LMFDB - Embedded newform 725.2.r.b.74.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(24,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 4]))

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

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

chi := DirichletCharacter("725.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.r (of order $14$, degree $6$, not 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:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	$\Q(\zeta_{28})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			74.1
Root			$-0.433884 - 0.900969i$ of defining polynomial
Character	$\chi$	$=$	725.74
Dual form			725.2.r.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.193096 + 0.400969i) q^{2} +(0.974928 + 0.777479i) q^{3} +(1.12349 + 1.40881i) q^{4} +(-0.500000 + 0.240787i) q^{6} +(0.279032 + 0.222521i) q^{7} +(-1.64960 + 0.376510i) q^{8} +(-0.321552 - 1.40881i) q^{9} +O(q^{10})$	\(q+(-0.193096 + 0.400969i) q^{2} +(0.974928 + 0.777479i) q^{3} +(1.12349 + 1.40881i) q^{4} +(-0.500000 + 0.240787i) q^{6} +(0.279032 + 0.222521i) q^{7} +(-1.64960 + 0.376510i) q^{8} +(-0.321552 - 1.40881i) q^{9} +(-1.09903 + 4.81517i) q^{11} +2.24698i q^{12} +(-5.51107 - 1.25786i) q^{13} +(-0.143104 + 0.0689153i) q^{14} +(-0.634375 + 2.77938i) q^{16} +4.49396i q^{17} +(0.626980 + 0.143104i) q^{18} +(1.46950 + 1.84270i) q^{19} +(0.0990311 + 0.433884i) q^{21} +(-1.71851 - 1.37047i) q^{22} +(0.996152 + 2.06853i) q^{23} +(-1.90097 - 0.915458i) q^{24} +(1.56853 - 1.96688i) q^{26} +(2.40496 - 4.99396i) q^{27} +0.643104i q^{28} +(5.09783 + 1.73553i) q^{29} +(6.02930 + 2.90356i) q^{31} +(-3.63770 - 2.90097i) q^{32} +(-4.81517 + 3.83997i) q^{33} +(-1.80194 - 0.867767i) q^{34} +(1.62349 - 2.03579i) q^{36} +(-4.81517 + 1.09903i) q^{37} +(-1.02262 + 0.233406i) q^{38} +(-4.39493 - 5.51107i) q^{39} +3.10992 q^{41} +(-0.193096 - 0.0440730i) q^{42} +(-1.47773 - 3.06853i) q^{43} +(-8.01842 + 3.86147i) q^{44} -1.02177 q^{46} +(6.28345 + 1.43416i) q^{47} +(-2.77938 + 2.21648i) q^{48} +(-1.52930 - 6.70031i) q^{49} +(-3.49396 + 4.38129i) q^{51} +(-4.41953 - 9.17725i) q^{52} +(2.03579 - 4.22737i) q^{53} +(1.53803 + 1.92863i) q^{54} +(-0.544073 - 0.262012i) q^{56} +2.93900i q^{57} +(-1.68027 + 1.70895i) q^{58} +12.4940 q^{59} +(-1.02446 + 1.28463i) q^{61} +(-2.32847 + 1.85690i) q^{62} +(0.223767 - 0.464656i) q^{63} +(-3.27144 + 1.57544i) q^{64} +(-0.609916 - 2.67222i) q^{66} +(-2.26480 + 0.516926i) q^{67} +(-6.33114 + 5.04892i) q^{68} +(-0.637063 + 2.79116i) q^{69} +(1.63222 - 7.15122i) q^{71} +(1.06086 + 2.20291i) q^{72} +(2.44088 + 5.06853i) q^{73} +(0.489115 - 2.14295i) q^{74} +(-0.945042 + 4.14050i) q^{76} +(-1.37814 + 1.09903i) q^{77} +(3.05841 - 0.698062i) q^{78} +(-1.03803 - 4.54792i) q^{79} +(2.32155 - 1.11800i) q^{81} +(-0.600514 + 1.24698i) q^{82} +(3.48285 - 