LMFDB - Embedded newform 43.2.e.a.16.1

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			16.1
Root			$0.900969 + 0.433884i$ of defining polynomial
Character	$\chi$	$=$	43.16
Dual form			43.2.e.a.35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0990311 - 0.433884i) q^{2} +(-0.400969 + 1.75676i) q^{3} +(1.62349 - 0.781831i) q^{4} +(-0.500000 - 0.626980i) q^{5} +0.801938 q^{6} -3.04892 q^{7} +(-1.05496 - 1.32288i) q^{8} +(-0.222521 - 0.107160i) q^{9} +O(q^{10})$	\(q+(-0.0990311 - 0.433884i) q^{2} +(-0.400969 + 1.75676i) q^{3} +(1.62349 - 0.781831i) q^{4} +(-0.500000 - 0.626980i) q^{5} +0.801938 q^{6} -3.04892 q^{7} +(-1.05496 - 1.32288i) q^{8} +(-0.222521 - 0.107160i) q^{9} +(-0.222521 + 0.279032i) q^{10} +(-4.77144 - 2.29780i) q^{11} +(0.722521 + 3.16557i) q^{12} +(2.46950 + 3.09666i) q^{13} +(0.301938 + 1.32288i) q^{14} +(1.30194 - 0.626980i) q^{15} +(1.77748 - 2.22889i) q^{16} +(-0.554958 + 0.695895i) q^{17} +(-0.0244587 + 0.107160i) q^{18} +(2.48039 - 1.19449i) q^{19} +(-1.30194 - 0.626980i) q^{20} +(1.22252 - 5.35621i) q^{21} +(-0.524459 + 2.29780i) q^{22} +(3.94989 + 1.90216i) q^{23} +(2.74698 - 1.32288i) q^{24} +(0.969501 - 4.24766i) q^{25} +(1.09903 - 1.37814i) q^{26} +(-3.09299 + 3.87849i) q^{27} +(-4.94989 + 2.38374i) q^{28} +(1.33513 + 5.84957i) q^{29} +(-0.400969 - 0.502799i) q^{30} +(1.54623 + 6.77447i) q^{31} +(-4.19202 - 2.01877i) q^{32} +(5.94989 - 7.46092i) q^{33} +(0.356896 + 0.171872i) q^{34} +(1.52446 + 1.91161i) q^{35} -0.445042 q^{36} -3.46681 q^{37} +(-0.763906 - 0.957907i) q^{38} +(-6.43027 + 3.09666i) q^{39} +(-0.301938 + 1.32288i) q^{40} +(-1.58211 - 6.93166i) q^{41} -2.44504 q^{42} +(-4.25786 - 4.98704i) q^{43} -9.54288 q^{44} +(0.0440730 + 0.193096i) q^{45} +(0.434157 - 1.90216i) q^{46} +(8.02930 - 3.86671i) q^{47} +(3.20291 + 4.01632i) q^{48} +2.29590 q^{49} -1.93900 q^{50} +(-1.00000 - 1.25396i) q^{51} +(6.43027 + 3.09666i) q^{52} +(-1.29105 + 1.61893i) q^{53} +(1.98911 + 0.957907i) q^{54} +(0.945042 + 4.14050i) q^{55} +(3.21648 + 4.03334i) q^{56} +(1.10388 + 4.83639i) q^{57} +(2.40581 - 1.15858i) q^{58} +(-0.538032 + 0.674671i) q^{59} +(1.62349 - 2.03579i) q^{60} +(0.307979 - 1.34934i) q^{61} +(2.78621 - 1.34177i) q^{62} +(0.678448 + 0.326723i) q^{63} +(0.807979 - 3.53999i) q^{64} +(0.706791 - 3.09666i) q^{65} +(-3.82640 - 1.84270i) q^{66} +(-6.04892 + 2.91301i) q^{67} +(-0.356896 + 1.56366i) q^{68} +(-4.92543 + 6.17629i) q^{69} +(0.678448 - 0.850747i) q^{70} +(14.9487 - 7.19891i) q^{71} +(0.0929903 + 0.407417i) q^{72} +(-7.76540 - 9.73750i) q^{73} +(0.343322 + 1.50419i) q^{74} +(7.07338 + 3.40636i) q^{75} +(3.09299 - 3.87849i) q^{76} +(14.5477 + 7.00581i) q^{77} +(1.98039 + 2.48333i) q^{78} -7.85086 q^{79} -2.28621 q^{80} +(-6.03534 - 7.56808i) q^{81} +(-2.85086 + 1.37290i) q^{82} +(-1.63922 + 7.18189i) q^{83} +(-2.20291 - 9.65156i) q^{84} +0.713792 q^{85} +(-1.74214 + 2.34129i) q^{86} -10.8116 q^{87} +(1.99396 + 8.73611i) q^{88} +(-3.13922 + 13.7538i) q^{89} +(0.0794168 - 0.0382451i) q^{90} +(-7.52930 - 9.44145i) q^{91} +7.89977 q^{92} -12.5211 q^{93} +(-2.47285 - 3.10086i) q^{94} +(-1.98911 - 0.957907i) q^{95} +(5.22737 - 6.55491i) q^{96} +(8.44989 + 4.06925i) q^{97} +(-0.227365 - 0.996152i) q^{98} +(0.815511 + 1.02262i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 5 q^{2} + 2 q^{3} + 5 q^{4} - 3 q^{5} - 4 q^{6} - 7 q^{8} - q^{9}+O(q^{10}) $ 6 * q - 5 * q^2 + 2 * q^3 + 5 * q^4 - 3 * q^5 - 4 * q^6 - 7 * q^8 - q^9	\( 6 q - 5 q^{2} + 2 q^{3} + 5 q^{4} - 3 q^{5} - 4 q^{6} - 7 q^{8} - q^{9} - q^{10} - 10 q^{11} + 4 q^{12} + 5 q^{13} - 7 q^{14} - q^{15} + 11 q^{16} - 4 q^{17} + 9 q^{18} + 2 q^{19} + q^{20} + 7 q^{21} + 6 q^{22} + q^{23} + 7 q^{24} - 4 q^{25} + 11 q^{26} - 4 q^{27} - 7 q^{28} + 6 q^{29} + 2 q^{30} - 6 q^{31} - 15 q^{32} + 13 q^{33} - 6 q^{34} - 2 q^{36} - 14 q^{37} - 11 q^{38} - 3 q^{39} + 7 q^{40} + 2 q^{41} - 14 q^{42} - 13 q^{43} - 20 q^{44} + 4 q^{45} + 5 q^{46} + 17 q^{47} + 6 q^{48} - 14 q^{49} + 8 q^{50} - 6 q^{51} + 3 q^{52} - 2 q^{53} + 15 q^{54} + 5 q^{55} - 11 q^{57} - 12 q^{58} + 12 q^{59} + 5 q^{60} + 12 q^{61} + 33 q^{62} + 15 q^{64} + 29 q^{65} - 5 q^{66} - 18 q^{67} + 6 q^{68} - 16 q^{69} + 26 q^{71} - 14 q^{72} - 9 q^{73} + 15 q^{75} + 4 q^{76} + 28 q^{77} - q^{78} - 20 q^{79} - 30 q^{80} - 24 q^{81} + 10 q^{82} + 20 q^{83} - 12 q^{85} - 23 q^{86} - 12 q^{87} - 7 q^{88} + 11 q^{89} - 8 q^{90} - 14 q^{91} + 2 q^{92} - 44 q^{93} - 27 q^{94} - 15 q^{95} + 9 q^{96} + 28 q^{97} + 21 q^{98} - 10 q^{99}+O(q^{100}) \) 6 * q - 5 * q^2 + 2 * q^3 + 5 * q^4 - 3 * q^5 - 4 * q^6 - 7 * q^8 - q^9 - q^10 - 10 * q^11 + 4 * q^12 + 5 * q^13 - 7 * q^14 - q^15 + 11 * q^16 - 4 * q^17 + 9 * q^18 + 2 * q^19 + q^20 + 7 * q^21 + 6 * q^22 + q^23 + 7 * q^24 - 4 * q^25 + 11 * q^26 - 4 * q^27 - 7 * q^28 + 6 * q^29 + 2 * q^30 - 6 * q^31 - 15 * q^32 + 13 * q^33 - 6 * q^34 - 2 * q^36 - 14 * q^37 - 11 * q^38 - 3 * q^39 + 7 * q^40 + 2 * q^41 - 14 * q^42 - 13 * q^43 - 20 * q^44 + 4 * q^45 + 5 * q^46 + 17 * q^47 + 6 * q^48 - 14 * q^49 + 8 * q^50 - 6 * q^51 + 3 * q^52 - 2 * q^53 + 15 * q^54 + 5 * q^55 - 11 * q^57 - 12 * q^58 + 12 * q^59 + 5 * q^60 + 12 * q^61 + 33 * q^62 + 15 * q^64 + 29 * q^65 - 5 * q^66 - 18 * q^67 + 6 * q^68 - 16 * q^69 + 26 * q^71 - 14 * q^72 - 9 * q^73 + 15 * q^75 + 4 * q^76 + 28 * q^77 - q^78 - 20 * q^79 - 30 * q^80 - 24 * q^81 + 10 * q^82 + 20 * q^83 - 12 * q^85 - 23 * q^86 - 12 * q^87 - 7 * q^88 + 11 * q^89 - 8 * q^90 - 14 * q^91 + 2 * q^92 - 44 * q^93 - 27 * q^94 - 15 * q^95 + 9 * q^96 + 28 * q^97 + 21 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{7}\right)$

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 $

$2$	−0.0990311	−	0.433884i	−0.0700256	−	0.306802i	0.927771	−	0.373150i	$-0.121722\pi$
$2$	−0.0990311	−	0.433884i	−0.0700256	−	0.306802i	−0.997797	+	0.0663480i	$0.978865\pi$
$3$	−0.400969	+	1.75676i	−0.231499	+	1.01427i	0.716897	+	0.697179i	$0.245562\pi$
$3$	−0.400969	+	1.75676i	−0.231499	+	1.01427i	−0.948397	+	0.317087i	$0.897295\pi$
$4$	1.62349	−	0.781831i	0.811745	−	0.390916i
$5$	−0.500000	−	0.626980i	−0.223607	−	0.280394i	0.657355	−	0.753581i	$-0.271675\pi$
$5$	−0.500000	−	0.626980i	−0.223607	−	0.280394i	−0.880962	+	0.473187i	$0.843104\pi$
$6$	0.801938			0.327390
$7$	−3.04892			−1.15238			−0.576191	−	0.817315i	$-0.695462\pi$
$7$	−3.04892			−1.15238			−0.576191	+	0.817315i	$0.695462\pi$
$8$	−1.05496	−	1.32288i	−0.372984	−	0.467707i
$9$	−0.222521	−	0.107160i	−0.0741736	−	0.0357201i
$10$	−0.222521	+	0.279032i	−0.0703673	+	0.0882378i
$11$	−4.77144	−	2.29780i	−1.43864	−	0.692814i	−0.458060	−	0.888921i	$-0.651456\pi$
$11$	−4.77144	−	2.29780i	−1.43864	−	0.692814i	−0.980582	+	0.196107i	$0.937170\pi$
$12$	0.722521	+	3.16557i	0.208574	+	0.913822i
$13$	2.46950	+	3.09666i	0.684916	+	0.858858i	0.995797	−	0.0915912i	$-0.0291953\pi$
$13$	2.46950	+	3.09666i	0.684916	+	0.858858i	−0.310880	+	0.950449i	$0.600624\pi$
$14$	0.301938	+	1.32288i	0.0806963	+	0.353553i
$15$	1.30194	−	0.626980i	0.336159	−	0.161886i
$16$	1.77748	−	2.22889i	0.444370	−	0.557222i
$17$	−0.554958	+	0.695895i	−0.134597	+	0.168779i	−0.844562	−	0.535457i	$-0.820139\pi$
$17$	−0.554958	+	0.695895i	−0.134597	+	0.168779i	0.709965	+	0.704237i	$0.248711\pi$
$18$	−0.0244587	+	0.107160i	−0.00576496	+	0.0252580i
$19$	2.48039	−	1.19449i	0.569039	−	0.274035i	−0.127161	−	0.991882i	$-0.540587\pi$
$19$	2.48039	−	1.19449i	0.569039	−	0.274035i	0.696201	+	0.717847i	$0.254872\pi$
$20$	−1.30194	−	0.626980i	−0.291122	−	0.140197i
$21$	1.22252	−	5.35621i	0.266776	−	1.16882i
$22$	−0.524459	+	2.29780i	−0.111815	+	0.489893i
$23$	3.94989	+	1.90216i	0.823608	+	0.396629i	0.797714	−	0.603036i	$-0.206042\pi$
$23$	3.94989	+	1.90216i	0.823608	+	0.396629i	0.0258941	+	0.999665i	$0.491757\pi$
$24$	2.74698	−	1.32288i	0.560725	−	0.270031i
$25$	0.969501	−	4.24766i	0.193900	−	0.849532i
$26$	1.09903	−	1.37814i	0.215538	−	0.270276i
$27$	−3.09299	+	3.87849i	−0.595246	+	0.746415i
$28$	−4.94989	+	2.38374i	−0.935441	+	0.450484i
$29$	1.33513	+	5.84957i	0.247927	+	1.08624i	0.933597	+	0.358325i	$0.116652\pi$
$29$	1.33513	+	5.84957i	0.247927	+	1.08624i	−0.685670	+	0.727912i	$0.740491\pi$
$30$	−0.400969	−	0.502799i	−0.0732066	−	0.0917981i
$31$	1.54623	+	6.77447i	0.277711	+	1.21673i	0.900679	+	0.434484i	$0.143069\pi$
$31$	1.54623	+	6.77447i	0.277711	+	1.21673i	−0.622969	+	0.782247i	$0.714074\pi$
$32$	−4.19202	−	2.01877i	−0.741052	−	0.356872i
$33$	5.94989	−	7.46092i	1.03574	−	1.29878i
$34$	0.356896	+	0.171872i	0.0612071	+	0.0294758i
$35$	1.52446	+	1.91161i	0.257681	+	0.323121i
$36$	−0.445042			−0.0741736
$37$	−3.46681			−0.569940			−0.284970	−	0.958536i	$-0.591984\pi$
$37$	−3.46681			−0.569940			−0.284970	+	0.958536i	$0.591984\pi$
$38$	−0.763906	−	0.957907i	−0.123922	−	0.155393i
$39$	−6.43027	+	3.09666i	−1.02967	+	0.495862i
$40$	−0.301938	+	1.32288i	−0.0477405	+	0.209165i
$41$	−1.58211	−	6.93166i	−0.247083	−	1.08254i	−0.934411	−	0.356196i	$-0.884074\pi$
$41$	−1.58211	−	6.93166i	−0.247083	−	1.08254i	0.687328	−	0.726347i	$-0.258783\pi$
$42$	−2.44504			−0.377278
$43$	−4.25786	−	4.98704i	−0.649318	−	0.760517i
$43$	−4.25786	−	4.98704i	−0.649318	−	0.760517i
$44$	−9.54288			−1.43864
$45$	0.0440730	+	0.193096i	0.00657001	+	0.0287851i
$46$	0.434157	−	1.90216i	0.0640129	−	0.280459i
$47$	8.02930	−	3.86671i	1.17119	−	0.564017i	0.255861	−	0.966714i	$-0.417641\pi$
$47$	8.02930	−	3.86671i	1.17119	−	0.564017i	0.915334	+	0.402696i	$0.131927\pi$
$48$	3.20291	+	4.01632i	0.462300	+	0.579706i
$49$	2.29590			0.327985
$50$	−1.93900			−0.274216
$51$	−1.00000	−	1.25396i	−0.140028	−	0.175590i
$52$	6.43027	+	3.09666i	0.891718	+	0.429429i
