208i	0.253551	+	0.122104i
$509$	−22.4494			−0.995050			−0.497525	−	0.867450i	$-0.665758\pi$
$509$	−22.4494			−0.995050			−0.497525	+	0.867450i	$0.665758\pi$
$510$	−8.35258			−0.369859
$511$	−6.01961	−	2.89889i	−0.266292	−	0.128239i
$512$	−1.38471	−	6.06680i	−0.0611960	−	0.268117i
$513$	−8.74698	−	10.9684i	−0.386189	−	0.484265i
$514$	−8.91066	+	11.1736i	−0.393032	+	0.492847i
$515$	−30.1715			−1.32952
$516$	−27.8463	−	7.69834i	−1.22587	−	0.338900i
$517$	0.335126			0.0147388
$518$	−2.70828	+	3.39608i	−0.118995	+	0.149215i
$519$	−4.42543	−	5.54931i	−0.194255	−	0.243588i
$520$	−6.04892	−	26.5020i	−0.265263	−	1.16219i
$521$	14.7066	+	7.08230i	0.644306	+	0.310281i	0.727352	−	0.686264i	$-0.240751\pi$
$521$	14.7066	+	7.08230i	0.644306	+	0.310281i	−0.0830464	+	0.996546i	$0.526465\pi$
$522$	29.3424			1.28428
$523$	4.42626			0.193547			0.0967733	−	0.995306i	$-0.469148\pi$
$523$	4.42626			0.193547			0.0967733	+	0.995306i	$0.469148\pi$
$524$	−5.37435	−	2.58815i	−0.234780	−	0.113064i
$525$	0.865625	−	3.79255i	0.0377790	−	0.165521i
$526$	23.0836	−	11.1165i	1.00649	−	0.484701i
$527$	−1.62133	+	7.10353i	−0.0706264	+	0.309435i
$528$	0.376510	−	0.472129i	0.0163855	−	0.0205468i
$529$	9.33609	+	4.49602i	0.405917	+	0.195479i
$530$	−2.66487	+	3.34165i	−0.115755	+	0.145152i
$531$	20.8225	+	91.2294i	0.903620	+	3.95902i
$532$	−1.39301	+	0.670838i	−0.0603946	+	0.0290845i
$533$	−26.3376	+	12.6835i	−1.14081	+	0.549384i
$534$	22.7005	+	28.4655i	0.982347	+	1.23182i
$535$	1.63533	+	7.16487i	0.0707017	+	0.309764i
$536$	−3.98523	+	17.4604i	−0.172136	+	0.754176i
$537$	−20.6848	−	25.9379i	−0.892614	−	1.11930i
$538$	−0.426624	−	0.534970i	−0.0183931	−	0.0230642i
$539$	−0.414969	+	1.81810i	−0.0178740	+	0.0783111i
$540$	8.90754	+	39.0265i	0.383320	+	1.67943i
$541$	−3.52595	−	4.42140i	−0.151592	−	0.190091i	0.700237	−	0.713911i	$-0.253078\pi$
$541$	−3.52595	−	4.42140i	−0.151592	−	0.190091i	−0.851829	+	0.523820i	$0.824506\pi$
$542$	−1.64622	+	0.792778i	−0.0707112	+	0.0340527i
$543$	−38.8451	+	18.7068i	−1.66700	+	0.802786i
$544$	2.08038	+	9.11472i	0.0891954	+	0.390791i
$545$	7.01507	−	8.79661i	0.300492	−	0.376806i
$546$	−14.1908	−	6.83394i	−0.607311	−	0.292466i
$547$	11.7424	−	14.7245i	0.502070	−	0.629576i	−0.464625	−	0.885508i	$-0.653811\pi$
$547$	11.7424	−	14.7245i	0.502070	−	0.629576i	0.966695	+	0.255932i	$0.0823822\pi$
$548$	1.69859	−	7.44203i	0.0725604	−	0.317908i
$549$	−31.4720	+	15.1561i	−1.34319	+	0.646846i
$550$	−0.0598025	+	0.262012i	−0.00254999	+	0.0111722i
$551$	−4.15668	−	2.00175i	−0.177080	−	0.0852774i
$552$	31.0737			1.32258
$553$	−5.25236			−0.223353
$554$	−2.51261	−	1.21001i	−0.106751	−	0.0514084i
$555$	−6.53319	−	28.6238i	−0.277318	−	1.21501i
$556$	−13.9955	−	17.5497i	−0.593539	−	0.744275i
$557$	23.7032	−	29.7229i	1.00434	−	1.25940i	0.0387688	−	0.999248i	$-0.487656\pi$
$557$	23.7032	−	29.7229i	1.00434	−	1.25940i	0.965568	−	0.260150i	$-0.0837722\pi$
$558$	−27.4795			−1.16330
$559$	−1.50000	+	33.0740i	−0.0634432	+	1.39888i
$560$	1.32975			0.0561921
$561$	−1.08815	+	1.36449i	−0.0459416	+	0.0576089i
$562$	−9.05107	−	11.3497i	−0.381796	−	0.478758i
$563$	9.62684	+	42.1780i	0.405723	+	1.77759i	0.603522	+	0.797346i	$0.293763\pi$
$563$	9.62684	+	42.1780i	0.405723	+	1.77759i	−0.197799	+	0.980243i	$0.563379\pi$
$564$	3.96950	+	1.91161i	0.167146	+	0.0804933i
$565$	5.03146			0.211675
$566$	−19.1390			−0.804471
$567$	27.2729	+	13.1340i	1.14536	+	0.551574i
$568$	−0.401501	+	1.75909i	−0.0168466	+	0.0738099i
$569$	31.9288	−	15.3761i	1.33853	−	0.644600i	0.378785	−	0.925485i	$-0.376342\pi$
$569$	31.9288	−	15.3761i	1.33853	−	0.644600i	0.959742	+	0.280884i	$0.0906277\pi$
$570$	−1.10215	+	4.82882i	−0.0461638	+	0.202257i
$571$	26.8391	−	33.6551i	1.12318	−	1.40842i	0.221963	−	0.975055i	$-0.428754\pi$
$571$	26.8391	−	33.6551i	1.12318	−	1.40842i	0.901217	−	0.433368i	$-0.142675\pi$
$572$	−2.06853	−	0.996152i	−0.0864897	−	0.0416512i
$573$	43.3901	−	54.4095i	1.81265	−	2.27299i
$574$	1.23782	+	5.42326i	0.0516658	+	0.226362i
$575$	3.20291	−	1.54244i	0.133570	−	0.0643241i
$576$	−24.2250	+	11.6661i	−1.00937	+	0.486089i
$577$	−9.76002	−	12.2387i	−0.406315	−	0.509503i	0.536006	−	0.844214i	$-0.319933\pi$
$577$	−9.76002	−	12.2387i	−0.406315	−	0.509503i	−0.942321	+	0.334712i	$0.891361\pi$
$578$	2.57457	+	11.2799i	0.107088	+	0.469184i
$579$	−6.31863	+	27.6837i	−0.262593	+	1.15050i
$580$	8.20775	+	10.2922i	0.340808	+	0.427360i
$581$	4.54593	+	5.70042i	0.188597	+	0.236493i
$582$	8.80601	−	38.5817i	0.365021	−	1.59926i
$583$	0.198726	+	0.870677i	0.00823040	+	0.0360597i
$584$	9.36025	+	11.7374i	0.387330	+	0.485696i