2.77748i) q^{83} +(-0.500000 + 0.626980i) q^{84} +1.51573 q^{86} +(3.62068 + 5.65548i) q^{87} -8.35690i q^{88} +(-5.11745 - 2.46443i) q^{89} +(-1.25786 - 1.57731i) q^{91} +(-1.79500 + 3.72737i) q^{92} +(3.62068 + 7.51842i) q^{93} +(-1.78836 + 2.24254i) q^{94} +(-1.29105 - 5.65647i) q^{96} +(0.141202 - 0.112605i) q^{97} +(2.98192 + 0.680604i) q^{98} +7.13706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 6 q^{6} - 12 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 - 6 * q^6 - 12 * q^9	$ 12 q + 4 q^{4} - 6 q^{6} - 12 q^{9} - 22 q^{11} - 18 q^{14} + 8 q^{16} - 2 q^{19} + 10 q^{21} - 14 q^{24} + 8 q^{26} - 12 q^{29} + 10 q^{31} - 4 q^{34} + 10 q^{36} - 6 q^{39} + 40 q^{41} - 40 q^{44} + 44 q^{49} - 4 q^{51} - 12 q^{54} - 14 q^{56} + 112 q^{59} + 6 q^{61} - 2 q^{64} - 10 q^{66} + 14 q^{69} + 42 q^{71} + 12 q^{74} - 10 q^{76} + 18 q^{79} + 36 q^{81} - 6 q^{84} - 32 q^{86} - 14 q^{89} + 10 q^{91} - 16 q^{94} - 4 q^{96} + 64 q^{99}+O(q^{100}) $ 12 * q + 4 * q^4 - 6 * q^6 - 12 * q^9 - 22 * q^11 - 18 * q^14 + 8 * q^16 - 2 * q^19 + 10 * q^21 - 14 * q^24 + 8 * q^26 - 12 * q^29 + 10 * q^31 - 4 * q^34 + 10 * q^36 - 6 * q^39 + 40 * q^41 - 40 * q^44 + 44 * q^49 - 4 * q^51 - 12 * q^54 - 14 * q^56 + 112 * q^59 + 6 * q^61 - 2 * q^64 - 10 * q^66 + 14 * q^69 + 42 * q^71 + 12 * q^74 - 10 * q^76 + 18 * q^79 + 36 * q^81 - 6 * q^84 - 32 * q^86 - 14 * q^89 + 10 * q^91 - 16 * q^94 - 4 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.193096	+	0.400969i	−0.136540	+	0.283528i	−0.958016	−	0.286715i	$-0.907437\pi$
$2$	−0.193096	+	0.400969i	−0.136540	+	0.283528i	0.821476	+	0.570243i	$0.193151\pi$
$3$	0.974928	+	0.777479i	0.562875	+	0.448878i	0.863130	−	0.504981i	$-0.168501\pi$
$3$	0.974928	+	0.777479i	0.562875	+	0.448878i	−0.300256	+	0.953859i	$0.597072\pi$
$4$	1.12349	+	1.40881i	0.561745	+	0.704406i
$5$		0			0
$5$		0			0
$6$	−0.500000	+	0.240787i	−0.204124	+	0.0983010i
$7$	0.279032	+	0.222521i	0.105464	+	0.0841050i	0.674802	−	0.737999i	$-0.264229\pi$
$7$	0.279032	+	0.222521i	0.105464	+	0.0841050i	−0.569338	+	0.822104i	$0.692800\pi$
$8$	−1.64960	+	0.376510i	−0.583221	+	0.133116i
$9$	−0.321552	−	1.40881i	−0.107184	−	0.469604i
$10$		0			0
$11$	−1.09903	+	4.81517i	−0.331370	+	1.45183i	0.485109	+	0.874454i	$0.338780\pi$
$11$	−1.09903	+	4.81517i	−0.331370	+	1.45183i	−0.816479	+	0.577375i	$0.804077\pi$
$12$			2.24698i			0.648647i
$13$	−5.51107	−	1.25786i	−1.52849	−	0.348869i	−0.626087	−	0.779753i	$-0.715345\pi$
$13$	−5.51107	−	1.25786i	−1.52849	−	0.348869i	−0.902407	+	0.430884i	$0.858202\pi$
$14$	−0.143104	+	0.0689153i	−0.0382462	+	0.0184184i
$15$		0			0
$16$	−0.634375	+	2.77938i	−0.158594	+	0.694845i
$17$			4.49396i			1.08995i	0.838454	+	0.544973i	$0.183460\pi$
$17$			4.49396i			1.08995i	−0.838454	+	0.544973i	$0.816540\pi$
$18$	0.626980	+	0.143104i	0.147781	+	0.0337300i
$19$	1.46950	+	1.84270i	0.337127	+	0.422743i	0.921280	−	0.388900i	$-0.127145\pi$