$53$	−1.29105	+	1.61893i	−0.177340	+	0.222377i	−0.862555	−	0.505964i	$-0.831137\pi$
$53$	−1.29105	+	1.61893i	−0.177340	+	0.222377i	0.685215	+	0.728341i	$0.259708\pi$
$54$	1.98911	+	0.957907i	0.270684	+	0.130355i
$55$	0.945042	+	4.14050i	0.127429	+	0.558305i
$56$	3.21648	+	4.03334i	0.429820	+	0.538978i
$57$	1.10388	+	4.83639i	0.146212	+	0.640596i
$58$	2.40581	−	1.15858i	0.315899	−	0.152129i
$59$	−0.538032	+	0.674671i	−0.0700458	+	0.0878347i	−0.815620	−	0.578588i	$-0.803604\pi$
$59$	−0.538032	+	0.674671i	−0.0700458	+	0.0878347i	0.745574	+	0.666423i	$0.232175\pi$
$60$	1.62349	−	2.03579i	0.209592	−	0.262820i
$61$	0.307979	−	1.34934i	0.0394326	−	0.172766i	−0.951377	−	0.308029i	$-0.900331\pi$
$61$	0.307979	−	1.34934i	0.0394326	−	0.172766i	0.990810	+	0.135263i	$0.0431879\pi$
$62$	2.78621	−	1.34177i	0.353849	−	0.170405i
$63$	0.678448	+	0.326723i	0.0854764	+	0.0411633i
$64$	0.807979	−	3.53999i	0.100997	−	0.442498i
$65$	0.706791	−	3.09666i	0.0876667	−	0.384093i
$66$	−3.82640	−	1.84270i	−0.470997	−	0.226820i
$67$	−6.04892	+	2.91301i	−0.738993	+	0.355880i	−0.765214	−	0.643776i	$-0.777367\pi$
$67$	−6.04892	+	2.91301i	−0.738993	+	0.355880i	0.0262212	+	0.999656i	$0.491653\pi$
$68$	−0.356896	+	1.56366i	−0.0432800	+	0.189622i
$69$	−4.92543	+	6.17629i	−0.592952	+	0.743538i
$70$	0.678448	−	0.850747i	0.0810900	−	0.101684i
$71$	14.9487	−	7.19891i	1.77408	−	0.854353i	0.811047	−	0.584981i	$-0.198898\pi$
$71$	14.9487	−	7.19891i	1.77408	−	0.854353i	0.963036	−	0.269372i	$-0.0868162\pi$
$72$	0.0929903	+	0.407417i	0.0109590	+	0.0480146i
$73$	−7.76540	−	9.73750i	−0.908871	−	1.13969i	−0.989728	−	0.142963i	$-0.954337\pi$
$73$	−7.76540	−	9.73750i	−0.908871	−	1.13969i	0.0808571	−	0.996726i	$-0.474234\pi$
$74$	0.343322	+	1.50419i	0.0399104	+	0.174859i
$75$	7.07338	+	3.40636i	0.816763	+	0.393332i
$76$	3.09299	−	3.87849i	0.354790	−	0.444893i
$77$	14.5477	+	7.00581i	1.65787	+	0.798387i
$78$	1.98039	+	2.48333i	0.224235	+	0.281181i
$79$	−7.85086			−0.883290			−0.441645	−	0.897190i	$-0.645605\pi$
$79$	−7.85086			−0.883290			−0.441645	+	0.897190i	$0.645605\pi$
$80$	−2.28621			−0.255606
$81$	−6.03534	−	7.56808i	−0.670594	−	0.840898i
$82$	−2.85086	+	1.37290i	−0.314824	+	0.151611i
$83$	−1.63922	+	7.18189i	−0.179928	+	0.788315i	0.801734	+	0.597681i	$0.203911\pi$
$83$	−1.63922	+	7.18189i	−0.179928	+	0.788315i	−0.981661	+	0.190633i	$0.938946\pi$
$84$	−2.20291	−	9.65156i	−0.240357	−	1.05307i
$85$	0.713792			0.0774216
$86$	−1.74214	+	2.34129i	−0.187859	+	0.252468i
$87$	−10.8116			−1.15913
$88$	1.99396	+	8.73611i	0.212557	+	0.931272i
$89$	−3.13922	+	13.7538i	−0.332757	+	1.45790i	0.481013	+	0.876714i	$0.340269\pi$
$89$	−3.13922	+	13.7538i	−0.332757	+	1.45790i	−0.813769	+	0.581188i	$0.802588\pi$
$90$	0.0794168	−	0.0382451i	0.00837127	−	0.00403139i
$91$	−7.52930	−	9.44145i	−0.789285	−	0.989733i
$92$	7.89977			0.823608
$93$	−12.5211			−1.29838
$94$	−2.47285	−	3.10086i	−0.255055	−	0.319829i
$95$	−1.98911	−	0.957907i	−0.204079	−	0.0982792i
$96$	5.22737	−	6.55491i	0.533516	−	0.669008i
$97$	8.44989	+	4.06925i	0.857956	+	0.413170i	0.810525	−	0.585705i	$-0.199182\pi$
$97$	8.44989	+	4.06925i	0.857956	+	0.413170i	0.0474314	+	0.998874i	$0.484896\pi$
$98$	−0.227365	−	0.996152i	−0.0229674	−	0.100627i
$99$	0.815511	+	1.02262i	0.0819620	+	0.102777i
$100$	−1.74698	−	7.65402i	−0.174698	−	0.765402i
$101$	−11.2811	+	5.43270i	−1.12251	+	0.540574i	−0.900668	−	0.434507i	$-0.856922\pi$
$101$	−11.2811	+	5.43270i	−1.12251	+	0.540574i	−0.221846	+	0.975082i	$0.571208\pi$
$102$	−0.445042	+	0.558065i	−0.0440657	+	0.0552567i
$103$	2.73341	−	3.42758i	0.269331	−	0.337730i	−0.628712	−	0.777638i	$-0.716418\pi$
$103$	2.73341	−	3.42758i	0.269331	−	0.337730i	0.898043	+	0.439908i	$0.144989\pi$
$104$	1.49127	−	6.53368i	0.146231	−	0.640680i
$105$	−3.96950	+	1.91161i	−0.387384	+	0.186554i
$106$	0.830281	+	0.399842i	0.0806440	+	0.0388361i
$107$	−0.143104	+	0.626980i	−0.0138344	+	0.0606125i	−0.981374	−	0.192107i	$-0.938468\pi$
$107$	−0.143104	+	0.626980i	−0.0138344	+	0.0606125i	0.967540	+	0.252720i	$0.0813250\pi$
$108$	−1.98911	+	8.71488i	−0.191403	+	0.838590i
$109$	1.69202	+	0.814835i	0.162066	+	0.0780470i	0.513158	−	0.858294i	$-0.328475\pi$
$109$	1.69202	+	0.814835i	0.162066	+	0.0780470i	−0.351092	+	0.936341i	$0.614190\pi$
$110$	1.70291	−	0.820077i	0.162366	−	0.0781912i
$111$	1.39008	−	6.09035i	0.131941	−	0.578071i
$112$	−5.41939	+	6.79570i	−0.512084	+	0.642133i
$113$	7.87382	−	9.87346i	0.740707	−	0.928817i	−0.258602	−	0.965984i	$-0.583262\pi$
$113$	7.87382	−	9.87346i	0.740707	−	0.928817i	0.999309	+	0.0371669i	$0.0118333\pi$
$114$	1.98911	−	0.957907i	0.186298	−	0.0897162i
$115$	−0.782323	−	3.42758i	−0.0729520	−	0.319624i
$116$	6.74094	+	8.45287i	0.625880	+	0.784829i
$117$	−0.217677	−	0.953703i	−0.0201242	−	0.0881699i
$118$	0.346011	+	0.166630i	0.0318529	+	0.0153395i
$119$	1.69202	−	2.12173i	0.155107	−	0.194498i
$120$	−2.20291	−	1.06086i	−0.201097	−	0.0968432i
$121$	10.6283	+	13.3275i	0.966212	+	1.21159i
$122$	−0.615957			−0.0557661
$123$	12.8116			1.15519
$124$	7.80678	+	9.78940i	0.701070	+	0.879114i
$125$	−6.76055	+	3.25571i	−0.604682	+	0.291200i
$126$	0.0745725	−	0.326723i	0.00664344	−	0.0291068i
$127$	−1.60603	−	7.03648i	−0.142512	−	0.624387i	−0.994847	−	0.101390i	$-0.967671\pi$
$127$	−1.60603	−	7.03648i	−0.142512	−	0.624387i	0.852335	−	0.522997i	$-0.175186\pi$
$128$	−10.9215			−0.965337
$129$	10.4683	−	5.48040i	0.921683	−	0.482522i
$130$	−1.41358			−0.123979
$131$	2.03199	+	8.90274i	0.177536	+	0.777836i	0.982763	+	0.184869i	$0.0591862\pi$
$131$	2.03199	+	8.90274i	0.177536	+	0.777836i	−0.805227	+	0.592966i	$0.797957\pi$
$132$	3.82640	−	16.7645i	0.333045	−	1.45917i
$133$	−7.56249	+	3.64190i	−0.655751	+	0.315793i
$134$	1.86294	+	2.33605i	0.160933	+	0.201804i
$135$	3.97823			0.342392
$136$	1.50604			0.129142
$137$	−3.79859	−	4.76328i	−0.324535	−	0.406954i	0.592622	−	0.805481i	$-0.298093\pi$
$137$	−3.79859	−	4.76328i	−0.324535	−	0.406954i	−0.917157	+	0.398527i	$0.869522\pi$
$138$	3.16756	+	1.52542i	0.269641	+	0.129852i
$139$	4.45593	−	5.58756i	0.377947	−	0.473930i	−0.556082	−	0.831127i	$-0.687696\pi$
$139$	4.45593	−	5.58756i	0.377947	−	0.473930i	0.934029	+	0.357197i	$0.116268\pi$
$140$	3.96950	+	1.91161i	0.335484	+	0.161561i
$141$	3.57338	+	15.6560i	0.300933	+	1.31847i
$142$	−4.60388	−	5.77308i	−0.386349	−	0.484466i
$143$	−4.66756	−	20.4499i	−0.390321	−	1.71011i
$144$	−0.634375	+	0.305499i	−0.0528646	+	0.0254582i
$145$	3.00000	−	3.76188i	0.249136	−	0.312407i
$146$	−3.45593	+	4.33360i	−0.286015	+	0.358651i
$147$	−0.920583	+	4.03334i	−0.0759284	+	0.332664i
$148$	−5.62833	+	2.71046i	−0.462646	+	0.222799i
$149$	4.00484	+	1.92863i	0.328090	+	0.158000i	0.590676	−	0.806909i	$-0.298861\pi$
$149$	4.00484	+	1.92863i	0.328090	+	0.158000i	−0.262586	+	0.964909i	$0.584575\pi$
$150$	0.777479	−	3.40636i	0.0634809	−	0.278128i
$151$	−3.16003	+	13.8450i	−0.257160	+	1.12669i	0.667113	+	0.744957i	$0.267530\pi$
$151$	−3.16003	+	13.8450i	−0.257160	+	1.12669i	−0.924273	+	0.381733i	$0.875327\pi$
$152$	−4.19687	−	2.02110i	−0.340411	−	0.163933i
$153$	0.198062	−	0.0953818i	0.0160124	−	0.00771116i
$154$	1.59903	−	7.00581i	0.128854	−	0.564545i
$155$	3.47434	−	4.35669i	0.279066	−	0.349938i
$156$	−8.01842	+	10.0548i	−0.641987	+	0.805027i
$157$	6.70560	−	3.22924i	0.535165	−	0.257722i	−0.146724	−	0.989177i	$-0.546873\pi$
$157$	6.70560	−	3.22924i	0.535165	−	0.257722i	0.681889	+	0.731456i	$0.261159\pi$
$158$	0.777479	+	3.40636i	0.0618529	+	0.270995i
$159$	−2.32640	−	2.91721i	−0.184495	−	0.231350i
$160$	0.830281	+	3.63770i	0.0656395	+	0.287585i
$161$	−12.0429	−	5.79954i	−0.949112	−	0.457068i
$162$	−2.68598	+	3.36811i	−0.211031	+	0.264624i
$163$	3.01573	+	1.45230i	0.236210	+	0.113753i	0.548245	−	0.836318i	$-0.315296\pi$
$163$	3.01573	+	1.45230i	0.236210	+	0.113753i	−0.312035	+	0.950071i	$0.601010\pi$
$164$	−7.98792	−	10.0165i	−0.623752	−	0.782160i
$165$	−7.65279			−0.595769
$166$	3.27844			0.254456
$167$	−1.26995	−	1.59246i	−0.0982714	−	0.123228i	0.730264	−	0.683165i	$-0.239397\pi$
$167$	−1.26995	−	1.59246i	−0.0982714	−	0.123228i	−0.828536	+	0.559936i	$0.810826\pi$
$168$	−8.37531	+	4.03334i	−0.646169	+	0.311179i
$169$	−0.598072	+	2.62032i	−0.0460055	+	0.201563i
$170$	−0.0706876	−	0.309703i	−0.00542149	−	0.0237531i
$171$	−0.679940			−0.0519963
$172$	−10.8116	−	4.76748i	−0.824379	−	0.363517i
$173$	1.02715			0.0780925			0.0390463	−	0.999237i	$-0.487568\pi$
$173$	1.02715			0.0780925			0.0390463	+	0.999237i	$0.487568\pi$
$174$	1.07069	+	4.69099i	0.0811686	+	0.355623i
$175$	−2.95593	+	12.9508i	−0.223447	+	0.978986i
$176$	−13.6027	+	6.55070i	−1.02534	+	0.493778i
$177$	−0.969501	−	1.21572i	−0.0728721	−	0.0913788i
$178$	6.27844			0.470589
$179$	9.75600			0.729198			0.364599	−	0.931165i	$-0.381206\pi$
$179$	9.75600			0.729198			0.364599	+	0.931165i	$0.381206\pi$
$180$	0.222521	+	0.279032i	0.0165857	+	0.0207978i
$181$	−7.55980	−	3.64061i	−0.561916	−	0.270604i	0.131290	−	0.991344i	$-0.458088\pi$
$181$	−7.55980	−	3.64061i	−0.561916	−	0.270604i	−0.693206	+	0.720740i	$0.743802\pi$
$182$	−3.35086	+	4.20184i	−0.248382	+	0.311461i
$183$	2.24698	+	1.08209i	0.166102	+	0.0799903i
$184$	−1.65064	−	7.23191i	−0.121687	−	0.533144i
$185$	1.73341	+	2.17362i	0.127443	+	0.159808i
$186$	1.23998	+	5.43270i	0.0909197	+	0.398345i
$187$	4.24698	−	2.04524i	0.310570	−	0.149563i
$188$	10.0124	−	12.5551i	0.730228	−	0.915677i
$189$	9.43027	−	11.8252i	0.685951	−	0.860156i
$190$	−0.218636	+	0.957907i	−0.0158615	+	0.0694939i
$191$	12.3056	−	5.92606i	0.890401	−	0.428794i	0.0679884	−	0.997686i	$-0.478342\pi$
$191$	12.3056	−	5.92606i	0.890401	−	0.428794i	0.822413	+	0.568892i	$0.192628\pi$