$585$	68.6238	−	33.0475i	2.83725	−	1.36635i
$586$	−19.8710	+	9.56937i	−0.820864	+	0.395307i
$587$	4.35258	+	19.0699i	0.179650	+	0.787100i	0.981791	+	0.189964i	$0.0608373\pi$
$587$	4.35258	+	19.0699i	0.179650	+	0.787100i	−0.802141	+	0.597135i	$0.796306\pi$
$588$	−15.2860	+	19.1680i	−0.630383	+	0.790475i
$589$	3.89277	+	1.87466i	0.160399	+	0.0772440i
$590$	12.4058	−	15.5564i	0.510739	−	0.640447i
$591$	13.3928	−	58.6776i	0.550905	−	2.41367i
$592$	−2.26055	+	1.08863i	−0.0929082	+	0.0447422i
$593$	9.01424	−	39.4940i	0.370170	−	1.62182i	−0.356124	−	0.934439i	$-0.615902\pi$
$593$	9.01424	−	39.4940i	0.370170	−	1.62182i	0.726294	−	0.687384i	$-0.241241\pi$
$594$	−3.57165	−	1.72001i	−0.146546	−	0.0705731i
$595$	−3.84309			−0.157551
$596$	−12.2252			−0.500764
$597$	−10.0075	−	4.81937i	−0.409581	−	0.197244i
$598$	−3.20291	−	14.0329i	−0.130977	−	0.573846i
$599$	−22.5371	−	28.2607i	−0.920842	−	1.15470i	−0.987610	−	0.156931i	$-0.949840\pi$
$599$	−22.5371	−	28.2607i	−0.920842	−	1.15470i	0.0667673	−	0.997769i	$-0.478731\pi$
$600$	−5.44989	+	6.83394i	−0.222491	+	0.278994i
$601$	−23.5743			−0.961617			−0.480809	−	0.876826i	$-0.659657\pi$
$601$	−23.5743			−0.961617			−0.480809	+	0.876826i	$0.659657\pi$
$602$	6.07242	+	1.67877i	0.247493	+	0.0684215i
$603$	−50.1812			−2.04354
$604$	2.44504	−	3.06599i	0.0994873	−	0.124753i
$605$	13.5767	+	17.0247i	0.551973	+	0.692152i
$606$	−9.26367	−	40.5868i	−0.376311	−	1.64873i
$607$	4.54407	+	2.18831i	0.184438	+	0.0888208i	0.523824	−	0.851826i	$-0.324505\pi$
$607$	4.54407	+	2.18831i	0.184438	+	0.0888208i	−0.339386	+	0.940647i	$0.610219\pi$
$608$	5.54394			0.224837
$609$	18.8702			0.764660
$610$	6.69202	+	3.22271i	0.270952	+	0.130484i
$611$	1.12349	−	4.92233i	0.0454515	−	0.199136i
$612$	−14.7899	+	7.12242i	−0.597845	+	0.287907i
$613$	−6.06398	+	26.5680i	−0.244922	+	1.07307i	0.691549	+	0.722329i	$0.256928\pi$
$613$	−6.06398	+	26.5680i	−0.244922	+	1.07307i	−0.936471	+	0.350744i	$0.885929\pi$
$614$	−10.1419	+	12.7175i	−0.409294	+	0.513239i
$615$	−33.8756	−	16.3136i	−1.36600	−	0.657829i
$616$	−0.673899	+	0.845043i	−0.0271522	+	0.0340477i
$617$	5.25076	+	23.0051i	0.211388	+	0.926150i	0.963625	+	0.267258i	$0.0861174\pi$
$617$	5.25076	+	23.0051i	0.211388	+	0.926150i	−0.752238	+	0.658892i	$0.771025\pi$
$618$	35.3913	−	17.0436i	1.42365	−	0.685593i
$619$	37.9686	−	18.2847i	1.52609	−	0.734925i	0.532335	−	0.846534i	$-0.321315\pi$
$619$	37.9686	−	18.2847i	1.52609	−	0.734925i	0.993752	+	0.111609i	$0.0356005\pi$
$620$	−7.68664	−	9.63875i	−0.308703	−	0.387101i
$621$	11.6685	+	51.1231i	0.468242	+	2.05150i
$622$	1.02004	−	4.46909i	0.0408999	−	0.179194i
$623$	10.4447	+	13.0972i	0.418457	+	0.524728i
$624$	−5.67241	−	7.11297i	−0.227078	−	0.284747i
$625$	4.22790	−	18.5236i	0.169116	−	0.740945i
$626$	4.34309	+	19.0283i	0.173585	+	0.760524i
$627$	0.645260	+	0.809131i	0.0257692	+	0.0323136i
$628$	28.2560	−	13.6074i	1.12754	−	0.542993i
$629$	6.53319	−	3.14622i	0.260495	−	0.125448i
$630$	−3.22521	−	14.1306i	−0.128495	−	0.562975i
$631$	−14.5070	+	18.1912i	−0.577515	+	0.724180i	−0.981687	−	0.190503i	$-0.938988\pi$
$631$	−14.5070	+	18.1912i	−0.577515	+	0.724180i	0.404172	+	0.914683i	$0.367560\pi$
$632$	10.6332	+	5.12067i	0.422965	+	0.203689i
$633$	−18.0281	+	22.6065i	−0.716553	+	0.898529i
$634$	−2.70464	+	11.8498i	−0.107415	+	0.470615i
$635$	8.42327	−	4.05643i	0.334267	−	0.160975i
$636$	−2.61260	+	11.4466i	−0.103597	+	0.453886i
$637$	25.3131	+	12.1902i	1.00294	+	0.482992i
$638$	−1.30367			−0.0516127
$639$	−5.05562			−0.199997
$640$	−15.8562	−	7.63596i	−0.626773	−	0.301838i
$641$	−2.50700	−	10.9839i	−0.0990206	−	0.433837i	0.900979	−	0.433862i	$-0.142849\pi$
$641$	−2.50700	−	10.9839i	−0.0990206	−	0.433837i	−1.00000		2.43722e-5i	$0.999992\pi$
$642$	−5.96562	−	7.48065i	−0.235444	−	0.295238i
$643$	−5.65817	+	7.09512i	−0.223136	+	0.279804i	−0.880781	−	0.473524i	$-0.842982\pi$
$643$	−5.65817	+	7.09512i	−0.223136	+	0.279804i	0.657644	+	0.753329i	$0.271553\pi$
$644$	5.77910			0.227729
$645$	−34.4620	+	25.0149i	−1.35694	+	0.984959i
$646$	−1.22329			−0.0481297
$647$	−3.99462	+	5.00910i	−0.157045	+	0.196928i	−0.854129	−	0.520061i	$-0.825909\pi$
$647$	−3.99462	+	5.00910i	−0.157045	+	0.196928i	0.697084	+	0.716989i	$0.254480\pi$
$648$	−42.4083	−	53.1783i	−1.66595	−	2.08904i
$649$	−0.925132	−	4.05327i	−0.0363146	−	0.159105i
$650$	3.64795	+	1.75676i	0.143084	+	0.0689058i
$651$	−17.6722			−0.692627
$652$	17.0431			0.667458
$653$	25.8315	+	12.4398i	1.01087	+	0.486807i	0.864612	−	0.502440i	$-0.167564\pi$
$653$	25.8315	+	12.4398i	1.01087	+	0.486807i	0.146254	+	0.989247i	$0.453278\pi$