$19$	1.46950	+	1.84270i	0.337127	+	0.422743i	−0.584153	+	0.811643i	$0.698573\pi$
$20$		0			0
$21$	0.0990311	+	0.433884i	0.0216104	+	0.0946812i
$22$	−1.71851	−	1.37047i	−0.366388	−	0.292185i
$23$	0.996152	+	2.06853i	0.207712	+	0.431319i	0.978634	−	0.205611i	$-0.0659183\pi$
$23$	0.996152	+	2.06853i	0.207712	+	0.431319i	−0.770922	+	0.636930i	$0.780204\pi$
$24$	−1.90097	−	0.915458i	−0.388034	−	0.186867i
$25$		0			0
$26$	1.56853	−	1.96688i	0.307614	−	0.385736i
$27$	2.40496	−	4.99396i	0.462836	−	0.961088i
$28$			0.643104i			0.121535i
$29$	5.09783	+	1.73553i	0.946644	+	0.322281i
$29$	5.09783	+	1.73553i	0.946644	+	0.322281i
$30$		0			0
$31$	6.02930	+	2.90356i	1.08289	+	0.521495i	0.888241	−	0.459377i	$-0.151927\pi$
$31$	6.02930	+	2.90356i	1.08289	+	0.521495i	0.194654	+	0.980872i	$0.437642\pi$
$32$	−3.63770	−	2.90097i	−0.643061	−	0.512824i
$33$	−4.81517	+	3.83997i	−0.838214	+	0.668453i
$34$	−1.80194	−	0.867767i	−0.309030	−	0.148821i
$35$		0			0
$36$	1.62349	−	2.03579i	0.270582	−	0.339299i
$37$	−4.81517	+	1.09903i	−0.791609	+	0.180680i	−0.599162	−	0.800628i	$-0.704499\pi$
$37$	−4.81517	+	1.09903i	−0.791609	+	0.180680i	−0.192447	+	0.981307i	$0.561642\pi$
$38$	−1.02262	+	0.233406i	−0.165891	+	0.0378635i
$39$	−4.39493	−	5.51107i	−0.703752	−	0.882477i
$40$		0			0
$41$	3.10992			0.485687			0.242844	−	0.970065i	$-0.421920\pi$
$41$	3.10992			0.485687			0.242844	+	0.970065i	$0.421920\pi$
$42$	−0.193096	−	0.0440730i	−0.0297954	−	0.00680061i
$43$	−1.47773	−	3.06853i	−0.225351	−	0.467947i	0.757383	−	0.652971i	$-0.226478\pi$
$43$	−1.47773	−	3.06853i	−0.225351	−	0.467947i	−0.982734	+	0.185025i	$0.940764\pi$
$44$	−8.01842	+	3.86147i	−1.20882	+	0.582138i
$45$		0			0
$46$	−1.02177			−0.150652
$47$	6.28345	+	1.43416i	0.916536	+	0.209193i	0.654673	−	0.755912i	$-0.272806\pi$
$47$	6.28345	+	1.43416i	0.916536	+	0.209193i	0.261862	+	0.965105i	$0.415663\pi$
$48$	−2.77938	+	2.21648i	−0.401169	+	0.319921i
$49$	−1.52930	−	6.70031i	−0.218472	−	0.957188i
$50$		0			0
$51$	−3.49396	+	4.38129i	−0.489252	+	0.613503i
$52$	−4.41953	−	9.17725i	−0.612879	−	1.27266i
$53$	2.03579	−	4.22737i	0.279638	−	0.580673i	−0.713088	−	0.701075i	$-0.752704\pi$
$53$	2.03579	−	4.22737i	0.279638	−	0.580673i	0.992725	+	0.120401i	$0.0384182\pi$
$54$	1.53803	+	1.92863i	0.209300	+	0.262453i
$55$		0			0
$56$	−0.544073	−	0.262012i	−0.0727048	−	0.0350128i
$57$			2.93900i			0.389280i
$58$	−1.68027	+	1.70895i	−0.220630	+	0.224396i
$59$	12.4940			1.62657			0.813287	−	0.581862i	$-0.197676\pi$
$59$	12.4940			1.62657			0.813287	+	0.581862i	$0.197676\pi$
$60$		0			0
$61$	−1.02446	+	1.28463i	−0.131168	+	0.164480i	−0.843078	−	0.537791i	$-0.819259\pi$
$61$	−1.02446	+	1.28463i	−0.131168	+	0.164480i	0.711910	+	0.702271i	$0.247830\pi$
$62$	−2.32847	+	1.85690i	−0.295716	+	0.235826i
$63$	0.223767	−	0.464656i	0.0281919	−	0.0585412i