$192$	5.89493	+	2.83885i	0.425430	+	0.204876i
$193$	−0.909698	+	3.98565i	−0.0654815	+	0.286893i	−0.997058	−	0.0766525i	$-0.975577\pi$
$193$	−0.909698	+	3.98565i	−0.0654815	+	0.286893i	0.931576	+	0.363546i	$0.118434\pi$
$194$	0.928780	−	4.06925i	0.0666825	−	0.292155i
$195$	5.15668	+	2.48333i	0.369277	+	0.177835i
$196$	3.72737	−	1.79500i	0.266240	−	0.128215i
$197$	−1.90970	+	8.36693i	−0.136060	+	0.596119i	0.860218	+	0.509926i	$0.170327\pi$
$197$	−1.90970	+	8.36693i	−0.136060	+	0.596119i	−0.996278	+	0.0861931i	$0.972530\pi$
$198$	0.362937	−	0.455108i	0.0257928	−	0.0323431i
$199$	−3.55980	+	4.46385i	−0.252348	+	0.316434i	−0.891829	−	0.452373i	$-0.850578\pi$
$199$	−3.55980	+	4.46385i	−0.252348	+	0.316434i	0.639481	+	0.768807i	$0.279149\pi$
$200$	−6.64191	+	3.19857i	−0.469654	+	0.226173i
$201$	−2.69202	−	11.7945i	−0.189881	−	0.831921i
$202$	3.47434	+	4.35669i	0.244454	+	0.306536i
$203$	−4.07069	−	17.8348i	−0.285706	−	1.25176i
$204$	−2.60388	−	1.25396i	−0.182308	−	0.0877948i
$205$	−3.55496	+	4.45778i	−0.248289	+	0.311345i
$206$	−1.75786	−	0.846543i	−0.122476	−	0.0589814i
$207$	−0.675096	−	0.846543i	−0.0469224	−	0.0588388i
$208$	11.2916			0.782931
$209$	−14.5797			−1.00850
$210$	1.22252	+	1.53299i	0.0843620	+	0.105787i
$211$	17.2594	−	8.31167i	1.18818	−	0.572199i	0.267898	−	0.963447i	$-0.413671\pi$
$211$	17.2594	−	8.31167i	1.18818	−	0.572199i	0.920285	+	0.391248i	$0.127957\pi$
$212$	−0.830281	+	3.63770i	−0.0570240	+	0.249838i
$213$	6.65279	+	29.1478i	0.455842	+	1.99717i
$214$	0.286208			0.0195648
$215$	−0.997844	+	5.16312i	−0.0680524	+	0.352122i
$216$	8.39373			0.571121
$217$	−4.71432	−	20.6548i	−0.320029	−	1.40214i
$218$	0.185981	−	0.814835i	0.0125962	−	0.0551876i
$219$	20.2201	−	9.73750i	1.36635	−	0.657999i
$220$	4.77144	+	5.98319i	0.321690	+	0.403387i
$221$	−3.52542			−0.237145
$222$	−2.78017			−0.186593
$223$	0.0643513	+	0.0806940i	0.00430928	+	0.00540367i	0.783981	−	0.620784i	$-0.213186\pi$
$223$	0.0643513	+	0.0806940i	0.00430928	+	0.00540367i	−0.779672	+	0.626188i	$0.784614\pi$
$224$	12.7811	+	6.15507i	0.853975	+	0.411253i
$225$	−0.670915	+	0.841301i	−0.0447277	+	0.0560867i
$226$	−5.06369	−	2.43854i	−0.336831	−	0.162209i
$227$	−2.97166	−	13.0197i	−0.197236	−	0.864146i	−0.972573	−	0.232599i	$-0.925277\pi$
$227$	−2.97166	−	13.0197i	−0.197236	−	0.864146i	0.775337	−	0.631548i	$-0.217580\pi$
$228$	5.57338	+	6.98879i	0.369106	+	0.462844i
$229$	6.31671	+	27.6753i	0.417420	+	1.82884i	0.546829	+	0.837244i	$0.315835\pi$
$229$	6.31671	+	27.6753i	0.417420	+	1.82884i	−0.129409	+	0.991591i	$0.541308\pi$
$230$	−1.40970	+	0.678875i	−0.0929527	+	0.0447637i
$231$	−18.1407	+	22.7477i	−1.19357	+	1.49669i
$232$	6.32975	−	7.93725i	0.415568	−	0.521106i
$233$	−2.43967	+	10.6889i	−0.159828	+	0.700251i	0.829974	+	0.557802i	$0.188355\pi$
$233$	−2.43967	+	10.6889i	−0.159828	+	0.700251i	−0.989802	+	0.142450i	$0.954502\pi$
$234$	−0.392240	+	0.188893i	−0.0256415	+	0.0123483i
$235$	−6.43900	−	3.10086i	−0.420034	−	0.202278i
$236$	−0.346011	+	1.51597i	−0.0225234	+	0.0986814i
$237$	3.14795	−	13.7921i	0.204481	−	0.895891i
$238$	−1.08815	−	0.524023i	−0.0705340	−	0.0339674i
$239$	−17.4976	+	8.42640i	−1.13183	+	0.545059i	−0.903527	−	0.428532i	$-0.859031\pi$
$239$	−17.4976	+	8.42640i	−1.13183	+	0.545059i	−0.228300	+	0.973591i	$0.573317\pi$
$240$	0.916698	−	4.01632i	0.0591726	−	0.259252i
$241$	−2.17845	+	2.73169i	−0.140326	+	0.175963i	−0.847028	−	0.531548i	$-0.821611\pi$
$241$	−2.17845	+	2.73169i	−0.140326	+	0.175963i	0.706702	+	0.707511i	$0.250182\pi$
$242$	4.73005	−	5.93130i	0.304059	−	0.381278i
$243$	2.30678	−	1.11089i	0.147980	−	0.0712635i
$244$	−0.554958	−	2.43143i	−0.0355276	−	0.155656i
$245$	−1.14795	−	1.43948i	−0.0733397	−	0.0919651i
$246$	−1.26875	−	5.55876i	−0.0808925	−	0.354413i
$247$	9.82424	+	4.73110i	0.625101	+	0.301033i
$248$	7.33058	−	9.19225i	0.465492	−	0.583709i
$249$	−11.9596	−	5.75943i	−0.757907	−	0.364989i
$250$	2.08211	+	2.61088i	0.131684	+	0.165126i
$251$	1.25129			0.0789808			0.0394904	−	0.999220i	$-0.487427\pi$
$251$	1.25129			0.0789808			0.0394904	+	0.999220i	$0.487427\pi$
$252$	1.35690			0.0854764
$253$	−14.4758	−	18.1521i	−0.910088	−	1.14121i
$254$	−2.89397	+	1.39366i	−0.181584	+	0.0874461i
$255$	−0.286208	+	1.25396i	−0.0179231	+	0.0785260i
$256$	−0.534384	−	2.34129i	−0.0333990	−	0.146331i
$257$	−7.74094			−0.482866			−0.241433	−	0.970417i	$-0.577617\pi$
$257$	−7.74094			−0.482866			−0.241433	+	0.970417i	$0.577617\pi$
$258$	−3.41454	−	3.99930i	−0.212580	−	0.248985i
$259$	10.5700			0.656789
$260$	−1.27359	−	5.57998i	−0.0789850	−	0.346056i
$261$	0.329749	−	1.44472i	0.0204109	−	0.0894262i
$262$	3.66152	−	1.76330i	0.226210	−	0.108937i
$263$	0.797093	+	0.999524i	0.0491509	+	0.0616333i	0.805799	−	0.592189i	$-0.201736\pi$
$263$	0.797093	+	0.999524i	0.0491509	+	0.0616333i	−0.756648	+	0.653822i	$0.773165\pi$
$264$	−16.1468			−0.993764
$265$	1.66056			0.102008
$266$	2.32908	+	2.92058i	0.142805	+	0.179072i
$267$	−22.9034	−	11.0297i	−1.40167	−	0.675007i
$268$	−7.54288	+	9.45847i	−0.460755	+	0.577768i
$269$	−22.8642	−	11.0108i	−1.39405	−	0.671341i	−0.422108	−	0.906545i	$-0.638710\pi$
$269$	−22.8642	−	11.0108i	−1.39405	−	0.671341i	−0.971946	+	0.235204i	$0.924424\pi$
$270$	−0.393969	−	1.72609i	−0.0239762	−	0.105046i
$271$	−5.58091	−	6.99824i	−0.339016	−	0.425113i	0.582875	−	0.812562i	$-0.301928\pi$
$271$	−5.58091	−	6.99824i	−0.339016	−	0.425113i	−0.921891	+	0.387449i	$0.873356\pi$
$272$	0.564647	+	2.47388i	0.0342367	+	0.150001i
$273$	19.6054	−	9.44145i	1.18657	−	0.571422i
$274$	−1.69053	+	2.11986i	−0.102129	+	0.128065i
$275$	−14.3862	+	18.0397i	−0.867520	+	1.08784i
$276$	−3.16756	+	13.8780i	−0.190665	+	0.835357i
$277$	6.03415	−	2.90589i	0.362557	−	0.174598i	−0.243732	−	0.969843i	$-0.578372\pi$
$277$	6.03415	−	2.90589i	0.362557	−	0.174598i	0.606289	+	0.795244i	$0.292657\pi$
$278$	−2.86563	−	1.38001i	−0.171869	−	0.0827676i
$279$	0.381887	−	1.67316i	0.0228630	−	0.100169i
$280$	0.920583	−	4.03334i	0.0550154	−	0.241038i
$281$	20.1516	+	9.70450i	1.20214	+	0.578922i	0.924286	−	0.381701i	$-0.124661\pi$
$281$	20.1516	+	9.70450i	1.20214	+	0.578922i	0.277857	+	0.960622i	$0.410376\pi$
$282$	6.43900	−	3.10086i	0.383437	−	0.184653i
$283$	−6.49934	+	28.4755i	−0.386345	+	1.69269i	0.290754	+	0.956798i	$0.406094\pi$
$283$	−6.49934	+	28.4755i	−0.386345	+	1.69269i	−0.677099	+	0.735892i	$0.736763\pi$
$284$	18.6407	−	23.3747i	1.10612	−	1.38703i
$285$	2.48039	−	3.11031i	0.146925	−	0.184239i
$286$	−8.41066	+	4.05036i	−0.497333	+	0.239503i
$287$	4.82371	+	21.1340i	0.284734	+	1.24750i
$288$	0.716480	+	0.898438i	0.0422190	+	0.0529409i
$289$	3.60656	+	15.8014i	0.212151	+	0.929493i
$290$	−1.92931	−	0.929108i	−0.113293	−	0.0545591i
$291$	−10.5368	+	13.2128i	−0.617680	+	0.774547i
$292$	−20.2201	−	9.73750i	−1.18329	−	0.569844i
$293$	−6.02177	−	7.55106i	−0.351796	−	0.441138i	0.574175	−	0.818732i	$-0.305323\pi$
$293$	−6.02177	−	7.55106i	−0.351796	−	0.441138i	−0.925971	+	0.377595i	$0.876751\pi$
$294$	1.84117			0.107379
$295$	0.692021			0.0402910
$296$	3.65734	+	4.58616i	0.212579	+	0.266565i
$297$	23.6700	−	11.3989i	1.37347	−	0.661430i
$298$	0.440198	−	1.92863i	0.0255000	−	0.111723i
$299$	3.86390	+	16.9288i	0.223455	+	0.979020i
$300$	14.1468			0.816763
$301$	12.9819	+	15.2051i	0.748263	+	0.876406i
$302$	6.32006			0.363679
$303$	−5.02057	−	21.9966i	−0.288424	−	1.26367i
$304$	1.74645	−	7.65168i	0.100166	−	0.438854i
$305$	−1.00000	+	0.481575i	−0.0572598	+	0.0275749i
$306$	−0.0609989	−	0.0764902i	−0.00348708	−	0.00437266i
$307$	−12.9855			−0.741123			−0.370562	−	0.928808i	$-0.620835\pi$
$307$	−12.9855			−0.741123			−0.370562	+	0.928808i	$0.620835\pi$
$308$	29.0954			1.65787
$309$	4.92543	+	6.17629i	0.280198	+	0.351357i
$310$	−2.23437	−	1.07601i	−0.126903	−	0.0611135i
$311$	−3.68933	+	4.62628i	−0.209203	+	0.262332i	−0.875352	−	0.483487i	$-0.839370\pi$
$311$	−3.68933	+	4.62628i	−0.209203	+	0.262332i	0.666149	+	0.745819i	$0.267942\pi$
$312$	10.8802	+	5.23961i	0.615968	+	0.296634i
$313$	−4.57673	−	20.0520i	−0.258692	−	1.13340i	−0.922651	−	0.385635i	$-0.873982\pi$
$313$	−4.57673	−	20.0520i	−0.258692	−	1.13340i	0.663959	−	0.747769i	$-0.268875\pi$
$314$	−2.06518	−	2.58965i	−0.116545	−	0.146143i
$315$	−0.134375	−	0.588735i	−0.00757117	−	0.0331715i
$316$	−12.7458	+	6.13805i	−0.717006	+	0.345292i
$317$	11.4487	−	14.3562i	0.643022	−	0.806325i	−0.348355	−	0.937363i	$-0.613260\pi$
$317$	11.4487	−	14.3562i	0.643022	−	0.806325i	0.991377	+	0.131038i	$0.0418310\pi$
$318$	−1.03534	+	1.29828i	−0.0580592	+	0.0728039i
$319$	7.07069	−	30.9787i	0.395883	−	1.73447i
$320$	−2.62349	+	1.26341i	−0.146658	+	0.0706265i
$321$	−1.04407	−	0.502799i	−0.0582745	−	0.0280635i
$322$	−1.32371	+	5.79954i	−0.0737674	+	0.323196i
$323$	−0.545269	+	2.38898i	−0.0303396	+	0.132926i
$324$	−15.7153	−	7.56808i	−0.873071	−	0.420449i
$325$	15.5477	−	7.48739i	0.862432	−	0.415326i
$326$	0.331478	−	1.45230i	0.0183589	−	0.0804354i
$327$	−2.10992	+	2.64575i	−0.116679	+	0.146310i
$328$	−7.50066	+	9.40554i	−0.414155	+	0.519334i
$329$	−24.4807	+	11.7893i	−1.34966	+	0.649964i
$330$	0.757865	+	3.32042i	0.0417191	+	0.182783i
$331$	1.02781	+	1.28883i	0.0564936	+	0.0708407i	0.809276	−	0.587429i	$-0.199860\pi$
$331$	1.02781	+	1.28883i	0.0564936	+	0.0708407i	−0.752782	+	0.658270i	$0.771289\pi$
$332$	2.95377	+	12.9413i	0.162109	+	0.710247i
$333$	0.771438	+	0.371505i	0.0422746	+	0.0203584i
$334$	−0.565179	+	0.708712i	−0.0309252	+	0.0387790i
$335$	4.85086	+	2.33605i	0.265031	+	0.127632i
$336$	−9.76540	−	12.2454i	−0.532746	−	0.668042i
$337$	29.1444			1.58759			0.793797	−	0.608183i	$-0.208101\pi$