$654$	−3.25959	+	14.2812i	−0.127460	+	0.558440i
$655$	−7.92154	+	3.81481i	−0.309520	+	0.149057i
$656$	−0.714988	+	3.13257i	−0.0279156	+	0.122306i
$657$	−26.2268	+	32.8874i	−1.02321	+	1.28306i
$658$	−0.865625	−	0.416863i	−0.0337456	−	0.0162510i
$659$	5.82118	−	7.29953i	0.226761	−	0.284349i	−0.655415	−	0.755269i	$-0.727506\pi$
$659$	5.82118	−	7.29953i	0.226761	−	0.284349i	0.882176	+	0.470919i	$0.156078\pi$
$660$	−0.657105	−	2.87896i	−0.0255778	−	0.112064i
$661$	−6.33901	+	3.05271i	−0.246559	+	0.118737i	−0.553082	−	0.833127i	$-0.686549\pi$
$661$	−6.33901	+	3.05271i	−0.246559	+	0.118737i	0.306523	+	0.951863i	$0.400834\pi$
$662$	−16.7524	+	8.06751i	−0.651099	+	0.313553i
$663$	16.3937	+	20.5571i	0.636680	+	0.798371i
$664$	−3.64556	−	15.9722i	−0.141475	−	0.619842i
$665$	−0.507106	+	2.22178i	−0.0196647	+	0.0861568i
$666$	17.0511	+	21.3814i	0.660716	+	0.828511i
$667$	10.7518	+	13.4824i	0.416312	+	0.522039i
$668$	−6.72305	+	29.4556i	−0.260123	+	1.13967i
$669$	−3.53319	−	15.4799i	−0.136601	−	0.598488i
$670$	6.65279	+	8.34234i	0.257020	+	0.322293i
$671$	1.39828	−	0.673376i	0.0539800	−	0.0259954i
$672$	−20.4300	+	9.83859i	−0.788106	+	0.379532i
$673$	0.0866540	+	0.379656i	0.00334027	+	0.0146347i	0.976571	−	0.215197i	$-0.0690395\pi$
$673$	0.0866540	+	0.379656i	0.00334027	+	0.0146347i	−0.973230	+	0.229832i	$0.926182\pi$
$674$	10.7322	−	13.4578i	0.413389	−	0.518374i
$675$	−13.2899	−	6.40006i	−0.511527	−	0.246338i
$676$	−10.5680	+	13.2519i	−0.406462	+	0.509687i
$677$	−0.809602	+	3.54710i	−0.0311155	+	0.136326i	−0.988100	−	0.153813i	$-0.950845\pi$
$677$	−0.809602	+	3.54710i	−0.0311155	+	0.136326i	0.956984	+	0.290139i	$0.0937017\pi$
$678$	−5.90193	+	2.84222i	−0.226662	+	0.109155i
$679$	4.05171	−	17.7517i	0.155490	−	0.681248i
$680$	7.78017	+	3.74673i	0.298356	+	0.143681i
$681$	13.4862			0.516792
$682$	1.22090			0.0467506
$683$	−25.1797	−	12.1259i	−0.963475	−	0.463985i	−0.115084	−	0.993356i	$-0.536714\pi$
$683$	−25.1797	−	12.1259i	−0.963475	−	0.463985i	−0.848391	+	0.529371i	$0.822428\pi$
$684$	2.16607	+	9.49018i	0.0828218	+	0.362866i
$685$	−7.01507	−	8.79661i	−0.268032	−	0.336101i
$686$	7.52661	−	9.43808i	0.287367	−	0.360347i
$687$	63.4728			2.42164
$688$	2.73945	+	2.39552i	0.104440	+	0.0913283i
$689$	13.4547			0.512584
$690$	11.5429	−	14.4743i	0.439430	−	0.551028i
$691$	16.1848	+	20.2951i	0.615698	+	0.772061i	0.987732	−	0.156158i	$-0.0499109\pi$
$691$	16.1848	+	20.2951i	0.615698	+	0.772061i	−0.372034	+	0.928219i	$0.621339\pi$
$692$	0.660030	+	2.89178i	0.0250906	+	0.109929i
$693$	−2.72856	−	1.31401i	−0.103649	−	0.0499150i
$694$	−20.5429			−0.779797
$695$	−33.0858			−1.25501
$696$	−38.2020	−	18.3971i	−1.44804	−	0.697341i
$697$	2.06638	−	9.05338i	0.0782696	−	0.342921i
$698$	6.99396	−	3.36811i	0.264725	−	0.127485i
$699$	−5.60560	+	24.5598i	−0.212023	+	0.928935i
$700$	−1.01357	+	1.27098i	−0.0383095	+	0.0480386i
$701$	38.4529	+	18.5179i	1.45234	+	0.699412i	0.983001	−	0.183603i	$-0.0587760\pi$
$701$	38.4529	+	18.5179i	1.45234	+	0.699412i	0.469344	+	0.883015i	$0.344490\pi$
$702$	−37.2373	+	46.6942i	−1.40543	+	1.76236i
$703$	−0.956828	−	4.19214i	−0.0360874	−	0.158109i
$704$	1.07630	−	0.518319i	0.0405646	−	0.0195349i
$705$	5.85086	−	2.81762i	0.220356	−	0.106118i
$706$	−0.207751	−	0.260511i	−0.00781881	−	0.00980448i
$707$	−4.26228	−	18.6743i	−0.160300	−	0.702319i
$708$	12.1625	−	53.2873i	0.457094	−	2.00266i
$709$	−17.4400	−	21.8690i	−0.654971	−	0.821308i	0.337814	−	0.941213i	$-0.390313\pi$
$709$	−17.4400	−	21.8690i	−0.654971	−	0.821308i	−0.992785	+	0.119905i	$0.961741\pi$
$710$	0.670251	+	0.840468i	0.0251541	+	0.0315422i
$711$	−7.35839	+	32.2392i	−0.275961	+	1.20906i
$712$	−8.37598	−	36.6976i	−0.313903	−	1.37530i
$713$	−10.0692	−	12.6264i	−0.377094	−	0.472861i
$714$	4.50796	−	2.17092i	0.168706	−	0.0812446i
$715$	−3.04892	+	1.46828i	−0.114023	+	0.0549106i
$716$	3.08503	+	13.5164i	0.115293	+	0.505132i
$717$	−31.6836	+	39.7300i	−1.18325	+	1.48374i
$718$	5.16152	+	2.48566i	0.192626	+	0.0927639i
$719$	23.7969	−	29.8403i	0.887473	−	1.11286i	−0.105489	−	0.994420i	$-0.533641\pi$
$719$	23.7969	−	29.8403i	0.887473	−	1.11286i	0.992962	−	0.118435i	$-0.0377879\pi$
$720$	1.86294	−	8.16206i	0.0694276	−	0.304182i
$721$	16.2838	−	7.84187i	0.606441	−	0.292047i
$722$	3.22909	−	14.1476i	0.120174	−	0.526519i
$723$	−28.0531	−	13.5097i	−1.04331	−	0.502430i
$724$	18.0175			0.669614
$725$	−4.85086			−0.180156
$726$	−25.5426	−	12.3007i	−0.947976	−	0.456521i
$727$	6.28687	+	27.5446i	0.233167	+	1.02157i	0.946994	+	0.321250i	$0.104103\pi$