$64$	−3.27144	+	1.57544i	−0.408930	+	0.196930i
$65$		0			0
$66$	−0.609916	−	2.67222i	−0.0750755	−	0.328927i
$67$	−2.26480	+	0.516926i	−0.276689	+	0.0631526i	−0.358614	−	0.933486i	$-0.616751\pi$
$67$	−2.26480	+	0.516926i	−0.276689	+	0.0631526i	0.0819245	+	0.996639i	$0.473893\pi$
$68$	−6.33114	+	5.04892i	−0.767764	+	0.612271i
$69$	−0.637063	+	2.79116i	−0.0766934	+	0.336016i
$70$		0			0
$71$	1.63222	−	7.15122i	0.193709	−	0.848694i	−0.780878	−	0.624683i	$-0.785228\pi$
$71$	1.63222	−	7.15122i	0.193709	−	0.848694i	0.974587	−	0.224010i	$-0.0719148\pi$
$72$	1.06086	+	2.20291i	0.125024	+	0.259615i
$73$	2.44088	+	5.06853i	0.285683	+	0.593227i	0.993586	−	0.113083i	$-0.0360727\pi$
$73$	2.44088	+	5.06853i	0.285683	+	0.593227i	−0.707903	+	0.706310i	$0.750358\pi$
$74$	0.489115	−	2.14295i	0.0568584	−	0.249113i
$75$		0			0
$76$	−0.945042	+	4.14050i	−0.108404	+	0.474948i
$77$	−1.37814	+	1.09903i	−0.157054	+	0.125246i
$78$	3.05841	−	0.698062i	0.346297	−	0.0790400i
$79$	−1.03803	−	4.54792i	−0.116788	−	0.511681i	−0.999154	−	0.0411178i	$-0.986908\pi$
$79$	−1.03803	−	4.54792i	−0.116788	−	0.511681i	0.882367	−	0.470563i	$-0.155949\pi$
$80$		0			0
$81$	2.32155	−	1.11800i	0.257950	−	0.124222i
$82$	−0.600514	+	1.24698i	−0.0663156	+	0.137706i
$83$	3.48285	−	2.77748i	0.382292	−	0.304868i	−0.413423	−	0.910539i	$-0.635667\pi$
$83$	3.48285	−	2.77748i	0.382292	−	0.304868i	0.795715	+	0.605671i	$0.207095\pi$
$84$	−0.500000	+	0.626980i	−0.0545545	+	0.0684091i
$85$		0			0
$86$	1.51573			0.163445
$87$	3.62068	+	5.65548i	0.388178	+	0.606331i
$88$		−	8.35690i		−	0.890848i
$89$	−5.11745	−	2.46443i	−0.542449	−	0.261229i	0.142533	−	0.989790i	$-0.454475\pi$
$89$	−5.11745	−	2.46443i	−0.542449	−	0.261229i	−0.684981	+	0.728561i	$0.740190\pi$
$90$		0			0
$91$	−1.25786	−	1.57731i	−0.131860	−	0.165347i
$92$	−1.79500	+	3.72737i	−0.187142	+	0.388605i
$93$	3.62068	+	7.51842i	0.375447	+	0.779624i
$94$	−1.78836	+	2.24254i	−0.184456	+	0.231300i
$95$		0			0
$96$	−1.29105	−	5.65647i	−0.131768	−	0.577311i
$97$	0.141202	−	0.112605i	0.0143369	−	0.0114333i	−0.616295	−	0.787515i	$-0.711367\pi$
$97$	0.141202	−	0.112605i	0.0143369	−	0.0114333i	0.630632	+	0.776082i	$0.282796\pi$
$98$	2.98192	+	0.680604i	0.301219	+	0.0687514i
$99$	7.13706			0.717302
$100$		0			0
$101$	−2.90970	+	1.40124i	−0.289526	+	0.139428i	−0.573009	−	0.819549i	$-0.694224\pi$
$101$	−2.90970	+	1.40124i	−0.289526	+	0.139428i	0.283484	+	0.958977i	$0.408510\pi$
$102$	−1.08209	−	2.24698i	−0.107143	−	0.222484i
$103$	−13.3105	−	3.03803i	−1.31152	−	0.299346i	−0.491099	−	0.871104i	$-0.663405\pi$
$103$	−13.3105	−	3.03803i	−1.31152	−	0.299346i	−0.820423	+	0.571758i	$0.806262\pi$
$104$	9.56465			0.937891
$105$		0			0
$106$	1.30194	+	1.63258i	0.126455	+	0.158570i
$107$	15.8373	−	3.61476i	1.53105	−	0.349452i	0.627734	−	0.778428i	$-0.283983\pi$
$107$	15.8373	−	3.61476i	1.53105	−	0.349452i	0.903316	+	0.428976i	$0.141126\pi$