$337$	29.1444			1.58759			0.793797	+	0.608183i	$0.208101\pi$
$338$	1.19614			0.0650616
$339$	14.1881	+	17.7914i	0.770594	+	0.966294i
$340$	1.15883	−	0.558065i	0.0628466	−	0.0302653i
$341$	8.18867	−	35.8769i	0.443441	−	1.94284i
$342$	0.0673352	+	0.295015i	0.00364107	+	0.0159526i
$343$	14.3424			0.774418
$344$	−2.10537	+	10.8937i	−0.113514	+	0.587351i
$345$	6.33513			0.341072
$346$	−0.101720	−	0.445662i	−0.00546848	−	0.0239590i
$347$	5.60992	−	24.5786i	0.301156	−	1.31945i	−0.567229	−	0.823560i	$-0.691984\pi$
$347$	5.60992	−	24.5786i	0.301156	−	1.31945i	0.868385	−	0.495891i	$-0.165158\pi$
$348$	−17.5526	+	8.45287i	−0.940916	+	0.453121i
$349$	0.163014	+	0.204413i	0.00872594	+	0.0109420i	0.786175	−	0.618004i	$-0.212058\pi$
$349$	0.163014	+	0.204413i	0.00872594	+	0.0109420i	−0.777449	+	0.628946i	$0.783487\pi$
$350$	5.91185			0.316002
$351$	−19.6485			−1.04876
$352$	15.3632	+	19.2649i	0.818863	+	1.02682i
$353$	12.8714	+	6.19855i	0.685077	+	0.329916i	0.743841	−	0.668356i	$-0.233002\pi$
$353$	12.8714	+	6.19855i	0.685077	+	0.329916i	−0.0587644	+	0.998272i	$0.518716\pi$
$354$	−0.431468	+	0.541044i	−0.0229323	+	0.0287562i
$355$	−11.9879	−	5.77308i	−0.636253	−	0.306403i
$356$	5.65668	+	24.7835i	0.299803	+	1.31352i
$357$	3.04892	+	3.82322i	0.161366	+	0.202346i
$358$	−0.966148	−	4.23297i	−0.0510625	−	0.223720i
$359$	0.862937	−	0.415568i	0.0455441	−	0.0219329i	−0.410973	−	0.911647i	$-0.634811\pi$
$359$	0.862937	−	0.415568i	0.0455441	−	0.0219329i	0.456517	+	0.889715i	$0.349097\pi$
$360$	0.208947	−	0.262012i	0.0110125	−	0.0138092i
$361$	−7.12080	+	8.92920i	−0.374779	+	0.469958i
$362$	−0.830945	+	3.64061i	−0.0436735	+	0.191346i
$363$	−27.6749	+	13.3275i	−1.45255	+	0.699513i
$364$	−19.6054	−	9.44145i	−1.02760	−	0.494866i
$365$	−2.22252	+	9.73750i	−0.116332	+	0.509684i
$366$	0.246980	−	1.08209i	0.0129098	−	0.0565617i
$367$	−11.0930	−	5.34210i	−0.579049	−	0.278855i	0.121346	−	0.992610i	$-0.461279\pi$
$367$	−11.0930	−	5.34210i	−0.579049	−	0.278855i	−0.700396	+	0.713755i	$0.746993\pi$
$368$	11.2606	−	5.42280i	0.586997	−	0.282683i
$369$	−0.390748	+	1.71198i	−0.0203415	+	0.0891220i
$370$	0.771438	−	0.967353i	0.0401052	−	0.0502903i
$371$	3.93631	−	4.93598i	0.204363	−	0.256263i
$372$	−20.3279	+	9.78940i	−1.05395	+	0.507556i
$373$	−2.43953	−	10.6883i	−0.126314	−	0.553419i	−0.997992	−	0.0633395i	$-0.979825\pi$
$373$	−2.43953	−	10.6883i	−0.126314	−	0.553419i	0.871678	−	0.490079i	$-0.163032\pi$
$374$	−1.30798	−	1.64015i	−0.0676340	−	0.0848103i
$375$	−3.00873	−	13.1821i	−0.155370	−	0.680721i
$376$	−13.5858	−	6.54255i	−0.700632	−	0.337406i
$377$	−14.8170	+	18.5799i	−0.763114	+	0.956915i
$378$	−6.06465	−	2.92058i	−0.311932	−	0.150218i
$379$	−6.92609	−	8.68504i	−0.355769	−	0.446121i	0.571451	−	0.820636i	$-0.306381\pi$
$379$	−6.92609	−	8.68504i	−0.355769	−	0.446121i	−0.927221	+	0.374515i	$0.877809\pi$
$380$	−3.97823			−0.204079
$381$	13.0054			0.666286
$382$	−3.78986	−	4.75233i	−0.193906	−	0.243150i
$383$	7.17510	−	3.45534i	0.366630	−	0.176560i	−0.241493	−	0.970403i	$-0.577637\pi$
$383$	7.17510	−	3.45534i	0.366630	−	0.176560i	0.608123	+	0.793843i	$0.291923\pi$
$384$	4.37920	−	19.1865i	0.223475	−	0.979108i
$385$	−2.88135	−	12.6240i	−0.146847	−	0.643381i
$386$	1.81940			0.0926048
$387$	0.413050	+	1.56600i	0.0209965	+	0.0796040i
$388$	16.8998			0.857956
$389$	2.53774	+	11.1186i	0.128668	+	0.563733i	0.997627	+	0.0688484i	$0.0219325\pi$
$389$	2.53774	+	11.1186i	0.128668	+	0.563733i	−0.868959	+	0.494884i	$0.835210\pi$
$390$	0.566803	−	2.48333i	0.0287012	−	0.125748i
$391$	−3.51573	+	1.69309i	−0.177798	+	0.0856230i
$392$	−2.42208	−	3.03719i	−0.122333	−	0.153401i
$393$	−16.4547			−0.830031
$394$	3.81940			0.192418
$395$	3.92543	+	4.92233i	0.197510	+	0.247669i
$396$	2.12349	+	1.02262i	0.106709	+	0.0513885i
$397$	−5.92543	+	7.43025i	−0.297389	+	0.372914i	−0.907967	−	0.419043i	$-0.862366\pi$
$397$	−5.92543	+	7.43025i	−0.297389	+	0.372914i	0.610578	+	0.791956i	$0.290937\pi$
$398$	2.28932	+	1.10248i	0.114753	+	0.0552623i
$399$	−3.36563	−	14.7458i	−0.168492	−	0.738212i
$400$	−7.74429	−	9.71103i	−0.387215	−	0.485552i
$401$	−2.41789	−	10.5935i	−0.120744	−	0.529014i	−0.998733	−	0.0503321i	$-0.983972\pi$
$401$	−2.41789	−	10.5935i	−0.120744	−	0.529014i	0.877989	−	0.478681i	$-0.158885\pi$
$402$	−4.85086	+	2.33605i	−0.241939	+	0.116512i
$403$	−17.1598	+	21.5177i	−0.854790	+	1.07187i
$404$	−14.0673	+	17.6399i	−0.699876	+	0.877617i
$405$	−1.72737	+	7.56808i	−0.0858335	+	0.376061i
$406$	−7.33513	+	3.53241i	−0.364036	+	0.175311i
$407$	16.5417	+	7.96605i	0.819941	+	0.394863i
$408$	−0.603875	+	2.64575i	−0.0298963	+	0.130984i
$409$	4.71164	−	20.6430i	0.232975	−	1.02073i	−0.714181	−	0.699961i	$-0.753201\pi$
$409$	4.71164	−	20.6430i	0.232975	−	1.02073i	0.947157	−	0.320771i	$-0.103942\pi$
$410$	2.28621	+	1.10098i	0.112908	+	0.0543735i
$411$	9.89104	−	4.76328i	0.487889	−	0.234955i
$412$	1.75786	−	7.70171i	0.0866038	−	0.379436i
$413$	1.64042	−	2.05702i	0.0807196	−	0.101219i
$414$	−0.300446	+	0.376747i	−0.0147661	+	0.0185161i
$415$	5.32251	−	2.56319i	0.261272	−	0.125822i
$416$	−4.10076	−	17.9666i	−0.201056	−	0.880885i
$417$	8.02930	+	10.0684i	0.393197	+	0.493053i
$418$	1.44385	+	6.32590i	0.0706208	+	0.309410i
$419$	28.9279	+	13.9309i	1.41322	+	0.680571i	0.975796	−	0.218685i	$-0.0701767\pi$
$419$	28.9279	+	13.9309i	1.41322	+	0.680571i	0.437424	+	0.899255i	$0.355891\pi$
$420$	−4.94989	+	6.20696i	−0.241530	+	0.302869i
$421$	−13.7126	−	6.60364i	−0.668311	−	0.321842i	0.0687832	−	0.997632i	$-0.478088\pi$
$421$	−13.7126	−	6.60364i	−0.668311	−	0.321842i	−0.737094	+	0.675790i	$0.763803\pi$
$422$	−5.31551	−	6.66544i	−0.258755	−	0.324469i
$423$	−2.20105			−0.107019
$424$	3.50365			0.170152
$425$	2.41789	+	3.03194i	0.117285	+	0.147071i
$426$	11.9879	−	5.77308i	0.580817	−	0.279707i
$427$	−0.939001	+	4.11403i	−0.0454414	+	0.199092i
$428$	0.257865	+	1.12978i	0.0124644	+	0.0546099i
$429$	37.7972			1.82486
$430$	2.33901	−	0.0783611i	0.112797	−	0.00377891i
$431$	37.4819			1.80544			0.902719	−	0.430230i	$-0.141568\pi$
$431$	37.4819			1.80544			0.902719	+	0.430230i	$0.141568\pi$
$432$	3.14699	+	13.7879i	0.151410	+	0.663369i
$433$	−5.11141	+	22.3945i	−0.245639	+	1.07621i	0.690154	+	0.723662i	$0.257543\pi$
$433$	−5.11141	+	22.3945i	−0.245639	+	1.07621i	−0.935793	+	0.352551i	$0.885314\pi$
$434$	−8.49492	+	4.09094i	−0.407769	+	0.196371i
$435$	5.40581	+	6.77868i	0.259189	+	0.325013i
$436$	3.38404			0.162066
$437$	12.0694			0.577356
$438$	−6.22737	−	7.80887i	−0.297555	−	0.373122i
$439$	−1.31282	−	0.632222i	−0.0626576	−	0.0301743i	0.402293	−	0.915511i	$-0.368213\pi$
$439$	−1.31282	−	0.632222i	−0.0626576	−	0.0301743i	−0.464950	+	0.885337i	$0.653928\pi$
$440$	4.48039	−	5.61823i	0.213594	−	0.267838i
$441$	−0.510885	−	0.246029i	−0.0243279	−	0.0117157i
$442$	0.349126	+	1.52962i	0.0166062	+	0.0727567i
$443$	−13.0640	−	16.3817i	−0.620689	−	0.778319i	0.367753	−	0.929924i	$-0.380127\pi$
$443$	−13.0640	−	16.3817i	−0.620689	−	0.778319i	−0.988441	+	0.151605i	$0.951556\pi$
$444$	−2.50484	−	10.9744i	−0.118875	−	0.520824i
$445$	10.1930	−	4.90868i	0.483194	−	0.232694i
$446$	0.0286390	−	0.0359122i	0.00135610	−	0.00170049i
$447$	−4.99396	+	6.26223i	−0.236206	+	0.296193i
$448$	−2.46346	+	10.7931i	−0.116388	+	0.509927i
$449$	−7.87316	+	3.79151i	−0.371557	+	0.178933i	−0.610338	−	0.792141i	$-0.708966\pi$
$449$	−7.87316	+	3.79151i	−0.371557	+	0.178933i	0.238781	+	0.971073i	$0.423252\pi$
$450$	0.431468	+	0.207784i	0.0203396	+	0.00979504i
$451$	−8.37867	+	36.7093i	−0.394536	+	1.72858i
$452$	5.06369	−	22.1855i	0.238176	−	1.04352i
$453$	−23.0553	−	11.1028i	−1.08323	−	0.521656i
$454$	−5.35474	+	2.57871i	−0.251310	+	0.121025i
$455$	−2.15495	+	9.44145i	−0.101026	+	0.442622i
$456$	5.23341	−	6.56248i	0.245077	−	0.307316i
$457$	19.7461	−	24.7608i	0.923683	−	1.15826i	−0.0633902	−	0.997989i	$-0.520191\pi$
$457$	19.7461	−	24.7608i	0.923683	−	1.15826i	0.987073	−	0.160273i	$-0.0512373\pi$
$458$	11.3823	−	5.48143i	0.531861	−	0.256131i
$459$	−0.982542	−	4.30480i	−0.0458611	−	0.200931i
$460$	−3.94989	−	4.95300i	−0.184164	−	0.230935i
$461$	−7.56010	−	33.1230i	−0.352109	−	1.54269i	−0.772302	−	0.635255i	$-0.780895\pi$
$461$	−7.56010	−	33.1230i	−0.352109	−	1.54269i	0.420193	−	0.907435i	$-0.361962\pi$
$462$	11.6664	+	5.61823i	0.542768	+	0.261384i
$463$	−3.99061	+	5.00406i	−0.185459	+	0.232559i	−0.865866	−	0.500276i	$-0.833232\pi$
$463$	−3.99061	+	5.00406i	−0.185459	+	0.232559i	0.680407	+	0.732835i	$0.261803\pi$
$464$	15.4112	+	7.42164i	0.715447	+	0.344541i
$465$	6.26055	+	7.85049i	0.290326	+	0.364058i
$466$	4.87933			0.226031
$467$	−40.9506			−1.89497			−0.947484	−	0.319803i	$-0.896383\pi$
$467$	−40.9506			−1.89497			−0.947484	+	0.319803i	$0.896383\pi$
$468$	−1.09903	−	1.37814i	−0.0508027	−	0.0637046i
$469$	18.4426	−	8.88151i	0.851602	−	0.410110i
$470$	−0.707751	+	3.10086i	−0.0326461	+	0.143032i
$471$	2.98427	+	13.0749i	0.137508	+	0.602462i
$472$	1.46011			0.0672069
$473$	8.85690	+	33.5791i	0.407241	+	1.54397i
$474$	−6.29590			−0.289180
$475$	−2.66905	−	11.6939i	−0.122465	−	0.536553i
$476$	1.08815	−	4.76748i	0.0498751	−	0.218517i
$477$	0.460771	−	0.221896i	0.0210973	−	0.0101599i
$478$	5.38889	+	6.75745i	0.246482	+	0.309079i
$479$	−19.8495			−0.906948			−0.453474	−	0.891269i	$-0.649816\pi$
$479$	−19.8495			−0.906948			−0.453474	+	0.891269i	$0.649816\pi$
$480$	−6.72348			−0.306883
$481$	−8.56129	−	10.7355i	−0.390361	−	0.489498i
$482$	1.40097	+	0.674671i	0.0638124	+	0.0307304i
$483$	15.0172	−	18.8310i	0.683307	−	0.856840i
$484$	27.6749	+	13.3275i	1.25795	+	0.605796i
$485$	−1.67360	−	7.33254i	−0.0759944	−	0.332953i