$727$	6.28687	+	27.5446i	0.233167	+	1.02157i	−0.713827	+	0.700322i	$0.753040\pi$
$728$	10.1528	+	12.7312i	0.376288	+	0.471850i
$729$	29.2392	−	36.6648i	1.08293	−	1.35796i
$730$	8.94438			0.331046
$731$	−7.91723	−	6.92325i	−0.292829	−	0.256066i
$732$	20.4034			0.754132
$733$	−5.51775	+	6.91904i	−0.203803	+	0.255561i	−0.873220	−	0.487326i	$-0.837972\pi$
$733$	−5.51775	+	6.91904i	−0.203803	+	0.255561i	0.669417	+	0.742887i	$0.266544\pi$
$734$	4.00216	+	5.01854i	0.147722	+	0.185238i
$735$	8.04115	+	35.2306i	0.296602	+	1.29950i
$736$	−18.6700	−	8.99100i	−0.688186	−	0.331413i
$737$	2.22952			0.0821255
$738$	35.0224			1.28919
$739$	−33.9729	−	16.3605i	−1.24971	−	0.601830i	−0.312279	−	0.949991i	$-0.601092\pi$
$739$	−33.9729	−	16.3605i	−1.24971	−	0.601830i	−0.937435	+	0.348160i	$0.886807\pi$
$740$	−2.73019	+	11.9617i	−0.100364	+	0.439722i
$741$	14.0477	−	6.76503i	0.516056	−	0.248519i
$742$	0.569728	−	2.49614i	0.0209154	−	0.0916363i
$743$	3.45779	−	4.33593i	0.126854	−	0.159070i	−0.714349	−	0.699790i	$-0.753277\pi$
$743$	3.45779	−	4.33593i	0.126854	−	0.159070i	0.841202	+	0.540720i	$0.181848\pi$
$744$	35.7766	+	17.2291i	1.31163	+	0.631649i
$745$	−11.2349	+	14.0881i	−0.411615	+	0.516149i
$746$	−3.51530	−	15.4015i	−0.128704	−	0.563891i
$747$	41.3582	−	19.9170i	1.51322	−	0.728726i
$748$	0.657105	−	0.316445i	0.0240261	−	0.0115704i
$749$	−2.74482	−	3.44190i	−0.100294	−	0.125764i
$750$	6.95300	+	30.4631i	0.253888	+	1.11235i
$751$	7.78621	−	34.1136i	0.284123	−	1.24482i	−0.608331	−	0.793684i	$-0.708161\pi$
$751$	7.78621	−	34.1136i	0.284123	−	1.24482i	0.892453	−	0.451140i	$-0.148982\pi$
$752$	−0.346011	−	0.433884i	−0.0126177	−	0.0158221i
$753$	26.5846	+	33.3360i	0.968795	+	1.21483i
$754$	−4.37047	+	19.1483i	−0.159163	+	0.697339i
$755$	−1.28621	−	5.63525i	−0.0468099	−	0.205088i
$756$	−14.9508	−	18.7478i	−0.543757	−	0.681850i
$757$	−39.1764	+	18.8663i	−1.42389	+	0.685709i	−0.977850	−	0.209305i	$-0.932880\pi$
$757$	−39.1764	+	18.8663i	−1.42389	+	0.685709i	−0.446038	+	0.895014i	$0.647165\pi$
$758$	9.47919	−	4.56494i	0.344300	−	0.165806i
$759$	−0.860781	−	3.77133i	−0.0312444	−	0.136890i
$760$	3.19269	−	4.00350i	0.115811	−	0.145222i
$761$	−23.5846	−	11.3577i	−0.854940	−	0.411717i	−0.0455308	−	0.998963i	$-0.514498\pi$
$761$	−23.5846	−	11.3577i	−0.854940	−	0.411717i	−0.809409	+	0.587246i	$0.800212\pi$
$762$	−7.58911	+	9.51644i	−0.274924	+	0.344744i
$763$	−1.49976	+	6.57089i	−0.0542951	+	0.237882i
$764$	−26.2022	+	12.6183i	−0.947964	+	0.456515i
$765$	−5.38404	+	23.5890i	−0.194660	+	0.852863i
$766$	4.35958	+	2.09947i	0.157518	+	0.0758568i
$767$	−62.6359			−2.26165
$768$	46.0616			1.66210
$769$	32.1836	+	15.4988i	1.16057	+	0.558901i	0.912192	−	0.409762i	$-0.134388\pi$
$769$	32.1836	+	15.4988i	1.16057	+	0.558901i	0.248378	+	0.968663i	$0.420103\pi$
$770$	0.143294	+	0.627813i	0.00516396	+	0.0226248i
$771$	36.0785	+	45.2410i	1.29934	+	1.62932i
$772$	7.39858	−	9.27752i	0.266281	−	0.333905i
$773$	−11.2241			−0.403704			−0.201852	−	0.979416i	$-0.564696\pi$
$773$	−11.2241			−0.403704			−0.201852	+	0.979416i	$0.564696\pi$
$774$	18.8116	−	34.9209i	0.676170	−	1.25520i
$775$	4.54288			0.163185
$776$	−25.5092	+	31.9875i	−0.915725	+	1.14828i
$777$	10.9656	+	13.7504i	0.393389	+	0.493295i
$778$	0.143874	+	0.630351i	0.00515812	+	0.0225992i
$779$	−4.96130	−	2.38924i	−0.177757	−	0.0856033i
$780$	−44.4892			−1.59297
$781$	0.224618			0.00803748
$782$	4.11960	+	1.98390i	0.147317	+	0.0709440i
$783$	15.9221	−	69.7592i	0.569009	−	2.49299i
$784$	2.78232	−	1.33990i	0.0993687	−	0.0478534i
$785$	10.2862	−	45.0668i	0.367131	−	1.60850i
$786$	7.13706	−	8.94959i	0.254571	−	0.319221i
$787$	−30.5030	−	14.6895i	−1.08731	−	0.523623i	−0.197666	−	0.980269i	$-0.563336\pi$
$787$	−30.5030	−	14.6895i	−1.08731	−	0.523623i	−0.889648	+	0.456647i	$0.849050\pi$
$788$	−15.6818	+	19.6644i	−0.558641	+	0.700514i
$789$	−23.0836	−	101.136i	−0.821798	−	3.60053i
$790$	6.33513	−	3.05084i	0.225394	−	0.108544i
$791$	−2.71552	+	1.30773i	−0.0965528	+	0.0464974i
$792$	4.24280	+	5.32030i	0.150761	+	0.189049i
$793$	−5.20291	−	22.7954i	−0.184761	−	0.809489i
$794$	−1.65764	+	7.26258i	−0.0588273	+	0.257739i
$795$	10.7899	+	13.5301i	0.382677	+	0.479861i
$796$	2.89410	+	3.62909i	0.102579	+	0.128630i
$797$	3.00269	−	13.1556i	0.106361	−	0.465997i	−0.893496	−	0.449071i	$-0.851755\pi$
$797$	3.00269	−	13.1556i	0.106361	−	0.465997i	0.999857	−	0.0169256i	$-0.00538784\pi$
$798$	−0.660220	−	2.89261i	−0.0233715	−	0.102397i
$799$	1.00000	+	1.25396i	0.0353775	+	0.0443619i
$800$	5.25182	−	2.52915i	0.185680	−	0.0894188i
$801$	95.0239	−	45.7611i	3.35750	−	1.61689i