$108$	9.73750	−	2.22252i	0.936991	−	0.213862i
$109$	−3.40850	+	4.27413i	−0.326475	+	0.409387i	−0.917798	−	0.397048i	$-0.870035\pi$
$109$	−3.40850	+	4.27413i	−0.326475	+	0.409387i	0.591323	+	0.806435i	$0.298606\pi$
$110$		0			0
$111$	−5.54892	−	2.67222i	−0.526680	−	0.253636i
$112$	−0.795481	+	0.634375i	−0.0751659	+	0.0599428i
$113$	8.34571	+	6.65548i	0.785098	+	0.626095i	0.931753	−	0.363093i	$-0.118279\pi$
$113$	8.34571	+	6.65548i	0.785098	+	0.626095i	−0.146655	+	0.989188i	$0.546851\pi$
$114$	−1.17845	−	0.567511i	−0.110372	−	0.0531522i
$115$		0			0
$116$	3.28232	+	9.13174i	0.304756	+	0.847861i
$117$			8.16852i			0.755180i
$118$	−2.41254	+	5.00969i	−0.222092	+	0.461179i
$119$	−1.00000	+	1.25396i	−0.0916698	+	0.114950i
$120$		0			0
$121$	−12.0673	−	5.81132i	−1.09703	−	0.528302i
$122$	−0.317278	−	0.658834i	−0.0287250	−	0.0596480i
$123$	3.03194	+	2.41789i	0.273381	+	0.218014i
$124$	2.68329	+	11.7563i	0.240967	+	1.05574i
$125$		0			0
$126$	0.143104	+	0.179447i	0.0127487	+	0.0159864i
$127$	1.01084	+	0.230718i	0.0896976	+	0.0204729i	0.267134	−	0.963659i	$-0.413923\pi$
$127$	1.01084	+	0.230718i	0.0896976	+	0.0204729i	−0.177437	+	0.984132i	$0.556780\pi$
$128$		−	10.9215i		−	0.965337i
$129$	0.945042	−	4.14050i	0.0832063	−	0.364551i
$130$		0			0
$131$	−7.22737	+	3.48052i	−0.631458	+	0.304094i	−0.722099	−	0.691790i	$-0.756823\pi$
$131$	−7.22737	+	3.48052i	−0.631458	+	0.304094i	0.0906414	+	0.995884i	$0.471108\pi$
$132$	−10.8196	−	2.46950i	−0.941724	−	0.214942i
$133$			0.841166i			0.0729384i
$134$	0.230054	−	1.00793i	0.0198736	−	0.0870720i
$135$		0			0
$136$	−1.69202	−	7.41323i	−0.145090	−	0.635679i
$137$	16.8005	−	3.83459i	1.43536	−	0.327611i	0.567070	−	0.823670i	$-0.308077\pi$
$137$	16.8005	−	3.83459i	1.43536	−	0.327611i	0.868289	+	0.496058i	$0.165220\pi$
$138$	−0.996152	−	0.794405i	−0.0847981	−	0.0676242i
$139$	−15.0172	+	7.23191i	−1.27374	+	0.613403i	−0.943775	−	0.330589i	$-0.892753\pi$
$139$	−15.0172	+	7.23191i	−1.27374	+	0.613403i	−0.329969	+	0.943992i	$0.607038\pi$
$140$		0			0
$141$	5.01089	+	6.28345i	0.421993	+	0.529162i
$142$	2.55224	+	2.03534i	0.214179	+	0.170802i
$143$	12.1137	−	25.1543i	1.01300	−	2.10351i
$144$	4.11960			0.343300
$145$		0			0
$146$	−2.50365			−0.207203
$147$	3.71839	−	7.72132i	0.306688	−	0.636844i
$148$	−6.95812	−	5.54892i	−0.571954	−	0.456118i
$149$	−11.6012	−	14.5474i	−0.950406	−	1.19177i	−0.981346	−	0.192251i	$-0.938421\pi$
$149$	−11.6012	−	14.5474i	−0.950406	−	1.19177i	0.0309396	−	0.999521i	$-0.490150\pi$
$150$		0			0
$151$	6.78232	−	3.26619i	0.551938	−	0.265799i	−0.137060	−	0.990563i	$-0.543765\pi$
$151$	6.78232	−	3.26619i	0.551938	−	0.265799i	0.688998	+	0.724764i	$0.258051\pi$
$152$	−3.11788	−	2.48643i	−0.252893	−	0.201676i
$153$	6.33114	−	1.44504i	0.511843	−	0.116825i
$154$	−0.174563	−	0.764811i	−0.0140667	−	0.0616302i