$486$	−0.710439	−	0.890863i	−0.0322262	−	0.0404104i
$487$	3.20291	+	14.0329i	0.145138	+	0.635889i	0.994195	+	0.107589i	$0.0343132\pi$
$487$	3.20291	+	14.0329i	0.145138	+	0.635889i	−0.849058	+	0.528300i	$0.822830\pi$
$488$	−2.10992	+	1.01608i	−0.0955114	+	0.0459959i
$489$	−3.76055	+	4.71558i	−0.170058	+	0.213246i
$490$	−0.510885	+	0.640630i	−0.0230794	+	0.0289407i
$491$	8.55137	−	37.4660i	0.385918	−	1.69082i	−0.292602	−	0.956234i	$-0.594521\pi$
$491$	8.55137	−	37.4660i	0.385918	−	1.69082i	0.678520	−	0.734582i	$-0.262622\pi$
$492$	20.7995	−	10.0165i	0.937716	−	0.451580i
$493$	−4.81163	−	2.31716i	−0.216705	−	0.104360i
$494$	1.07984	−	4.73110i	0.0485845	−	0.212862i
$495$	0.233406	−	1.02262i	0.0104908	−	0.0459633i
$496$	17.8479	+	8.59511i	0.801396	+	0.385932i
$497$	−45.5773	+	21.9489i	−2.04442	+	0.984542i
$498$	−1.31455	+	5.75943i	−0.0589065	+	0.258086i
$499$	−13.1670	+	16.5109i	−0.589437	+	0.739131i	−0.983690	−	0.179871i	$-0.942432\pi$
$499$	−13.1670	+	16.5109i	−0.589437	+	0.739131i	0.394253	+	0.919002i	$0.371003\pi$
$500$	−8.43027	+	10.5712i	−0.377013	+	0.472760i
$501$	3.30678	−	1.59246i	0.147736	−	0.0711460i
$502$	−0.123917	−	0.542915i	−0.00553068	−	0.0242315i
$503$	4.40664	+	5.52575i	0.196482	+	0.246381i	0.870306	−	0.492511i	$-0.163921\pi$
$503$	4.40664	+	5.52575i	0.196482	+	0.246381i	−0.673824	+	0.738892i	$0.735349\pi$
$504$	−0.283520	−	1.24218i	−0.0126290	−	0.0553312i
$505$	9.04676	+	4.35669i	0.402576	+	0.193870i
$506$	−6.44235	+	8.07846i	−0.286398	+	0.359131i
$507$	−4.36347	−	2.10134i	−0.193788	−	0.0933236i
$508$	−8.10872	−	10.1680i	−0.359766	−	0.451133i
$509$	−27.6136			−1.22395			−0.611975	−	0.790877i	$-0.709625\pi$
$509$	−27.6136			−1.22395			−0.611975	+	0.790877i	$0.709625\pi$
$510$	0.572417			0.0253470
$511$	23.6761	+	29.6888i	1.04737	+	1.31336i
$512$	−20.6429	+	9.94108i	−0.912294	+	0.439338i
$513$	−3.03899	+	13.3147i	−0.134175	+	0.587858i
$514$	0.766594	+	3.35867i	0.0338130	+	0.148144i
$515$	−3.51573			−0.154922
$516$	12.7104	−	17.0818i	0.559546	−	0.751985i
$517$	−47.1963			−2.07569
$518$	−1.04676	−	4.58616i	−0.0459921	−	0.201504i
$519$	−0.411854	+	1.80445i	−0.0180784	+	0.0792066i
$520$	−4.84213	+	2.33184i	−0.212341	+	0.102258i
$521$	−26.8925	−	33.7222i	−1.17818	−	1.47740i	−0.845190	−	0.534466i	$-0.820513\pi$
$521$	−26.8925	−	33.7222i	−1.17818	−	1.47740i	−0.332993	−	0.942929i	$-0.608059\pi$
$522$	−0.659498			−0.0288654
$523$	13.6420			0.596525			0.298262	−	0.954484i	$-0.403593\pi$
$523$	13.6420			0.596525			0.298262	+	0.954484i	$0.403593\pi$
$524$	10.2594	+	12.8648i	0.448182	+	0.562003i
$525$	−21.5661	−	10.3857i	−0.941223	−	0.453269i
$526$	0.354740	−	0.444830i	0.0154674	−	0.0193955i
$527$	−5.57242	−	2.68353i	−0.242738	−	0.116897i
$528$	−6.05376	−	26.5233i	−0.263456	−	1.15428i
$529$	−2.35690	−	2.95545i	−0.102474	−	0.128498i
$530$	−0.164447	−	0.720491i	−0.00714314	−	0.0312961i
$531$	0.192021	−	0.0924727i	0.00833302	−	0.00401297i
$532$	−9.43027	+	11.8252i	−0.408854	+	0.512687i
$533$	17.5579	−	22.0170i	0.760519	−	0.953661i
$534$	−2.51746	+	11.0297i	−0.108941	+	0.477302i
$535$	0.464656	−	0.223767i	0.0200888	−	0.00967428i
$536$	10.2349	+	4.92887i	0.442080	+	0.212895i
$537$	−3.91185	+	17.1390i	−0.168809	+	0.739600i
$538$	−2.51315	+	11.0108i	−0.108349	+	0.474710i
$539$	−10.9547	−	5.27552i	−0.471854	−	0.227233i
$540$	6.45862	−	3.11031i	0.277935	−	0.133846i
$541$	5.46562	−	23.9464i	0.234985	−	1.02954i	−0.710455	−	0.703742i	$-0.751511\pi$
$541$	5.46562	−	23.9464i	0.234985	−	1.02954i	0.945440	−	0.325795i	$-0.105632\pi$
$542$	−2.48374	+	3.11451i	−0.106686	+	0.133780i
$543$	9.42692	−	11.8210i	0.404548	−	0.507287i
$544$	3.73125	−	1.79688i	0.159976	−	0.0770404i
$545$	−0.335126	−	1.46828i	−0.0143552	−	0.0628943i
$546$	−6.03803	−	7.57145i	−0.258404	−	0.324028i
$547$	−4.85517	−	21.2719i	−0.207592	−	0.909520i	−0.966164	−	0.257930i	$-0.916960\pi$
$547$	−4.85517	−	21.2719i	−0.207592	−	0.909520i	0.758572	−	0.651590i	$-0.225898\pi$
$548$	−9.89104	−	4.76328i	−0.422524	−	0.203477i
$549$	−0.213128	+	0.267254i	−0.00909607	+	0.0114061i
$550$	9.25182	+	4.45544i	0.394499	+	0.189981i
$551$	10.2989	+	12.9144i	0.438747	+	0.550171i
$552$	13.3666			0.568920
$553$	23.9366			1.01789
$554$	−1.85839	−	2.33034i	−0.0789553	−	0.0990069i
$555$	−4.51357	+	2.17362i	−0.191591	+	0.0922651i
$556$	2.86563	−	12.5551i	0.121530	−	0.532456i
$557$	9.10065	+	39.8726i	0.385607	+	1.68946i	0.679548	+	0.733631i	$0.262176\pi$
$557$	9.10065	+	39.8726i	0.385607	+	1.68946i	−0.293940	+	0.955824i	$0.594967\pi$
$558$	−0.763774			−0.0323331
$559$	4.92835	−	25.5006i	0.208447	−	1.07856i
$560$	6.97046			0.294556
$561$	1.89008	+	8.28100i	0.0797994	+	0.349624i
$562$	2.21499	−	9.70450i	0.0934336	−	0.409360i
$563$	−0.612605	+	0.295015i	−0.0258182	+	0.0124334i	−0.446748	−	0.894660i	$-0.647418\pi$
$563$	−0.612605	+	0.295015i	−0.0258182	+	0.0124334i	0.420930	+	0.907093i	$0.361704\pi$
$564$	18.0417	+	22.6236i	0.759692	+	0.952623i
$565$	−10.1274			−0.426062
$566$	12.9987			0.546375
$567$	18.4013	+	23.0745i	0.772780	+	0.969036i
$568$	−25.2935	−	12.1807i	−1.06129	−	0.511091i
$569$	−10.2476	+	12.8501i	−0.429604	+	0.538706i	−0.948770	−	0.315967i	$-0.897671\pi$
$569$	−10.2476	+	12.8501i	−0.429604	+	0.538706i	0.519167	+	0.854673i	$0.326242\pi$
$570$	−1.59515	−	0.768182i	−0.0668133	−	0.0321756i
$571$	−4.67821	−	20.4966i	−0.195777	−	0.857755i	−0.973416	−	0.229044i	$-0.926440\pi$
$571$	−4.67821	−	20.4966i	−0.195777	−	0.857755i	0.777639	−	0.628711i	$-0.216417\pi$
$572$	−23.5661	−	29.5510i	−0.985350	−	1.23559i
$573$	5.47650	+	23.9941i	0.228784	+	1.00237i
$574$	8.69202	−	4.18586i	0.362798	−	0.174714i
$575$	11.9092	−	14.9336i	0.496647	−	0.622775i
$576$	−0.559138	+	0.701137i	−0.0232974	+	0.0292141i
$577$	−9.11237	+	39.9239i	−0.379353	+	1.66205i	0.320107	+	0.947381i	$0.396281\pi$
$577$	−9.11237	+	39.9239i	−0.379353	+	1.66205i	−0.699460	+	0.714672i	$0.746576\pi$
$578$	6.49880	−	3.12966i	0.270315	−	0.130177i
$579$	−6.63706	−	3.19624i	−0.275827	−	0.132831i
$580$	1.92931	−	8.45287i	0.0801103	−	0.350986i
$581$	4.99784	−	21.8970i	0.207346	−	0.908440i
$582$	6.77628	+	3.26329i	0.280886	+	0.135268i
$583$	9.88016	−	4.75803i	0.409194	−	0.197058i
$584$	−4.68933	+	20.5453i	−0.194046	+	0.850171i
$585$	−0.489115	+	0.613331i	−0.0202224	+	0.0253581i
$586$	−2.67994	+	3.36054i	−0.110707	+	0.138823i
$587$	7.40097	−	3.56412i	0.305471	−	0.147107i	−0.274868	−	0.961482i	$-0.588634\pi$
$587$	7.40097	−	3.56412i	0.305471	−	0.147107i	0.580339	+	0.814375i	$0.302920\pi$
$588$	1.65883	+	7.26782i	0.0684091	+	0.299720i
$589$	11.9273	+	14.9563i	0.491455	+	0.616266i
$590$	−0.0685317	−	0.300257i	−0.00282140	−	0.0123614i
$591$	−13.9330	−	6.70976i	−0.573125	−	0.276003i
$592$	−6.16219	+	7.72714i	−0.253264	+	0.317583i
$593$	16.0661	+	7.73704i	0.659757	+	0.317722i	0.733634	−	0.679545i	$-0.237823\pi$
$593$	16.0661	+	7.73704i	0.659757	+	0.317722i	−0.0738765	+	0.997267i	$0.523537\pi$
$594$	−7.28986	−	9.14119i	−0.299106	−	0.375068i
$595$	−2.17629			−0.0892193
$596$	8.00969			0.328090
$597$	−6.41454	−	8.04358i	−0.262530	−	0.329202i
$598$	6.96250	−	3.35296i	0.284718	−	0.137113i
$599$	−7.94020	+	34.7883i	−0.324428	+	1.42141i	0.505156	+	0.863028i	$0.331435\pi$
$599$	−7.94020	+	34.7883i	−0.324428	+	1.42141i	−0.829584	+	0.558382i	$0.811422\pi$
$600$	−2.95593	−	12.9508i	−0.120675	−	0.528713i
$601$	−8.47219			−0.345588			−0.172794	−	0.984958i	$-0.555279\pi$
$601$	−8.47219			−0.345588			−0.172794	+	0.984958i	$0.555279\pi$
$602$	5.31163	−	7.13840i	0.216486	−	0.290940i
$603$	1.65817			0.0675259
$604$	5.69418	+	24.9478i	0.231693	+	1.01511i
$605$	3.04192	−	13.3275i	0.123672	−	0.541840i
$606$	−9.04676	+	4.35669i	−0.367500	+	0.176978i
$607$	21.0993	+	26.4577i	0.856395	+	1.07389i	0.996487	+	0.0837472i	$0.0266888\pi$
$607$	21.0993	+	26.4577i	0.856395	+	1.07389i	−0.140092	+	0.990139i	$0.544740\pi$
$608$	−12.8092			−0.519483
$609$	32.9638			1.33576
$610$	0.307979	+	0.386193i	0.0124697	+	0.0156365i
$611$	31.8022	+	15.3151i	1.28658	+	0.619585i
$612$	0.246980	−	0.309703i	0.00998356	−	0.0125190i
$613$	32.2630	+	15.5370i	1.30309	+	0.627535i	0.951220	−	0.308513i	$-0.0998315\pi$
$613$	32.2630	+	15.5370i	1.30309	+	0.627535i	0.351870	+	0.936049i	$0.385546\pi$
$614$	1.28597	+	5.63421i	0.0518976	+	0.227378i
$615$	−6.40581	−	8.03264i	−0.258307	−	0.323907i
$616$	−6.07942	−	26.6357i	−0.244947	−	1.07318i
$617$	−3.56638	+	1.71748i	−0.143577	+	0.0691430i	−0.504293	−	0.863533i	$-0.668247\pi$
$617$	−3.56638	+	1.71748i	−0.143577	+	0.0691430i	0.360716	+	0.932676i	$0.382532\pi$
$618$	2.19202	−	2.74871i	0.0881760	−	0.110569i
$619$	14.0233	−	17.5846i	0.563642	−	0.706785i	−0.415584	−	0.909555i	$-0.636423\pi$
$619$	14.0233	−	17.5846i	0.563642	−	0.706785i	0.979227	+	0.202769i	$0.0649942\pi$
$620$	2.23437	−	9.78940i	0.0897343	−	0.393152i
$621$	−19.5945	+	9.43621i	−0.786299	+	0.378662i
$622$	2.37263	+	1.14260i	0.0951336	+	0.0458139i
$623$	9.57122	−	41.9343i	0.383463	−	1.68006i
$624$	−4.52757	+	19.8366i	−0.181248	+	0.794099i
$625$	−14.2056	−	6.84105i	−0.568224	−	0.273642i
$626$	−8.24698	+	3.97154i	−0.329616	+	0.158735i
$627$	5.84601	−	25.6130i	0.233467	−	1.02289i
$628$	8.36174	−	10.4853i	0.333670	−	0.418409i
$629$	1.92394	−	2.41254i	0.0767123	−	0.0961942i
$630$	−0.242135	+	0.116606i	−0.00964690	+	0.00464570i
$631$	−2.60776	−	11.4253i	−0.103813	−	0.454836i	−0.999939	−	0.0110357i	$-0.996487\pi$
$631$	−2.60776	−	11.4253i	−0.103813	−	0.454836i	0.896126	−	0.443800i	$-0.146370\pi$
$632$	8.28232	+	10.3857i	0.329453	+	0.413121i
$633$	7.68114	+	33.6533i	0.305298	+	1.33760i
$634$	−7.36270	−	3.54569i	−0.292410	−	0.140817i
$635$	−3.60872	+	4.52519i	−0.143208	+	0.179577i
$636$	−6.05765	−	2.91721i	−0.240201	−	0.115675i