$802$	4.88135	+	21.3866i	0.172367	+	0.755188i
$803$	1.16524	−	1.46117i	0.0411205	−	0.0515635i
$804$	26.4083	+	12.7175i	0.931348	+	0.448513i
$805$	5.31096	−	6.65974i	0.187187	−	0.234725i
$806$	4.09299	−	17.9326i	0.144169	−	0.631648i
$807$	−2.49612	+	1.20207i	−0.0878674	+	0.0423147i
$808$	−9.57726	+	41.9607i	−0.336927	+	1.47617i
$809$	−34.9894	−	16.8500i	−1.23016	−	0.592415i	−0.298038	−	0.954554i	$-0.596332\pi$
$809$	−34.9894	−	16.8500i	−1.23016	−	0.592415i	−0.932124	+	0.362139i	$0.882047\pi$
$810$	−40.5241			−1.42387
$811$	−14.9589			−0.525276			−0.262638	−	0.964894i	$-0.584593\pi$
$811$	−14.9589			−0.525276			−0.262638	+	0.964894i	$0.584593\pi$
$812$	−7.10483	−	3.42151i	−0.249331	−	0.120071i
$813$	1.64622	+	7.21256i	0.0577354	+	0.252955i
$814$	−0.757569	−	0.949962i	−0.0265528	−	0.0332961i
$815$	15.6625	−	19.6401i	0.548633	−	0.687964i
$816$	2.89008			0.101173
$817$	−5.04719	+	3.66359i	−0.176579	+	0.128173i
$818$	−2.95108			−0.103182
$819$	−28.4475	+	35.6720i	−0.994036	+	1.24648i
$820$	9.79656	+	12.2845i	0.342111	+	0.428993i
$821$	−5.52489	−	24.2061i	−0.192820	−	0.844799i	−0.975081	−	0.221848i	$-0.928791\pi$
$821$	−5.52489	−	24.2061i	−0.192820	−	0.844799i	0.782261	−	0.622950i	$-0.214066\pi$
$822$	13.1978	+	6.35574i	0.460327	+	0.221682i
$823$	40.9788			1.42843			0.714216	−	0.699925i	$-0.246783\pi$
$823$	40.9788			1.42843			0.714216	+	0.699925i	$0.246783\pi$
$824$	−40.6112			−1.41476
$825$	0.980386	+	0.472129i	0.0341326	+	0.0164374i
$826$	−2.65226	+	11.6203i	−0.0922839	+	0.404322i
$827$	−35.8848	+	17.2812i	−1.24784	+	0.600926i	−0.936931	−	0.349515i	$-0.886346\pi$
$827$	−35.8848	+	17.2812i	−1.24784	+	0.600926i	−0.310905	+	0.950441i	$0.600632\pi$
$828$	8.09634	−	35.4724i	0.281367	−	1.23275i
$829$	10.1540	−	12.7327i	0.352663	−	0.442225i	−0.573582	−	0.819148i	$-0.694447\pi$
$829$	10.1540	−	12.7327i	0.352663	−	0.442225i	0.926244	+	0.376923i	$0.123018\pi$
$830$	−8.79417	−	4.23505i	−0.305250	−	0.147001i
$831$	−7.04019	+	8.82812i	−0.244221	+	0.306244i
$832$	−4.00484	−	17.5464i	−0.138843	−	0.608311i
$833$	−8.04115	+	3.87241i	−0.278609	+	0.134171i
$834$	38.8098	−	18.6898i	1.34387	−	0.647175i
$835$	27.7657	+	34.8171i	0.960871	+	1.20489i
$836$	−0.0962373	−	0.421643i	−0.00332844	−	0.0145828i
$837$	−14.9112	+	65.3302i	−0.515406	+	2.25814i
$838$	−12.6468	−	15.8585i	−0.436875	−	0.547824i
$839$	−15.7303	−	19.7252i	−0.543072	−	0.680991i	0.432256	−	0.901751i	$-0.357718\pi$
$839$	−15.7303	−	19.7252i	−0.543072	−	0.680991i	−0.975328	+	0.220760i	$0.929146\pi$
$840$	−4.66056	+	20.4193i	−0.160805	+	0.704531i
$841$	1.21701	+	5.33208i	0.0419660	+	0.183865i
$842$	8.60172	+	10.7862i	0.296435	+	0.371718i
$843$	−52.9565	+	25.5025i	−1.82392	+	0.878353i
$844$	10.8867	−	5.24277i	0.374737	−	0.180464i
$845$	5.55927	+	24.3568i	0.191245	+	0.837898i
$846$	−3.77144	+	4.72923i	−0.129665	+	0.162594i
$847$	−11.7524	−	5.65964i	−0.403816	−	0.194467i
$848$	0.922075	−	1.15625i	0.0316642	−	0.0397056i
$849$	−17.2436	+	75.5493i	−0.591800	+	2.59284i
$850$	−1.15883	+	0.558065i	−0.0397477	+	0.0191415i
$851$	−3.57643	+	15.6694i	−0.122599	+	0.537139i
$852$	2.66056	+	1.28126i	0.0911494	+	0.0438952i
$853$	24.0062			0.821958			0.410979	−	0.911645i	$-0.365187\pi$
$853$	24.0062			0.821958			0.410979	+	0.911645i	$0.365187\pi$
$854$	−4.44935			−0.152254
$855$	12.9269	+	6.22528i	0.442091	+	0.212900i
$856$	2.20118	+	9.64399i	0.0752347	+	0.329625i
$857$	19.8512	+	24.8926i	0.678102	+	0.850313i	0.995178	−	0.0980868i	$-0.0312723\pi$
$857$	19.8512	+	24.8926i	0.678102	+	0.850313i	−0.317075	+	0.948400i	$0.602701\pi$
$858$	2.74698	−	3.44460i	0.0937803	−	0.117597i
$859$	21.3575			0.728708			0.364354	−	0.931261i	$-0.381290\pi$
$859$	21.3575			0.728708			0.364354	+	0.931261i	$0.381290\pi$
$860$	17.5109	−	3.16977i	0.597118	−	0.108088i
$861$	22.5230			0.767583
$862$	1.86682	−	2.34092i	0.0635842	−	0.0797321i
$863$	−12.0817	−	15.1500i	−0.411267	−	0.515713i	0.532452	−	0.846460i	$-0.321271\pi$
$863$	−12.0817	−	15.1500i	−0.411267	−	0.515713i	−0.943719	+	0.330747i	$0.892699\pi$
$864$	19.1329	+	83.8269i	0.650916	+	2.85185i
$865$	3.93900	+	1.89692i	0.133930	+	0.0644973i
$866$	17.2194			0.585138
$867$	46.8461			1.59098
$868$	6.65375	+	3.20428i	0.225843	+	0.108760i
$869$	0.326929	−	1.43237i	0.0110903	−	0.0485898i
$870$	−22.7603	+	10.9608i	−0.771647	+	0.371606i
$871$	7.47434	−	32.7472i	0.253259	−	1.10960i
$872$	9.44235	−	11.8403i	0.319758	−	0.400964i
$873$	−103.284	−	49.7392i	−3.49565	−	1.68342i
$874$	1.69053	−	2.11986i	0.0571830	−	0.0717052i
$875$	3.19913	+	14.0163i	0.108150	+	0.473837i
$876$	22.1368	−	10.6605i	0.747934	−	0.360186i