$155$		0			0
$156$	2.82640	−	12.3833i	0.226293	−	0.991454i
$157$		−	18.2392i		−	1.45565i	−0.685764	−	0.727824i	$-0.740532\pi$
$157$		−	18.2392i		−	1.45565i	0.685764	−	0.727824i	$-0.259468\pi$
$158$	2.02401	+	0.461968i	0.161022	+	0.0367522i
$159$	5.27144	−	2.53859i	0.418052	−	0.201323i
$160$		0			0
$161$	−0.182333	+	0.798852i	−0.0143698	+	0.0629584i
$162$			1.14675i			0.0900973i
$163$	12.3238	+	2.81282i	0.965273	+	0.220317i	0.675977	−	0.736922i	$-0.263722\pi$
$163$	12.3238	+	2.81282i	0.965273	+	0.220317i	0.289296	+	0.957240i	$0.406579\pi$
$164$	3.49396	+	4.38129i	0.272832	+	0.342121i
$165$		0			0
$166$	0.441157	+	1.93284i	0.0342404	+	0.150017i
$167$	−0.622776	−	0.496648i	−0.0481919	−	0.0384317i	0.599098	−	0.800676i	$-0.295526\pi$
$167$	−0.622776	−	0.496648i	−0.0481919	−	0.0384317i	−0.647290	+	0.762244i	$0.724098\pi$
$168$	−0.326723	−	0.678448i	−0.0252073	−	0.0523434i
$169$	17.0770	+	8.22386i	1.31362	+	0.632605i
$170$		0			0
$171$	2.12349	−	2.66277i	0.162387	−	0.203627i
$172$	2.66277	−	5.52930i	0.203034	−	0.421605i
$173$			9.15346i			0.695924i	0.937509	+	0.347962i	$0.113126\pi$
$173$			9.15346i			0.695924i	−0.937509	+	0.347962i	$0.886874\pi$
$174$	−2.96681	+	0.359726i	−0.224913	+	0.0272708i
$175$		0			0
$176$	−12.6860	−	6.10925i	−0.956242	−	0.460502i
$177$	12.1807	+	9.71379i	0.915558	+	0.730133i
$178$	1.97632	−	1.57606i	0.148132	−	0.118131i
$179$	3.06853	+	1.47773i	0.229353	+	0.110450i	0.545031	−	0.838416i	$-0.316518\pi$
$179$	3.06853	+	1.47773i	0.229353	+	0.110450i	−0.315678	+	0.948866i	$0.602232\pi$
$180$		0			0
$181$	7.90246	−	9.90937i	0.587385	−	0.736558i	−0.395967	−	0.918265i	$-0.629591\pi$
$181$	7.90246	−	9.90937i	0.587385	−	0.736558i	0.983353	+	0.181707i	$0.0581621\pi$
$182$	0.875342	−	0.199791i	0.0648847	−	0.0148095i
$183$	−1.99755	+	0.455927i	−0.147663	+	0.0337031i
$184$	−2.42208	−	3.03719i	−0.178558	−	0.223904i
$185$		0			0
$186$	−3.71379			−0.272308
$187$	−21.6392	−	4.93900i	−1.58241	−	0.361176i
$188$	5.03894	+	10.4635i	0.367502	+	0.763126i
$189$	1.78232	−	0.858322i	0.129645	−	0.0624337i
$190$		0			0
$191$	−10.6703			−0.772072			−0.386036	−	0.922484i	$-0.626156\pi$
$191$	−10.6703			−0.772072			−0.386036	+	0.922484i	$0.626156\pi$
$192$	−4.41429	−	1.00753i	−0.318574	−	0.0727124i
$193$	17.7701	−	14.1712i	1.27912	−	1.02007i	0.280945	−	0.959724i	$-0.409352\pi$
$193$	17.7701	−	14.1712i	1.27912	−	1.02007i	0.998178	−	0.0603421i	$-0.0192192\pi$
$194$	0.0178854	+	0.0783611i	0.00128410	+	0.00562600i
$195$		0			0
$196$	7.72132	−	9.68223i	0.551523	−	0.691588i
$197$	8.48587	+	17.6211i	0.604593	+	1.25545i	0.948598	+	0.316483i	$0.102502\pi$
$197$	8.48587	+	17.6211i	0.604593	+	1.25545i	−0.344005	+	0.938968i	$0.611784\pi$
$198$	−1.37814	+	2.86174i	−0.0979402	+	0.203375i
$199$	0.545565	+	0.684117i	0.0386741	+	0.0484958i	0.800792	−	0.598942i	$-0.204412\pi$