$637$	5.66972	+	7.10960i	0.224642	+	0.281693i
$638$	−14.1414			−0.559862
$639$	−4.09783			−0.162108
$640$	5.46077	+	6.84759i	0.215856	+	0.270675i
$641$	−37.8303	+	18.2181i	−1.49421	+	0.719573i	−0.989610	−	0.143781i	$-0.954074\pi$
$641$	−37.8303	+	18.2181i	−1.49421	+	0.719573i	−0.504599	+	0.863354i	$0.668360\pi$
$642$	−0.114761	+	0.502799i	−0.00452924	+	0.0198439i
$643$	−4.28083	−	18.7555i	−0.168820	−	0.739647i	−0.986471	−	0.163934i	$-0.947582\pi$
$643$	−4.28083	−	18.7555i	−0.168820	−	0.739647i	0.817652	−	0.575713i	$-0.195275\pi$
$644$	−24.0858			−0.949112
$645$	−8.67025	−	3.82322i	−0.341391	−	0.150539i
$646$	1.09054			0.0429067
$647$	−3.49193	−	15.2992i	−0.137282	−	0.601472i	−0.996026	−	0.0890667i	$-0.971612\pi$
$647$	−3.49193	−	15.2992i	−0.137282	−	0.601472i	0.858744	−	0.512406i	$-0.171246\pi$
$648$	−3.64460	+	15.9680i	−0.143173	+	0.627283i
$649$	4.11745	−	1.98286i	0.161624	−	0.0778340i
$650$	−4.78836	−	6.00442i	−0.187815	−	0.235513i
$651$	38.1758			1.49623
$652$	6.03146			0.236210
$653$	−28.8267	−	36.1475i	−1.12808	−	1.41456i	−0.897225	−	0.441573i	$-0.854421\pi$
$653$	−28.8267	−	36.1475i	−1.12808	−	1.41456i	−0.230850	−	0.972989i	$-0.574151\pi$
$654$	1.35690	+	0.653447i	0.0530588	+	0.0255518i
$655$	4.56584	−	5.72539i	0.178402	−	0.223709i
$656$	−18.2620	−	8.79454i	−0.713013	−	0.343369i
$657$	0.684489	+	2.99894i	0.0267044	+	0.117000i
$658$	7.53952	+	9.45426i	0.293921	+	0.368566i
$659$	−1.76218	−	7.72060i	−0.0686447	−	0.300752i	0.928939	−	0.370234i	$-0.120722\pi$
$659$	−1.76218	−	7.72060i	−0.0686447	−	0.300752i	−0.997583	+	0.0694821i	$0.977865\pi$
$660$	−12.4242	+	5.98319i	−0.483613	+	0.232896i
$661$	24.7521	−	31.0382i	0.962746	−	1.20725i	−0.0155177	−	0.999880i	$-0.504940\pi$
$661$	24.7521	−	31.0382i	0.962746	−	1.20725i	0.978264	−	0.207366i	$-0.0664889\pi$
$662$	0.457419	−	0.573585i	0.0177781	−	0.0222930i
$663$	1.41358	−	6.19331i	0.0548990	−	0.240528i
$664$	11.2301	−	5.40811i	0.435811	−	0.209875i
$665$	6.06465	+	2.92058i	0.235177	+	0.113255i
$666$	0.0847936	−	0.371505i	0.00328569	−	0.0143955i
$667$	−5.85325	+	25.6448i	−0.226639	+	0.992969i
$668$	−3.30678	−	1.59246i	−0.127943	−	0.0616142i
$669$	−0.167563	+	0.0806940i	−0.00647835	+	0.00311981i
$670$	0.533188	−	2.33605i	0.0205988	−	0.0902494i
$671$	−4.57002	+	5.73063i	−0.176424	+	0.221228i
$672$	−15.9378	+	19.9854i	−0.614814	+	0.770953i
$673$	−27.3702	+	13.1808i	−1.05504	+	0.508083i	−0.879258	−	0.476345i	$-0.841961\pi$
$673$	−27.3702	+	13.1808i	−1.05504	+	0.508083i	−0.175787	+	0.984428i	$0.556247\pi$
$674$	−2.88620	−	12.6453i	−0.111172	−	0.487077i
$675$	13.4758	+	16.8982i	0.518685	+	0.650411i
$676$	1.07769	+	4.72166i	0.0414495	+	0.181602i
$677$	10.6184	+	5.11356i	0.408099	+	0.196530i	0.626659	−	0.779293i	$-0.284422\pi$
$677$	10.6184	+	5.11356i	0.408099	+	0.196530i	−0.218561	+	0.975823i	$0.570136\pi$
$678$	6.31431	−	7.91790i	0.242500	−	0.304085i
$679$	−25.7630	−	12.4068i	−0.988693	−	0.476130i
$680$	−0.753020	−	0.944258i	−0.0288770	−	0.0362106i
$681$	24.0640			0.922134
$682$	−16.3773			−0.627121
$683$	−10.3319	−	12.9558i	−0.395339	−	0.495740i	0.543829	−	0.839196i	$-0.316974\pi$
$683$	−10.3319	−	12.9558i	−0.395339	−	0.495740i	−0.939169	+	0.343456i	$0.888402\pi$
$684$	−1.10388	+	0.531598i	−0.0422077	+	0.0203262i
$685$	−1.08719	+	4.76328i	−0.0415393	+	0.181995i
$686$	−1.42035	−	6.22294i	−0.0542291	−	0.237593i
$687$	−51.1517			−1.95156
$688$	−18.6838	+	0.625942i	−0.712314	+	0.0238638i
$689$	−8.20152			−0.312453
$690$	−0.627375	−	2.74871i	−0.0238837	−	0.104642i
$691$	−4.19537	+	18.3811i	−0.159600	+	0.699251i	0.830281	+	0.557346i	$0.188180\pi$
$691$	−4.19537	+	18.3811i	−0.159600	+	0.699251i	−0.989880	+	0.141906i	$0.954677\pi$
$692$	1.66756	−	0.803056i	0.0633912	−	0.0305276i
$693$	−2.48643	−	3.11788i	−0.0944515	−	0.118438i
$694$	−11.2198			−0.425899
$695$	−5.73125			−0.217399
$696$	11.4058	+	14.3024i	0.432336	+	0.542132i
$697$	5.70171	+	2.74580i	0.215968	+	0.104005i
$698$	0.0725480	−	0.0909724i	0.00274598	−	0.00344335i
$699$	−17.7995	−	8.57181i	−0.673241	−	0.324216i
$700$	5.32640	+	23.3365i	0.201319	+	0.882036i
$701$	18.8545	+	23.6428i	0.712125	+	0.892976i	0.997864	−	0.0653313i	$-0.0208104\pi$
$701$	18.8545	+	23.6428i	0.712125	+	0.892976i	−0.285739	+	0.958308i	$0.592239\pi$
$702$	1.94581	+	8.52516i	0.0734399	+	0.321761i
$703$	−8.59903	+	4.14108i	−0.324319	+	0.156184i
$704$	−11.9894	+	15.0342i	−0.451868	+	0.566624i
$705$	8.02930	−	10.0684i	0.302401	−	0.379199i
$706$	1.41478	−	6.19855i	0.0532459	−	0.233286i
$707$	34.3952	−	16.5639i	1.29357	−	0.622948i
$708$	−2.52446	−	1.21572i	−0.0948750	−	0.0456894i
$709$	0.0151970	−	0.0665824i	0.000570735	−	0.00250055i	−0.974642	−	0.223771i	$-0.928163\pi$
$709$	0.0151970	−	0.0665824i	0.000570735	−	0.00250055i	0.975212	+	0.221270i	$0.0710204\pi$
$710$	−1.31767	+	5.77308i	−0.0494512	+	0.216660i
$711$	1.74698	+	0.841301i	0.0655169	+	0.0315513i
$712$	21.5063	−	10.3569i	0.805984	−	0.388141i
$713$	−6.77873	+	29.6996i	−0.253866	+	1.11226i
$714$	1.35690	−	1.70149i	0.0507806	−	0.0636768i
$715$	−10.4879	+	13.1514i	−0.392226	+	0.491836i
$716$	15.8388	−	7.62755i	0.591923	−	0.285055i
$717$	−7.78717	−	34.1178i	−0.290817	−	1.27415i
$718$	−0.265766	−	0.333260i	−0.00991830	−	0.0124372i
$719$	−5.97339	−	26.1711i	−0.222770	−	0.976018i	−0.955382	−	0.295372i	$-0.904556\pi$
$719$	−5.97339	−	26.1711i	−0.222770	−	0.976018i	0.732613	−	0.680646i	$-0.238301\pi$
$720$	0.508729	+	0.244991i	0.0189592	+	0.00913028i
$721$	−8.33393	+	10.4504i	−0.310372	+	0.389194i
$722$	4.57942	+	2.20533i	0.170428	+	0.0820739i
$723$	−3.92543	−	4.92233i	−0.145988	−	0.183063i
$724$	−15.1196			−0.561916
$725$	26.1414			0.970866
$726$	8.52326	+	10.6878i	0.316328	+	0.396663i
$727$	7.03630	−	3.38851i	0.260962	−	0.125673i	−0.298829	−	0.954307i	$-0.596596\pi$
$727$	7.03630	−	3.38851i	0.260962	−	0.125673i	0.559791	+	0.828634i	$0.310882\pi$
$728$	−4.54676	+	19.9207i	−0.168514	+	0.738309i
$729$	−5.43535	−	23.8138i	−0.201309	−	0.881994i
$730$	4.44504			0.164518
$731$	5.83340	−	0.195429i	0.215756	−	0.00722822i
$732$	4.49396			0.166102
$733$	2.73609	+	11.9876i	0.101060	+	0.442773i	0.999989	+	0.00467846i	$0.00148920\pi$
$733$	2.73609	+	11.9876i	0.101060	+	0.442773i	−0.898929	+	0.438094i	$0.855654\pi$
$734$	−1.21930	+	5.34210i	−0.0450052	+	0.197181i
$735$	2.98911	−	1.43948i	0.110255	−	0.0530961i
$736$	−12.7180	−	15.9478i	−0.468791	−	0.587845i
$737$	35.5555			1.30971
$738$	0.781495			0.0287672
$739$	−2.44571	−	3.06682i	−0.0899667	−	0.112815i	0.734811	−	0.678272i	$-0.237271\pi$
$739$	−2.44571	−	3.06682i	−0.0899667	−	0.112815i	−0.824777	+	0.565458i	$0.808700\pi$
$740$	4.51357	+	2.17362i	0.165922	+	0.0799040i
$741$	−12.2506	+	15.3618i	−0.450038	+	0.564330i
$742$	−2.53146	−	1.21909i	−0.0929328	−	0.0447541i
$743$	5.01195	+	21.9588i	0.183871	+	0.805590i	0.979765	+	0.200154i	$0.0641441\pi$
$743$	5.01195	+	21.9588i	0.183871	+	0.805590i	−0.795894	+	0.605436i	$0.792999\pi$
$744$	13.2092	+	16.5639i	0.484274	+	0.607261i
$745$	−0.793209	−	3.47527i	−0.0290609	−	0.127324i
$746$	−4.39589	+	2.11695i	−0.160945	+	0.0775070i
$747$	1.13437	−	1.42246i	0.0415046	−	0.0520451i
$748$	5.29590	−	6.64084i	0.193637	−	0.242813i
$749$	0.436313	−	1.91161i	0.0159425	−	0.0698487i
$750$	−5.42154	+	2.61088i	−0.197967	+	0.0953358i
$751$	−2.33244	−	1.12324i	−0.0851118	−	0.0409877i	0.390844	−	0.920457i	$-0.372183\pi$
$751$	−2.33244	−	1.12324i	−0.0851118	−	0.0409877i	−0.475955	+	0.879469i	$0.657898\pi$
$752$	5.65346	−	24.7694i	0.206160	−	0.903248i
$753$	−0.501729	+	2.19822i	−0.0182840	+	0.0801075i
$754$	9.52888	+	4.58886i	0.347021	+	0.167117i
$755$	10.2606	−	4.94122i	0.373420	−	0.179829i
$756$	6.06465	−	26.5710i	0.220569	−	0.966376i
$757$	6.98978	−	8.76491i	0.254048	−	0.318566i	−0.638410	−	0.769696i	$-0.720408\pi$
$757$	6.98978	−	8.76491i	0.254048	−	0.318566i	0.892458	+	0.451130i	$0.148979\pi$
$758$	−3.08240	+	3.86521i	−0.111958	+	0.140391i
$759$	37.6933	−	18.1521i	1.36818	−	0.658880i
$760$	0.831241	+	3.64190i	0.0301523	+	0.132106i
$761$	−6.52260	−	8.17908i	−0.236444	−	0.296491i	0.649426	−	0.760425i	$-0.275009\pi$
$761$	−6.52260	−	8.17908i	−0.236444	−	0.296491i	−0.885870	+	0.463933i	$0.846438\pi$
$762$	−1.28794	−	5.64282i	−0.0466570	−	0.204418i
$763$	−5.15883	−	2.48436i	−0.186762	−	0.0899400i
$764$	15.3448	−	19.2418i	0.555156	−	0.696143i
$765$	−0.158834	−	0.0764902i	−0.00574264	−	0.00276551i
$766$	−2.20978	−	2.77097i	−0.0798424	−	0.100119i
$767$	−3.41789			−0.123413
$768$	4.32736			0.156150
$769$	−5.59150	−	7.01152i	−0.201635	−	0.252842i	0.670725	−	0.741706i	$-0.265983\pi$
$769$	−5.59150	−	7.01152i	−0.201635	−	0.252842i	−0.872360	+	0.488864i	$0.837411\pi$
$770$	−5.19202	+	2.50035i	−0.187107	+	0.0901062i
$771$	3.10388	−	13.5990i	0.111783	−	0.489755i
$772$	1.63922	+	7.18189i	0.0589968	+	0.258482i
$773$	46.0995			1.65808			0.829042	−	0.559187i	$-0.188887\pi$
$773$	46.0995			1.65808			0.829042	+	0.559187i	$0.188887\pi$
$774$	0.638555	−	0.334298i	0.0229524	−	0.0120161i
$775$	30.2747			1.08750
$776$	−3.53116	−	15.4710i	−0.126761	−	0.555378i
$777$	−4.23825	+	18.5690i	−0.152046	+	0.666159i
$778$	4.57284	−	2.20217i	0.163944	−	0.0789515i
$779$	−12.2040	−	15.3034i	−0.437255	−	0.548300i
$780$	10.3134			0.369277
$781$	−87.8684			−3.14418
$782$	1.08277	+	1.35775i	0.0387197	+	0.0485530i
$783$	−26.8170	−	12.9144i	−0.958362	−	0.461523i
$784$	4.08091	−	5.11730i	0.145747	−	0.182761i
$785$	−5.37747	−	2.58965i	−0.191930	−	0.0924287i
$786$	1.62953	+	7.13944i	0.0581234	+	0.254655i
$787$	18.2872	+	22.9314i	0.651867	+	0.817416i	0.992431	−	0.122806i	$-0.0391893\pi$
$787$	18.2872	+	22.9314i	0.651867	+	0.817416i	−0.340564	+	0.940221i	$0.610618\pi$