$877$	−25.6857	+	12.3696i	−0.867346	+	0.417692i	−0.813987	−	0.580884i	$-0.802707\pi$
$877$	−25.6857	+	12.3696i	−0.867346	+	0.417692i	−0.0533593	+	0.998575i	$0.516993\pi$
$878$	−6.59395	−	8.26855i	−0.222535	−	0.279050i
$879$	19.8710	+	87.0605i	0.670232	+	2.93648i
$880$	−0.0827692	+	0.362636i	−0.00279015	+	0.0122244i
$881$	18.2216	+	22.8492i	0.613902	+	0.769809i	0.987472	−	0.157793i	$-0.0504379\pi$
$881$	18.2216	+	22.8492i	0.613902	+	0.769809i	−0.373570	+	0.927602i	$0.621867\pi$
$882$	−20.9867	−	26.3165i	−0.706660	−	0.886123i
$883$	−4.60925	+	20.1945i	−0.155114	+	0.679597i	0.836238	+	0.548366i	$0.184750\pi$
$883$	−4.60925	+	20.1945i	−0.155114	+	0.679597i	−0.991352	+	0.131231i	$0.958107\pi$
$884$	−2.44504	−	10.7124i	−0.0822357	−	0.360298i
$885$	−50.2301	−	62.9866i	−1.68847	−	2.11727i
$886$	20.3811	−	9.81503i	0.684717	−	0.329742i
$887$	26.1673	−	12.6015i	0.878613	−	0.423118i	0.0604952	−	0.998168i	$-0.480732\pi$
$887$	26.1673	−	12.6015i	0.878613	−	0.423118i	0.818118	+	0.575051i	$0.195018\pi$
$888$	−8.79374	−	38.5279i	−0.295099	−	1.29291i
$889$	−3.49180	+	4.37858i	−0.117111	+	0.146853i
$890$	−20.2054	−	9.73039i	−0.677285	−	0.326163i
$891$	−5.27934	+	6.62008i	−0.176865	+	0.221781i
$892$	−1.47650	+	6.46897i	−0.0494369	+	0.216597i
$893$	0.856896	−	0.412659i	0.0286749	−	0.0138091i
$894$	5.22037	−	22.8719i	0.174595	−	0.764951i
$895$	18.4112	+	8.86636i	0.615418	+	0.296370i
$896$	10.5424			0.352197
$897$	−58.2790			−1.94588
$898$	−17.4998	−	8.42744i	−0.583975	−	0.281227i
$899$	4.90366	+	21.4843i	0.163546	+	0.716542i
$900$	6.38135	+	8.00197i	0.212712	+	0.266732i
$901$	−2.66487	+	3.34165i	−0.0887798	+	0.111326i
$902$	−1.55602			−0.0518099
$903$	12.0978	−	22.4578i	0.402591	−	0.747347i
$904$	6.77240			0.225247
$905$	16.5579	−	20.7630i	0.550405	−	0.690186i
$906$	4.69202	+	5.88361i	0.155882	+	0.195470i
$907$	−2.97823	−	13.0485i	−0.0988905	−	0.433268i	0.901109	−	0.433592i	$-0.142754\pi$
$907$	−2.97823	−	13.0485i	−0.0988905	−	0.433268i	−1.00000		0.000324123i	$0.999897\pi$
$908$	−5.07769	−	2.44529i	−0.168509	−	0.0811497i
$909$	−120.595			−3.99988
$910$	9.70171			0.321609
$911$	−26.4511	−	12.7382i	−0.876365	−	0.422035i	−0.0590697	−	0.998254i	$-0.518813\pi$
$911$	−26.4511	−	12.7382i	−0.876365	−	0.422035i	−0.817296	+	0.576219i	$0.804528\pi$
$912$	0.381355	−	1.67082i	0.0126279	−	0.0553265i
$913$	−1.83752	+	0.884902i	−0.0608130	+	0.0292860i
$914$	−4.18406	+	18.3316i	−0.138396	+	0.606355i
$915$	18.7506	−	23.5125i	0.619877	−	0.777301i
$916$	−23.8981	−	11.5087i	−0.789617	−	0.380260i
$917$	3.28382	−	4.11777i	0.108441	−	0.135981i
$918$	−4.22175	−	18.4967i	−0.139339	−	0.610482i
$919$	−33.1688	+	15.9733i	−1.09414	+	0.526909i	−0.891811	−	0.452409i	$-0.850565\pi$
$919$	−33.1688	+	15.9733i	−1.09414	+	0.526909i	−0.202328	+	0.979318i	$0.564851\pi$
$920$	−17.2446	+	8.30456i	−0.568537	+	0.273793i
$921$	41.0637	+	51.4923i	1.35310	+	1.69673i
$922$	2.96585	+	12.9942i	0.0976752	+	0.427943i
$923$	0.753020	−	3.29920i	0.0247860	−	0.108594i
$924$	1.10292	+	1.38301i	0.0362833	+	0.0454978i
$925$	−2.81886	−	3.53474i	−0.0926837	−	0.116222i
$926$	1.02619	−	4.49602i	0.0337226	−	0.147748i
$927$	−25.3207	−	110.937i	−0.831639	−	3.64365i
$928$	17.6298	+	22.1071i	0.578727	+	0.725701i
$929$	26.0330	−	12.5368i	0.854113	−	0.411319i	0.0450106	−	0.998987i	$-0.485668\pi$
$929$	26.0330	−	12.5368i	0.854113	−	0.411319i	0.809103	+	0.587667i	$0.199954\pi$
$930$	21.3153	−	10.2649i	0.698955	−	0.336599i
$931$	1.17768	+	5.15975i	0.0385969	+	0.169104i
$932$	6.56369	−	8.23060i	0.215001	−	0.269602i
$933$	−16.7223	−	8.05303i	−0.547463	−	0.263644i
$934$	11.7274	−	14.7057i	0.383731	−	0.481184i
$935$	0.239210	−	1.04805i	0.00782300	−	0.0342748i
$936$	92.3684	−	44.4823i	3.01916	−	1.45395i
$937$	0.664874	−	2.91301i	0.0217205	−	0.0951637i	−0.962906	−	0.269838i	$-0.913030\pi$
$937$	0.664874	−	2.91301i	0.0217205	−	0.0951637i	0.984626	+	0.174674i	$0.0558871\pi$
$938$	−5.75882	−	2.77330i	−0.188032	−	0.0905516i
$939$	79.0253			2.57889
$940$	−2.71379			−0.0885141
$941$	1.03827	+	0.500004i	0.0338466	+	0.0162997i	0.450730	−	0.892660i	$-0.351164\pi$
$941$	1.03827	+	0.500004i	0.0338466	+	0.0162997i	−0.416884	+	0.908960i	$0.636878\pi$
$942$	13.3920	+	58.6742i	0.436335	+	1.91171i
$943$	12.8331	+	16.0922i	0.417903	+	0.524034i
$944$	−4.29254	+	5.38268i	−0.139710	+	0.175191i
$945$	−35.3443			−1.14975
$946$	−0.835790	+	1.55151i	−0.0271739	+	0.0504441i
$947$	33.6939			1.09491			0.547453	−	0.836836i	$-0.315597\pi$
$947$	33.6939			1.09491			0.547453	+	0.836836i	$0.315597\pi$
$948$	12.0429	−	15.1013i	0.391134	−	0.490467i