$199$	0.545565	+	0.684117i	0.0386741	+	0.0484958i	−0.762118	+	0.647438i	$0.775841\pi$
$200$		0			0
$201$	−2.60992	−	1.25687i	−0.184089	−	0.0886527i
$202$		−	1.43727i		−	0.101126i
$203$	1.03627	+	1.61865i	0.0727318	+	0.113607i
$204$	−10.0978			−0.706990
$205$		0			0
$206$	3.78836	−	4.75046i	0.263948	−	0.330980i
$207$	2.59386	−	2.06853i	0.180286	−	0.143773i
$208$	6.99216	−	14.5194i	0.484819	−	1.00674i
$209$	−10.4879	+	5.05072i	−0.725464	+	0.349365i
$210$		0			0
$211$	4.06518	+	17.8107i	0.279858	+	1.22614i	0.897972	+	0.440052i	$0.145040\pi$
$211$	4.06518	+	17.8107i	0.279858	+	1.22614i	−0.618114	+	0.786088i	$0.712103\pi$
$212$	8.24275	−	1.88135i	0.566115	−	0.129212i
$213$	7.15122	−	5.70291i	0.489993	−	0.390757i
$214$	−1.60872	+	7.04826i	−0.109970	+	0.481809i
$215$		0			0
$216$	−2.08695	+	9.14352i	−0.141999	+	0.622138i
$217$	1.03627	+	2.15183i	0.0703465	+	0.146076i
$218$	−1.05562	−	2.19202i	−0.0714957	−	0.148462i
$219$	−1.56100	+	6.83918i	−0.105483	+	0.462149i
$220$		0			0
$221$	5.65279	−	24.7665i	0.380248	−	1.66598i
$222$	2.14295	−	1.70895i	0.143826	−	0.114697i
$223$	1.77274	−	0.404617i	0.118712	−	0.0270951i	−0.162752	−	0.986667i	$-0.552037\pi$
$223$	1.77274	−	0.404617i	0.118712	−	0.0270951i	0.281464	+	0.959572i	$0.409180\pi$
$224$	−0.369510	−	1.61893i	−0.0246889	−	0.108169i
$225$		0			0
$226$	−4.28017	+	2.06122i	−0.284713	+	0.137110i
$227$	−6.01199	+	12.4840i	−0.399030	+	0.828594i	0.600549	+	0.799588i	$0.294949\pi$
$227$	−6.01199	+	12.4840i	−0.399030	+	0.828594i	−0.999579	+	0.0290066i	$0.990766\pi$
$228$	−4.14050	+	3.30194i	−0.274211	+	0.218676i
$229$	7.96346	−	9.98586i	0.526240	−	0.659884i	−0.445681	−	0.895192i	$-0.647038\pi$
$229$	7.96346	−	9.98586i	0.526240	−	0.659884i	0.971921	+	0.235308i	$0.0756098\pi$
$230$		0			0
$231$	−2.19806			−0.144622
$232$	−9.06283	−	0.943550i	−0.595004	−	0.0619471i
$233$			8.86592i			0.580826i	0.956901	+	0.290413i	$0.0937926\pi$
$233$			8.86592i			0.580826i	−0.956901	+	0.290413i	$0.906207\pi$
$234$	−3.27532	−	1.57731i	−0.214115	−	0.103112i
$235$		0			0
$236$	14.0368	+	17.6016i	0.913720	+	1.14577i
$237$	2.52390	−	5.24094i	0.163945	−	0.340436i
$238$	−0.309703	−	0.643104i	−0.0200750	−	0.0416862i
$239$	15.9393	−	19.9872i	1.03103	−	1.29287i	0.0757593	−	0.997126i	$-0.475862\pi$
$239$	15.9393	−	19.9872i	1.03103	−	1.29287i	0.955268	−	0.295741i	$-0.0955666\pi$
$240$		0			0
$241$	−2.16541	−	9.48727i	−0.139486	−	0.611129i	−0.995548	−	0.0942554i	$-0.969953\pi$
$241$	−2.16541	−	9.48727i	−0.139486	−	0.611129i	0.856062	−	0.516873i	$-0.172904\pi$
$242$	4.66032	−	3.71648i	0.299577	−	0.238904i
$243$	−13.0791	−	2.98523i	−0.839028	−	0.191503i
$244$	−2.96077			−0.189544
$245$		0			0
$246$	−1.55496	+	0.748828i	−0.0991405	+	0.0477436i
$247$	−5.78065	−	12.0036i	−0.367814	−	0.763774i
$248$	−11.0392	−	2.51961i	−0.700987	−	0.159996i
$249$	5.55496			0.352031
$250$		0			0
$251$	−6.08546	−	7.63092i	−0.384111	−	0.481660i	0.551760	−	0.834003i	$-0.313956\pi$