$788$	3.44116	+	15.0767i	0.122586	+	0.537085i
$789$	−2.07553	+	0.999524i	−0.0738909	+	0.0355840i
$790$	1.74698	−	2.19064i	0.0621547	−	0.0779396i
$791$	−24.0066	+	30.1034i	−0.853578	+	1.07035i
$792$	0.492467	−	2.15764i	0.0174991	−	0.0766684i
$793$	4.93900	−	2.37850i	0.175389	−	0.0844629i
$794$	3.81067	+	1.83512i	0.135236	+	0.0651260i
$795$	−0.665834	+	2.91721i	−0.0236147	+	0.103463i
$796$	−2.28932	+	10.0302i	−0.0811429	+	0.355510i
$797$	37.0758	+	17.8548i	1.31329	+	0.632449i	0.953728	−	0.300671i	$-0.0972107\pi$
$797$	37.0758	+	17.8548i	1.31329	+	0.632449i	0.359565	+	0.933120i	$0.382925\pi$
$798$	−6.06465	+	2.92058i	−0.214686	+	0.103387i
$799$	−1.76510	+	7.73342i	−0.0624448	+	0.273589i
$800$	−12.6392	+	15.8491i	−0.446864	+	0.560350i
$801$	2.17241	−	2.72411i	0.0767582	−	0.0962518i
$802$	−4.35690	+	2.09817i	−0.153847	+	0.0740890i
$803$	14.6773	+	64.3052i	0.517949	+	2.26928i
$804$	−13.5918	−	17.0436i	−0.479346	−	0.601080i
$805$	2.38524	+	10.4504i	0.0840686	+	0.368329i
$806$	11.0355	+	5.31443i	0.388710	+	0.187193i
$807$	28.5112	−	35.7519i	1.00364	−	1.25853i
$808$	19.0879	+	9.19225i	0.671510	+	0.323382i
$809$	21.8564	+	27.4070i	0.768429	+	0.963579i	0.999957	−	0.00924889i	$-0.00294405\pi$
$809$	21.8564	+	27.4070i	0.768429	+	0.963579i	−0.231528	+	0.972828i	$0.574373\pi$
$810$	3.45473			0.121387
$811$	27.4476			0.963814			0.481907	−	0.876222i	$-0.339944\pi$
$811$	27.4476			0.963814			0.481907	+	0.876222i	$0.339944\pi$
$812$	−20.5526	−	25.7721i	−0.721254	−	0.904423i
$813$	14.5320	−	6.99824i	0.509659	−	0.245439i
$814$	1.81820	−	7.96605i	0.0637279	−	0.279210i
$815$	−0.597302	−	2.61695i	−0.0209226	−	0.0916678i
$816$	−4.57242			−0.160067
$817$	−16.5181	−	7.28381i	−0.577896	−	0.254828i
$818$	−9.42327			−0.329477
$819$	0.663678	+	2.90776i	0.0231908	+	0.101605i
$820$	−2.28621	+	10.0165i	−0.0798379	+	0.349793i
$821$	8.95257	−	4.31133i	0.312447	−	0.150467i	−0.271088	−	0.962555i	$-0.587383\pi$
$821$	8.95257	−	4.31133i	0.312447	−	0.150467i	0.583535	+	0.812088i	$0.301669\pi$
$822$	−3.04623	−	3.81985i	−0.106249	−	0.133233i
$823$	3.46489			0.120779			0.0603893	−	0.998175i	$-0.480766\pi$
$823$	3.46489			0.120779			0.0603893	+	0.998175i	$0.480766\pi$
$824$	−7.41789			−0.258415
$825$	−25.9230	−	32.5065i	−0.902524	−	1.13173i
$826$	−1.05496	−	0.508041i	−0.0367067	−	0.0176770i
$827$	0.291421	−	0.365430i	0.0101337	−	0.0127073i	−0.776739	−	0.629823i	$-0.783127\pi$
$827$	0.291421	−	0.365430i	0.0101337	−	0.0127073i	0.786873	+	0.617116i	$0.211699\pi$
$828$	−1.75786	−	0.846543i	−0.0610900	−	0.0294194i
$829$	5.34883	+	23.4348i	0.185773	+	0.813923i	0.978813	+	0.204754i	$0.0656395\pi$
$829$	5.34883	+	23.4348i	0.185773	+	0.813923i	−0.793041	+	0.609168i	$0.791503\pi$
$830$	−1.63922	−	2.05552i	−0.0568981	−	0.0713480i
$831$	2.68545	+	11.7657i	0.0931572	+	0.408148i
$832$	12.9574	−	6.23996i	0.449218	−	0.216332i
$833$	−1.27413	+	1.59770i	−0.0441459	+	0.0553572i
$834$	3.57338	−	4.48087i	0.123736	−	0.155160i
$835$	−0.363469	+	1.59246i	−0.0125784	+	0.0551094i
$836$	−23.6700	+	11.3989i	−0.818645	+	0.394238i
$837$	−31.0572	−	14.9563i	−1.07349	−	0.516967i
$838$	3.17964	−	13.9309i	0.109839	−	0.481236i
$839$	−2.45742	+	10.7667i	−0.0848395	+	0.371706i	−0.999469	−	0.0325871i	$-0.989625\pi$
$839$	−2.45742	+	10.7667i	−0.0848395	+	0.371706i	0.914629	+	0.404293i	$0.132483\pi$
$840$	6.71648	+	3.23449i	0.231741	+	0.111600i
$841$	−6.30678	+	3.03719i	−0.217475	+	0.104731i
$842$	−1.50724	+	6.60364i	−0.0519428	+	0.227576i
$843$	−25.1286	+	31.5103i	−0.865476	+	1.08527i
$844$	21.5221	−	26.9878i	0.740820	−	0.928959i
$845$	1.94193	−	0.935182i	0.0668043	−	0.0321713i
$846$	0.217972	+	0.954998i	0.00749403	+	0.0328335i
$847$	−32.4049	−	40.6345i	−1.11345	−	1.39622i
$848$	1.31359	+	5.75522i	0.0451089	+	0.197635i
$849$	−47.4185	−	22.8355i	−1.62740	−	0.783714i
$850$	1.07606	−	1.34934i	0.0369087	−	0.0462821i
$851$	−13.6935	−	6.59445i	−0.469408	−	0.226055i
$852$	33.5894	+	42.1198i	1.15075	+	1.44300i
$853$	−47.2804			−1.61885			−0.809424	−	0.587224i	$-0.800221\pi$
$853$	−47.2804			−1.61885			−0.809424	+	0.587224i	$0.800221\pi$
$854$	1.87800			0.0642639
$855$	0.339970	+	0.426309i	0.0116267	+	0.0145795i
$856$	0.980386	−	0.472129i	0.0335089	−	0.0161370i
$857$	0.201710	−	0.883750i	0.00689029	−	0.0301883i	−0.971366	−	0.237588i	$-0.923643\pi$
$857$	0.201710	−	0.883750i	0.00689029	−	0.0301883i	0.978256	+	0.207400i	$0.0665002\pi$
$858$	−3.74309	−	16.3996i	−0.127787	−	0.559872i
$859$	−35.4486			−1.20949			−0.604746	−	0.796419i	$-0.706725\pi$
$859$	−35.4486			−1.20949			−0.604746	+	0.796419i	$0.706725\pi$
$860$	2.41670	+	9.16241i	0.0824087	+	0.312436i
$861$	−39.0616			−1.33122
$862$	−3.71187	−	16.2628i	−0.126427	−	0.553912i
$863$	2.30804	−	10.1122i	0.0785665	−	0.344222i	−0.920332	−	0.391137i	$-0.872082\pi$
$863$	2.30804	−	10.1122i	0.0785665	−	0.344222i	0.998899	+	0.0469149i	$0.0149389\pi$
$864$	20.7957	−	10.0147i	0.707483	−	0.340706i
$865$	−0.513574	−	0.644001i	−0.0174620	−	0.0218967i
$866$	10.2228			0.347385
$867$	−29.2054			−0.991866
$868$	−23.8022	−	29.8471i	−0.807900	−	1.01308i
$869$	37.4599	+	18.0397i	1.27074	+	0.611956i
$870$	2.40581	−	3.01679i	0.0815647	−	0.102279i
$871$	−23.9584	−	11.5377i	−0.811799	−	0.390942i
$872$	−0.707087	−	3.09795i	−0.0239450	−	0.104910i
$873$	−1.44421	−	1.81099i	−0.0488792	−	0.0612926i
$874$	−1.19524	−	5.23670i	−0.0404297	−	0.177134i
$875$	20.6124	−	9.92639i	0.696825	−	0.335573i
$876$	25.2141	−	31.6175i	0.851905	−	1.06826i
$877$	−4.61141	+	5.78252i	−0.155716	+	0.195262i	−0.853570	−	0.520978i	$-0.825567\pi$
$877$	−4.61141	+	5.78252i	−0.155716	+	0.195262i	0.697854	+	0.716240i	$0.254139\pi$
$878$	−0.144301	+	0.632222i	−0.00486991	+	0.0213365i
$879$	15.6799	−	7.55106i	0.528871	−	0.254691i
$880$	10.9085	+	5.25326i	0.367726	+	0.177087i
$881$	1.37406	−	6.02014i	0.0462932	−	0.202824i	−0.946493	−	0.322726i	$-0.895401\pi$
$881$	1.37406	−	6.02014i	0.0462932	−	0.202824i	0.992786	+	0.119902i	$0.0382580\pi$
$882$	−0.0561546	+	0.246029i	−0.00189082	+	0.00828424i
$883$	20.9199	+	10.0745i	0.704011	+	0.339034i	0.751404	−	0.659842i	$-0.229377\pi$
$883$	20.9199	+	10.0745i	0.704011	+	0.339034i	−0.0473927	+	0.998876i	$0.515091\pi$
$884$	−5.72348	+	2.75628i	−0.192501	+	0.0927038i
$885$	−0.277479	+	1.21572i	−0.00932736	+	0.0408658i
$886$	−5.81402	+	7.29055i	−0.195326	+	0.244931i
$887$	−8.81850	+	11.0580i	−0.296096	+	0.371293i	−0.907519	−	0.420011i	$-0.862026\pi$
$887$	−8.81850	+	11.0580i	−0.296096	+	0.371293i	0.611423	+	0.791304i	$0.290598\pi$
$888$	−9.52326	+	4.58616i	−0.319580	+	0.153901i
$889$	4.89666	+	21.4537i	0.164229	+	0.719533i
$890$	−3.13922	−	3.93646i	−0.105227	−	0.131950i
$891$	11.4073	+	49.9787i	0.382159	+	1.67435i
$892$	0.167563	+	0.0806940i	0.00561042	+	0.00270183i
$893$	15.2970	−	19.1819i	0.511895	−	0.641896i
$894$	3.21164	+	1.54664i	0.107413	+	0.0517275i
$895$	−4.87800	−	6.11682i	−0.163054	−	0.204463i
$896$	33.2989			1.11244
$897$	−31.2892			−1.04472
$898$	2.42476	+	3.04056i	0.0809154	+	0.101465i
$899$	−37.5633	+	18.0895i	−1.25281	+	0.603320i
$900$	−0.431468	+	1.89039i	−0.0143823	+	0.0630129i
$901$	−0.410125	−	1.79688i	−0.0136632	−	0.0598626i
$902$	16.7573			0.557958
$903$	−31.9170	+	16.7093i	−1.06213	+	0.556050i
$904$	−21.3679			−0.710686
$905$	1.49731	+	6.56015i	0.0497723	+	0.218067i
$906$	−2.53415	+	11.1028i	−0.0841914	+	0.368867i
$907$	34.5170	−	16.6225i	1.14612	−	0.551941i	0.238252	−	0.971203i	$-0.423425\pi$
$907$	34.5170	−	16.6225i	1.14612	−	0.551941i	0.907865	+	0.419262i	$0.137711\pi$
$908$	−15.0036	−	18.8140i	−0.497914	−	0.624364i
$909$	3.09246			0.102570
$910$	4.30990			0.142872
$911$	3.42878	+	4.29955i	0.113601	+	0.142451i	0.835381	−	0.549672i	$-0.185247\pi$
$911$	3.42878	+	4.29955i	0.113601	+	0.142451i	−0.721780	+	0.692122i	$0.756676\pi$
$912$	12.7419	+	6.13617i	0.421926	+	0.203189i
$913$	24.3240	−	30.5013i	0.805007	−	1.00945i
$914$	−12.6988	−	6.11541i	−0.420038	−	0.202280i
$915$	−0.445042	−	1.94986i	−0.0147126	−	0.0644602i
$916$	31.8925	+	39.9920i	1.05376	+	1.32137i
$917$	−6.19537	−	27.1437i	−0.204589	−	0.896364i
$918$	−1.77048	+	0.852618i	−0.0584345	+	0.0281406i
$919$	−28.8139	+	36.1315i	−0.950484	+	1.19187i	0.0308429	+	0.999524i	$0.490181\pi$
$919$	−28.8139	+	36.1315i	−0.950484	+	1.19187i	−0.981327	+	0.192345i	$0.938391\pi$
$920$	−3.70895	+	4.65087i	−0.122280	+	0.153335i
$921$	5.20679	−	22.8124i	0.171570	−	0.751696i
$922$	−13.6228	+	6.56041i	−0.448644	+	0.216056i
$923$	59.2083	+	28.5132i	1.94887	+	0.938525i
$924$	−11.6664	+	51.1137i	−0.383795	+	1.68152i
$925$	−3.36108	+	14.7258i	−0.110512	+	0.484183i
$926$	2.56638	+	1.23590i	0.0843363	+	0.0406142i
$927$	−0.975541	+	0.469796i	−0.0320410	+	0.0154301i
$928$	6.21206	−	27.2168i	0.203921	−	0.893436i
$929$	37.4490	−	46.9595i	1.22866	−	1.54069i	0.480813	−	0.876823i	$-0.340342\pi$
$929$	37.4490	−	46.9595i	1.22866	−	1.54069i	0.747849	−	0.663869i	$-0.231087\pi$
$930$	2.78621	−	3.49379i	0.0913634	−	0.114566i
$931$	5.69471	−	2.74243i	0.186637	−	0.0898794i
$932$	4.39612	+	19.2607i	0.144000	+	0.630905i
$933$	−6.64795	−	8.33626i	−0.217644	−	0.272917i
$934$	4.05539	+	17.7678i	0.132696	+	0.581380i
$935$	−3.40581	−	1.64015i	−0.111382	−	0.0536387i
$936$	−1.03199	+	1.29408i	−0.0337317	+	0.0422982i
$937$	29.1325	+	14.0295i	0.951718	+	0.458323i	0.844288	−	0.535890i	$-0.180024\pi$
$937$	29.1325	+	14.0295i	0.951718	+	0.458323i	0.107430	+	0.994213i	$0.465738\pi$
$938$	−5.67994	−	7.12242i	−0.185457	−	0.232555i
$939$	37.0616			1.20946
$940$	−12.8780			−0.420034
$941$	−17.3549	−	21.7623i	−0.565753	−	0.709431i	0.413857	−	0.910342i	$-0.364181\pi$
$941$	−17.3549	−	21.7623i	−0.565753	−	0.709431i	−0.979610	+	0.200911i	$0.935610\pi$