$949$	−17.5553	−	22.0136i	−0.569868	−	0.714591i
$950$	0.169719	+	0.743586i	0.00550640	+	0.0241251i
$951$	44.3391	+	21.3526i	1.43779	+	0.692405i
$952$	−5.17283			−0.167653
$953$	−23.9463			−0.775697			−0.387848	−	0.921723i	$-0.626782\pi$
$953$	−23.9463			−0.775697			−0.387848	+	0.921723i	$0.626782\pi$
$954$	−14.5233	−	6.99403i	−0.470208	−	0.226440i
$955$	−9.53856	+	41.7912i	−0.308661	+	1.35233i
$956$	19.1329	−	9.21394i	0.618804	−	0.298000i
$957$	−1.17456	+	5.14610i	−0.0379682	+	0.166350i
$958$	13.3639	−	16.7578i	0.431768	−	0.541420i
$959$	6.07242	+	2.92432i	0.196089	+	0.0944313i
$960$	14.4330	−	18.0984i	0.465822	−	0.584122i
$961$	2.30582	+	10.1025i	0.0743814	+	0.325886i
$962$	−16.4928	+	7.94250i	−0.531748	+	0.256076i
$963$	−24.9720	+	12.0259i	−0.804710	+	0.387528i
$964$	8.11274	+	10.1730i	0.261294	+	0.327652i
$965$	−3.89200	−	17.0520i	−0.125288	−	0.548923i
$966$	−2.46777	+	10.8120i	−0.0793993	+	0.347871i
$967$	−21.6147	−	27.1040i	−0.695081	−	0.871605i	0.301564	−	0.953446i	$-0.402491\pi$
$967$	−21.6147	−	27.1040i	−0.695081	−	0.871605i	−0.996645	+	0.0818414i	$0.973920\pi$
$968$	18.2744	+	22.9154i	0.587362	+	0.736529i
$969$	−1.10215	+	4.82882i	−0.0354060	+	0.155124i
$970$	5.42413	+	23.7646i	0.174158	+	0.763037i
$971$	−12.4936	−	15.6665i	−0.400938	−	0.502761i	0.539847	−	0.841763i	$-0.318482\pi$
$971$	−12.4936	−	15.6665i	−0.400938	−	0.502761i	−0.940786	+	0.339002i	$0.889911\pi$
$972$	−46.1960	+	22.2468i	−1.48174	+	0.713567i
$973$	17.8567	−	8.59931i	0.572458	−	0.275681i
$974$	1.78913	+	7.83871i	0.0573275	+	0.251168i
$975$	10.2213	−	12.8171i	0.327344	−	0.410477i
$976$	−2.31551	−	1.11509i	−0.0741177	−	0.0356932i
$977$	33.5812	−	42.1095i	1.07436	−	1.34720i	0.140289	−	0.990111i	$-0.455197\pi$
$977$	33.5812	−	42.1095i	1.07436	−	1.34720i	0.934069	−	0.357092i	$-0.116232\pi$
$978$	−7.27767	+	31.8856i	−0.232714	+	1.01959i
$979$	−4.22186	+	2.03314i	−0.134931	+	0.0649794i
$980$	3.36035	−	14.7227i	0.107343	−	0.470298i
$981$	38.2313	+	18.4112i	1.22063	+	0.587825i
$982$	−16.8640			−0.538152
$983$	37.8993			1.20880			0.604400	−	0.796681i	$-0.293413\pi$
$983$	37.8993			1.20880			0.604400	+	0.796681i	$0.293413\pi$
$984$	−45.5969	−	21.9583i	−1.45358	−	0.700006i
$985$	8.24937	+	36.1429i	0.262847	+	1.15161i
$986$	−3.89008	−	4.87801i	−0.123886	−	0.155348i
$987$	−2.42543	+	3.04139i	−0.0772022	+	0.0968085i
$988$	−6.51573			−0.207293
$989$	22.9386	−	4.15228i	0.729406	−	0.132035i
$990$	4.05429			0.128854
$991$	−15.6852	+	19.6686i	−0.498255	+	0.624792i	−0.965835	−	0.259159i	$-0.916555\pi$
$991$	−15.6852	+	19.6686i	−0.498255	+	0.624792i	0.467579	+	0.883951i	$0.345126\pi$
$992$	−16.5105	−	20.7035i	−0.524209	−	0.657338i
$993$	16.7524	+	73.3969i	0.531620	+	2.32918i
$994$	−0.580186	−	0.279403i	−0.0184024	−	0.00886212i
$995$	6.84176			0.216898
$996$	−26.8127			−0.849593
$997$	41.5245	+	19.9972i	1.31509	+	0.633316i	0.954166	−	0.299277i	$-0.0967456\pi$
$997$	41.5245	+	19.9972i	1.31509	+	0.633316i	0.360928	+	0.932594i	$0.382460\pi$
$998$	−5.51165	+	24.1481i	−0.174468	+	0.764396i
$999$	60.0849	−	28.9353i	1.90100	−	0.915474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.e.b.4.1	✓	6
3.2	odd	2		387.2.u.a.262.1		6
4.3	odd	2		688.2.u.c.305.1		6
43.11	even	7	inner	43.2.e.b.11.1	yes	6
43.21	even	7		1849.2.a.i.1.3		3
43.22	odd	14		1849.2.a.l.1.1		3
129.11	odd	14		387.2.u.a.226.1		6
172.11	odd	14		688.2.u.c.97.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.e.b.4.1	✓	6	1.1	even	1	trivial
43.2.e.b.11.1	yes	6	43.11	even	7	inner
387.2.u.a.226.1		6	129.11	odd	14
387.2.u.a.262.1		6	3.2	odd	2
688.2.u.c.97.1		6	172.11	odd	14
688.2.u.c.305.1		6	4.3	odd	2
1849.2.a.i.1.3		3	43.21	even	7
1849.2.a.l.1.1		3	43.22	odd	14

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.626980i) q^{2} +(-2.02446 - 2.53859i) q^{3} +(0.301938 + 1.32288i) q^{4} +(1.80194 + 0.867767i) q^{5} -2.60388 q^{6} -1.19806 q^{7} +(2.42543 + 1.16802i) q^{8} +(-1.67845 + 7.35376i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.626980i) q^{2} +(-2.02446 - 2.53859i) q^{3} +(0.301938 + 1.32288i) q^{4} +(1.80194 + 0.867767i) q^{5} -2.60388 q^{6} -1.19806 q^{7} +(2.42543 + 1.16802i) q^{8} +(-1.67845 + 7.35376i) q^{9} +(1.44504 - 0.695895i) q^{10} +(0.0745725 - 0.326723i) q^{11} +(2.74698 - 3.44460i) q^{12} +(-4.54892 - 2.19064i) q^{13} +(-0.599031 + 0.751161i) q^{14} +(-1.44504 - 6.33114i) q^{15} +(-0.500000 + 0.240787i) q^{16} +(1.44504 - 0.695895i) q^{17} +(3.77144 + 4.72923i) q^{18} +(-0.211636 - 0.927237i) q^{19} +(-0.603875 + 2.64575i) q^{20} +(2.42543 + 3.04139i) q^{21} +(-0.167563 - 0.210117i) q^{22} +(-0.791053 + 3.46583i) q^{23} +(-1.94504 - 8.52179i) q^{24} +(-0.623490 - 0.781831i) q^{25} +(-3.64795 + 1.75676i) q^{26} +(13.2899 - 6.40006i) q^{27} +(-0.361740 - 1.58489i) q^{28} +(3.02446 - 3.79255i) q^{29} +(-4.69202 - 2.25956i) q^{30} +(-2.83244 + 3.55176i) q^{31} +(-1.29709 + 5.68294i) q^{32} +(-0.980386 + 0.472129i) q^{33} +(0.286208 - 1.25396i) q^{34} +(-2.15883 - 1.03964i) q^{35} -10.2349 q^{36} +4.52111 q^{37} +(-0.687177 - 0.330927i) q^{38} +(3.64795 + 15.9827i) q^{39} +(3.35690 + 4.20941i) q^{40} +(3.60992 - 4.52669i) q^{41} +3.11960 q^{42} +(-2.57457 - 6.03089i) q^{43} +0.454731 q^{44} +(-9.40581 + 11.7945i) q^{45} +(1.77748 + 2.22889i) q^{46} +(0.222521 + 0.974928i) q^{47} +(1.62349 + 0.781831i) q^{48} -5.56465 q^{49} -0.801938 q^{50} +(-4.69202 - 2.25956i) q^{51} +(1.52446 - 6.67909i) q^{52} +(-2.40097 + 1.15625i) q^{53} +(2.63222 - 11.5325i) q^{54} +(0.417895 - 0.524023i) q^{55} +(-2.90581 - 1.39937i) q^{56} +(-1.92543 + 2.41441i) q^{57} +(-0.865625 - 3.79255i) q^{58} +(11.1773 - 5.38268i) q^{59} +(7.93900 - 3.82322i) q^{60} +(2.88740 + 3.62068i) q^{61} +(0.810667 + 3.55176i) q^{62} +(2.01089 - 8.81026i) q^{63} +(2.22252 + 2.78695i) q^{64} +(-6.29590 - 7.89481i) q^{65} +(-0.194177 + 0.850747i) q^{66} +(1.48039 + 6.48599i) q^{67} +(1.35690 + 1.70149i) q^{68} +(10.3998 - 5.00827i) q^{69} +(-1.73125 + 0.833726i) q^{70} +(0.149145 + 0.653447i) q^{71} +(-12.6603 + 15.8755i) q^{72} +(5.02446 + 2.41965i) q^{73} +(2.26055 - 2.83464i) q^{74} +(-0.722521 + 3.16557i) q^{75} +(1.16272 - 0.559936i) q^{76} +(-0.0893425 + 0.391435i) q^{77} +(11.8448 + 5.70416i) q^{78} +4.38404 q^{79} -1.10992 q^{80} +(-22.7642 - 10.9627i) q^{81} +(-1.03319 - 4.52669i) q^{82} +(-3.79440 - 4.75803i) q^{83} +(-3.29105 + 4.12685i) q^{84} +3.20775 q^{85} +(-5.06853 - 1.40124i) q^{86} -15.7506 q^{87} +(0.562491 - 0.705341i) q^{88} +(-8.71797 - 10.9320i) q^{89} +(2.69202 + 11.7945i) q^{90} +(5.44989 + 2.62453i) q^{91} -4.82371 q^{92} +14.7506 q^{93} +(0.722521 + 0.347948i) q^{94} +(0.423272 - 1.85447i) q^{95} +(17.0526 - 8.21208i) q^{96} +(-3.38189 + 14.8170i) q^{97} +(-2.78232 + 3.48892i) q^{98} +(2.27748 + 1.09678i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{3} - 7 q^{4} + 2 q^{5} + 2 q^{6} - 16 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^3 - 7 * q^4 + 2 * q^5 + 2 * q^6 - 16 * q^7 + q^8 - 6 * q^9	\( 6 q + 3 q^{2} - 3 q^{3} - 7 q^{4} + 2 q^{5} + 2 q^{6} - 16 q^{7} + q^{8} - 6 q^{9} + 8 q^{10} + 14 q^{11} + 7 q^{12} - 9 q^{13} - 8 q^{14} - 8 q^{15} - 3 q^{16} + 8 q^{17} + 4 q^{18} - 4 q^{19} + 14 q^{20} + q^{21} + q^{23} - 11 q^{24} + q^{25} - 8 q^{26} + 33 q^{27} + 28 q^{28} + 9 q^{29} - 18 q^{30} - 18 q^{31} - 21 q^{32} + 7 q^{33} + 18 q^{34} + 4 q^{35} - 14 q^{36} - 4 q^{37} - 16 q^{38} + 8 q^{39} + 12 q^{40} + 23 q^{41} - 24 q^{42} - 29 q^{43} - 42 q^{44} - 30 q^{45} + 11 q^{46} + q^{47} + 5 q^{48} + 10 q^{49} + 4 q^{50} - 18 q^{51} - 10 q^{53} + 27 q^{54} + 14 q^{55} + 9 q^{56} + 2 q^{57} - 13 q^{58} + 22 q^{59} + 28 q^{60} + 19 q^{61} + 12 q^{62} + 9 q^{63} + 13 q^{64} - 10 q^{65} + 28 q^{66} - 4 q^{67} + 17 q^{69} - 26 q^{70} + 28 q^{71} - 15 q^{72} + 21 q^{73} - 2 q^{74} - 4 q^{75} + 28 q^{76} - 49 q^{77} + 25 q^{78} + 6 q^{79} - 8 q^{80} - 58 q^{81} - 13 q^{82} - 39 q^{83} - 14 q^{84} - 16 q^{85} - 25 q^{86} - 22 q^{87} - 21 q^{88} + 11 q^{89} + 6 q^{90} + 10 q^{91} - 14 q^{92} + 16 q^{93} + 4 q^{94} + 8 q^{95} + 21 q^{96} - 19 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^3 - 7 * q^4 + 2 * q^5 + 2 * q^6 - 16 * q^7 + q^8 - 6 * q^9 + 8 * q^10 + 14 * q^11 + 7 * q^12 - 9 * q^13 - 8 * q^14 - 8 * q^15 - 3 * q^16 + 8 * q^17 + 4 * q^18 - 4 * q^19 + 14 * q^20 + q^21 + q^23 - 11 * q^24 + q^25 - 8 * q^26 + 33 * q^27 + 28 * q^28 + 9 * q^29 - 18 * q^30 - 18 * q^31 - 21 * q^32 + 7 * q^33 + 18 * q^34 + 4 * q^35 - 14 * q^36 - 4 * q^37 - 16 * q^38 + 8 * q^39 + 12 * q^40 + 23 * q^41 - 24 * q^42 - 29 * q^43 - 42 * q^44 - 30 * q^45 + 11 * q^46 + q^47 + 5 * q^48 + 10 * q^49 + 4 * q^50 - 18 * q^51 - 10 * q^53 + 27 * q^54 + 14 * q^55 + 9 * q^56 + 2 * q^57 - 13 * q^58 + 22 * q^59 + 28 * q^60 + 19 * q^61 + 12 * q^62 + 9 * q^63 + 13 * q^64 - 10 * q^65 + 28 * q^66 - 4 * q^67 + 17 * q^69 - 26 * q^70 + 28 * q^71 - 15 * q^72 + 21 * q^73 - 2 * q^74 - 4 * q^75 + 28 * q^76 - 49 * q^77 + 25 * q^78 + 6 * q^79 - 8 * q^80 - 58 * q^81 - 13 * q^82 - 39 * q^83 - 14 * q^84 - 16 * q^85 - 25 * q^86 - 22 * q^87 - 21 * q^88 + 11 * q^89 + 6 * q^90 + 10 * q^91 - 14 * q^92 + 16 * q^93 + 4 * q^94 + 8 * q^95 + 21 * q^96 - 19 * q^97 + 5 * q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more