$942$	5.37747	−	2.58965i	0.175207	−	0.0843755i
$943$	6.93602	−	30.3887i	0.225868	−	0.989591i
$944$	0.547425	+	2.39843i	0.0178172	+	0.0780622i
$945$	−12.1293			−0.394566
$946$	13.6923	−	7.16824i	0.445176	−	0.233060i
$947$	−32.2707			−1.04866			−0.524328	−	0.851516i	$-0.675683\pi$
$947$	−32.2707			−1.04866			−0.524328	+	0.851516i	$0.675683\pi$
$948$	−5.67241	−	24.8524i	−0.184231	−	0.807170i
$949$	10.9770	−	48.0935i	0.356330	−	1.56118i
$950$	−4.80947	+	2.31612i	−0.156040	+	0.0751448i
$951$	20.6298	+	25.8690i	0.668968	+	0.838859i
$952$	−4.59179			−0.148821
$953$	15.0032			0.486003			0.243001	−	0.970026i	$-0.421868\pi$
$953$	15.0032			0.486003			0.243001	+	0.970026i	$0.421868\pi$
$954$	−0.141908	−	0.177947i	−0.00459443	−	0.00576123i
$955$	−9.86831	−	4.75233i	−0.319331	−	0.153782i
$956$	−21.8192	+	27.3604i	−0.705682	+	0.884897i
$957$	51.5870	+	24.8430i	1.66757	+	0.803060i
$958$	1.96572	+	8.61239i	0.0635096	+	0.278254i
$959$	11.5816	+	14.5228i	0.373988	+	0.468967i
$960$	−1.16756	−	5.11543i	−0.0376829	−	0.165100i
$961$	−15.5726	+	7.49937i	−0.502342	+	0.241915i
$962$	−3.81013	+	4.77776i	−0.122844	+	0.154041i
$963$	0.0990311	−	0.124181i	0.00319123	−	0.00400168i
$964$	−1.40097	+	6.13805i	−0.0451222	+	0.197693i
$965$	2.95377	−	1.42246i	0.0950853	−	0.0457906i
$966$	−9.65764	−	4.65087i	−0.310729	−	0.149639i
$967$	5.57822	−	24.4398i	0.179383	−	0.785930i	−0.802532	−	0.596609i	$-0.796514\pi$
$967$	5.57822	−	24.4398i	0.179383	−	0.785930i	0.981915	−	0.189321i	$-0.0606287\pi$
$968$	6.41819	−	28.1199i	0.206288	−	0.903809i
$969$	−3.97823	−	1.91581i	−0.127799	−	0.0615448i
$970$	−3.01573	+	1.45230i	−0.0968292	+	0.0466305i
$971$	−0.609252	+	2.66931i	−0.0195518	+	0.0856622i	−0.983763	−	0.179475i	$-0.942560\pi$
$971$	−0.609252	+	2.66931i	−0.0195518	+	0.0856622i	0.964211	+	0.265137i	$0.0854172\pi$
$972$	2.87651	−	3.60703i	0.0922641	−	0.115696i
$973$	−13.5858	+	17.0360i	−0.435539	+	0.546149i
$974$	5.77144	−	2.77938i	0.184929	−	0.0890570i
$975$	6.91939	+	30.3158i	0.221598	+	0.970883i
$976$	−2.46011	−	3.08488i	−0.0787461	−	0.0987445i
$977$	3.87986	+	16.9988i	0.124128	+	0.543839i	0.998303	+	0.0582292i	$0.0185454\pi$
$977$	3.87986	+	16.9988i	0.124128	+	0.543839i	−0.874175	+	0.485610i	$0.838597\pi$
$978$	2.41843	+	1.16465i	0.0773328	+	0.0372415i
$979$	46.5822	−	58.4122i	1.48877	−	1.86686i
$980$	−2.98911	−	1.43948i	−0.0954838	−	0.0459826i
$981$	−0.289192	−	0.362636i	−0.00923320	−	0.0115781i
$982$	−17.1027			−0.545770
$983$	−51.2747			−1.63541			−0.817705	−	0.575638i	$-0.804754\pi$
$983$	−51.2747			−1.63541			−0.817705	+	0.575638i	$0.804754\pi$
$984$	−13.5157	−	16.9482i	−0.430866	−	0.540289i
$985$	6.20075	−	2.98612i	0.197572	−	0.0951458i
$986$	−0.528876	+	2.31716i	−0.0168428	+	0.0737933i
$987$	−10.8949	−	47.7338i	−0.346789	−	1.51938i
$988$	19.6485			0.625101
$989$	−7.33190	−	27.7974i	−0.233141	−	0.883906i
$990$	−0.466812			−0.0148363
$991$	10.1175	+	44.3277i	0.321393	+	1.40812i	0.835076	+	0.550135i	$0.185424\pi$
$991$	10.1175	+	44.3277i	0.321393	+	1.40812i	−0.513682	+	0.857980i	$0.671719\pi$
$992$	7.19428	−	31.5202i	0.228419	−	1.00077i
$993$	−2.67629	+	1.28883i	−0.0849296	+	0.0408999i
$994$	14.0368	+	17.6016i	0.445221	+	0.558290i
$995$	4.57865			0.145153
$996$	−23.9191			−0.757907
$997$	32.5386	+	40.8021i	1.03051	+	1.29222i	0.955486	+	0.295035i	$0.0953313\pi$
$997$	32.5386	+	40.8021i	1.03051	+	1.29222i	0.0750221	+	0.997182i	$0.476097\pi$
$998$	8.46777	+	4.07786i	0.268043	+	0.129083i
$999$	10.7228	−	13.4460i	0.339255	−	0.425412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.e.a.16.1	✓	6
3.2	odd	2		387.2.u.c.145.1		6
4.3	odd	2		688.2.u.b.145.1		6
43.11	even	7		1849.2.a.k.1.2		3
43.32	odd	14		1849.2.a.j.1.2		3
43.35	even	7	inner	43.2.e.a.35.1	yes	6
129.35	odd	14		387.2.u.c.379.1		6
172.35	odd	14		688.2.u.b.465.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.e.a.16.1	✓	6	1.1	even	1	trivial
43.2.e.a.35.1	yes	6	43.35	even	7	inner
387.2.u.c.145.1		6	3.2	odd	2
387.2.u.c.379.1		6	129.35	odd	14
688.2.u.b.145.1		6	4.3	odd	2
688.2.u.b.465.1		6	172.35	odd	14
1849.2.a.j.1.2		3	43.32	odd	14
1849.2.a.k.1.2		3	43.11	even	7

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)

\(f(q)\)	\(=\)	\(q+(-0.0990311 - 0.433884i) q^{2} +(-0.400969 + 1.75676i) q^{3} +(1.62349 - 0.781831i) q^{4} +(-0.500000 - 0.626980i) q^{5} +0.801938 q^{6} -3.04892 q^{7} +(-1.05496 - 1.32288i) q^{8} +(-0.222521 - 0.107160i) q^{9} +O(q^{10})\)	\(q+(-0.0990311 - 0.433884i) q^{2} +(-0.400969 + 1.75676i) q^{3} +(1.62349 - 0.781831i) q^{4} +(-0.500000 - 0.626980i) q^{5} +0.801938 q^{6} -3.04892 q^{7} +(-1.05496 - 1.32288i) q^{8} +(-0.222521 - 0.107160i) q^{9} +(-0.222521 + 0.279032i) q^{10} +(-4.77144 - 2.29780i) q^{11} +(0.722521 + 3.16557i) q^{12} +(2.46950 + 3.09666i) q^{13} +(0.301938 + 1.32288i) q^{14} +(1.30194 - 0.626980i) q^{15} +(1.77748 - 2.22889i) q^{16} +(-0.554958 + 0.695895i) q^{17} +(-0.0244587 + 0.107160i) q^{18} +(2.48039 - 1.19449i) q^{19} +(-1.30194 - 0.626980i) q^{20} +(1.22252 - 5.35621i) q^{21} +(-0.524459 + 2.29780i) q^{22} +(3.94989 + 1.90216i) q^{23} +(2.74698 - 1.32288i) q^{24} +(0.969501 - 4.24766i) q^{25} +(1.09903 - 1.37814i) q^{26} +(-3.09299 + 3.87849i) q^{27} +(-4.94989 + 2.38374i) q^{28} +(1.33513 + 5.84957i) q^{29} +(-0.400969 - 0.502799i) q^{30} +(1.54623 + 6.77447i) q^{31} +(-4.19202 - 2.01877i) q^{32} +(5.94989 - 7.46092i) q^{33} +(0.356896 + 0.171872i) q^{34} +(1.52446 + 1.91161i) q^{35} -0.445042 q^{36} -3.46681 q^{37} +(-0.763906 - 0.957907i) q^{38} +(-6.43027 + 3.09666i) q^{39} +(-0.301938 + 1.32288i) q^{40} +(-1.58211 - 6.93166i) q^{41} -2.44504 q^{42} +(-4.25786 - 4.98704i) q^{43} -9.54288 q^{44} +(0.0440730 + 0.193096i) q^{45} +(0.434157 - 1.90216i) q^{46} +(8.02930 - 3.86671i) q^{47} +(3.20291 + 4.01632i) q^{48} +2.29590 q^{49} -1.93900 q^{50} +(-1.00000 - 1.25396i) q^{51} +(6.43027 + 3.09666i) q^{52} +(-1.29105 + 1.61893i) q^{53} +(1.98911 + 0.957907i) q^{54} +(0.945042 + 4.14050i) q^{55} +(3.21648 + 4.03334i) q^{56} +(1.10388 + 4.83639i) q^{57} +(2.40581 - 1.15858i) q^{58} +(-0.538032 + 0.674671i) q^{59} +(1.62349 - 2.03579i) q^{60} +(0.307979 - 1.34934i) q^{61} +(2.78621 - 1.34177i) q^{62} +(0.678448 + 0.326723i) q^{63} +(0.807979 - 3.53999i) q^{64} +(0.706791 - 3.09666i) q^{65} +(-3.82640 - 1.84270i) q^{66} +(-6.04892 + 2.91301i) q^{67} +(-0.356896 + 1.56366i) q^{68} +(-4.92543 + 6.17629i) q^{69} +(0.678448 - 0.850747i) q^{70} +(14.9487 - 7.19891i) q^{71} +(0.0929903 + 0.407417i) q^{72} +(-7.76540 - 9.73750i) q^{73} +(0.343322 + 1.50419i) q^{74} +(7.07338 + 3.40636i) q^{75} +(3.09299 - 3.87849i) q^{76} +(14.5477 + 7.00581i) q^{77} +(1.98039 + 2.48333i) q^{78} -7.85086 q^{79} -2.28621 q^{80} +(-6.03534 - 7.56808i) q^{81} +(-2.85086 + 1.37290i) q^{82} +(-1.63922 + 7.18189i) q^{83} +(-2.20291 - 9.65156i) q^{84} +0.713792 q^{85} +(-1.74214 + 2.34129i) q^{86} -10.8116 q^{87} +(1.99396 + 8.73611i) q^{88} +(-3.13922 + 13.7538i) q^{89} +(0.0794168 - 0.0382451i) q^{90} +(-7.52930 - 9.44145i) q^{91} +7.89977 q^{92} -12.5211 q^{93} +(-2.47285 - 3.10086i) q^{94} +(-1.98911 - 0.957907i) q^{95} +(5.22737 - 6.55491i) q^{96} +(8.44989 + 4.06925i) q^{97} +(-0.227365 - 0.996152i) q^{98} +(0.815511 + 1.02262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 5 q^{2} + 2 q^{3} + 5 q^{4} - 3 q^{5} - 4 q^{6} - 7 q^{8} - q^{9}+O(q^{10}) \) 6 * q - 5 * q^2 + 2 * q^3 + 5 * q^4 - 3 * q^5 - 4 * q^6 - 7 * q^8 - q^9	\( 6 q - 5 q^{2} + 2 q^{3} + 5 q^{4} - 3 q^{5} - 4 q^{6} - 7 q^{8} - q^{9} - q^{10} - 10 q^{11} + 4 q^{12} + 5 q^{13} - 7 q^{14} - q^{15} + 11 q^{16} - 4 q^{17} + 9 q^{18} + 2 q^{19} + q^{20} + 7 q^{21} + 6 q^{22} + q^{23} + 7 q^{24} - 4 q^{25} + 11 q^{26} - 4 q^{27} - 7 q^{28} + 6 q^{29} + 2 q^{30} - 6 q^{31} - 15 q^{32} + 13 q^{33} - 6 q^{34} - 2 q^{36} - 14 q^{37} - 11 q^{38} - 3 q^{39} + 7 q^{40} + 2 q^{41} - 14 q^{42} - 13 q^{43} - 20 q^{44} + 4 q^{45} + 5 q^{46} + 17 q^{47} + 6 q^{48} - 14 q^{49} + 8 q^{50} - 6 q^{51} + 3 q^{52} - 2 q^{53} + 15 q^{54} + 5 q^{55} - 11 q^{57} - 12 q^{58} + 12 q^{59} + 5 q^{60} + 12 q^{61} + 33 q^{62} + 15 q^{64} + 29 q^{65} - 5 q^{66} - 18 q^{67} + 6 q^{68} - 16 q^{69} + 26 q^{71} - 14 q^{72} - 9 q^{73} + 15 q^{75} + 4 q^{76} + 28 q^{77} - q^{78} - 20 q^{79} - 30 q^{80} - 24 q^{81} + 10 q^{82} + 20 q^{83} - 12 q^{85} - 23 q^{86} - 12 q^{87} - 7 q^{88} + 11 q^{89} - 8 q^{90} - 14 q^{91} + 2 q^{92} - 44 q^{93} - 27 q^{94} - 15 q^{95} + 9 q^{96} + 28 q^{97} + 21 q^{98} - 10 q^{99}+O(q^{100}) \) 6 * q - 5 * q^2 + 2 * q^3 + 5 * q^4 - 3 * q^5 - 4 * q^6 - 7 * q^8 - q^9 - q^10 - 10 * q^11 + 4 * q^12 + 5 * q^13 - 7 * q^14 - q^15 + 11 * q^16 - 4 * q^17 + 9 * q^18 + 2 * q^19 + q^20 + 7 * q^21 + 6 * q^22 + q^23 + 7 * q^24 - 4 * q^25 + 11 * q^26 - 4 * q^27 - 7 * q^28 + 6 * q^29 + 2 * q^30 - 6 * q^31 - 15 * q^32 + 13 * q^33 - 6 * q^34 - 2 * q^36 - 14 * q^37 - 11 * q^38 - 3 * q^39 + 7 * q^40 + 2 * q^41 - 14 * q^42 - 13 * q^43 - 20 * q^44 + 4 * q^45 + 5 * q^46 + 17 * q^47 + 6 * q^48 - 14 * q^49 + 8 * q^50 - 6 * q^51 + 3 * q^52 - 2 * q^53 + 15 * q^54 + 5 * q^55 - 11 * q^57 - 12 * q^58 + 12 * q^59 + 5 * q^60 + 12 * q^61 + 33 * q^62 + 15 * q^64 + 29 * q^65 - 5 * q^66 - 18 * q^67 + 6 * q^68 - 16 * q^69 + 26 * q^71 - 14 * q^72 - 9 * q^73 + 15 * q^75 + 4 * q^76 + 28 * q^77 - q^78 - 20 * q^79 - 30 * q^80 - 24 * q^81 + 10 * q^82 + 20 * q^83 - 12 * q^85 - 23 * q^86 - 12 * q^87 - 7 * q^88 + 11 * q^89 - 8 * q^90 - 14 * q^91 + 2 * q^92 - 44 * q^93 - 27 * q^94 - 15 * q^95 + 9 * q^96 + 28 * q^97 + 21 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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