$251$	−6.08546	−	7.63092i	−0.384111	−	0.481660i	−0.935871	+	0.352343i	$0.885385\pi$
$252$	0.906013	−	0.206791i	0.0570734	−	0.0130266i
$253$	−11.0551	+	2.52326i	−0.695030	+	0.158636i
$254$	−0.287700	+	0.360765i	−0.0180519	+	0.0226364i
$255$		0			0
$256$	−2.16368	−	1.04197i	−0.135230	−	0.0651233i
$257$	−12.7883	+	10.1984i	−0.797714	+	0.636156i	−0.935109	−	0.354360i	$-0.884699\pi$
$257$	−12.7883	+	10.1984i	−0.797714	+	0.636156i	0.137394	+	0.990516i	$0.456127\pi$
$258$	1.47773	+	1.17845i	0.0919993	+	0.0733670i
$259$	−1.58815	−	0.764811i	−0.0986826	−	0.0475230i
$260$		0			0
$261$	0.805823	−	7.73995i	0.0498792	−	0.479091i
$262$		−	3.57002i		−	0.220557i
$263$	−10.2932	+	21.3741i	−0.634708	+	1.31798i	0.297035	+	0.954867i	$0.404002\pi$
$263$	−10.2932	+	21.3741i	−0.634708	+	1.31798i	−0.931743	+	0.363118i	$0.881712\pi$
$264$	6.49731	−	8.14737i	0.399882	−	0.501436i
$265$		0			0
$266$	−0.337282	−	0.162426i	−0.0206801	−	0.00995899i
$267$	−3.07310	−	6.38135i	−0.188071	−	0.390533i
$268$	−3.27273	−	2.60992i	−0.199914	−	0.159426i
$269$	5.64191	+	24.7188i	0.343993	+	1.50713i	0.790561	+	0.612383i	$0.209789\pi$
$269$	5.64191	+	24.7188i	0.343993	+	1.50713i	−0.446568	+	0.894750i	$0.647354\pi$
$270$		0			0
$271$	−0.750332	−	0.940887i	−0.0455794	−	0.0571548i	0.758519	−	0.651651i	$-0.225923\pi$
$271$	−0.750332	−	0.940887i	−0.0455794	−	0.0571548i	−0.804099	+	0.594496i	$0.797352\pi$
$272$	−12.4904	−	2.85086i	−0.757342	−	0.172858i
$273$		−	2.51573i		−	0.152259i
$274$	−1.70655	+	7.47690i	−0.103097	+	0.451696i
$275$		0			0
$276$	−4.64795	+	2.23833i	−0.279774	+	0.134732i
$277$	−10.3975	−	2.37316i	−0.624724	−	0.142589i	−0.101572	−	0.994828i	$-0.532387\pi$
$277$	−10.3975	−	2.37316i	−0.624724	−	0.142589i	−0.523153	+	0.852239i	$0.675244\pi$
$278$		−	7.41789i		−	0.444896i
$279$	2.15183	−	9.42780i	0.128827	−	0.564427i
$280$		0			0
$281$	3.62253	+	15.8713i	0.216102	+	0.946805i	0.960327	+	0.278876i	$0.0899618\pi$
$281$	3.62253	+	15.8713i	0.216102	+	0.946805i	−0.744225	+	0.667929i	$0.767181\pi$
$282$	−3.48705	+	0.795897i	−0.207651	+	0.0473950i
$283$	4.10225	+	3.27144i	0.243854	+	0.194467i	0.737788	−	0.675032i	$-0.235870\pi$
$283$	4.10225	+	3.27144i	0.243854	+	0.194467i	−0.493935	+	0.869499i	$0.664442\pi$
$284$	11.9085	−	5.73483i	0.706640	−	0.340300i
$285$		0			0
$286$	7.74698	+	9.71441i	0.458089	+	0.574425i
$287$	0.867767	+	0.692021i	0.0512227	+	0.0408487i
$288$	−2.91721	+	6.05765i	−0.171898	+	0.356950i
$289$	−3.19567			−0.187981
$290$		0			0
$291$	0.225209			0.0132020
$292$	−4.39831	+	9.13318i	−0.257391	+	0.534479i
$293$	−5.28813	−	4.21714i	−0.308936	−	0.246368i	0.456732	−	0.889604i	$-0.349020\pi$
$293$	−5.28813	−	4.21714i	−0.308936	−	0.246368i	−0.765668	+	0.643236i	$0.777591\pi$
$294$	2.37800	+	2.98192i	0.138688	+	0.173909i
$295$		0			0
$296$	7.52930	−	3.62592i	0.437632	−	0.210752i
$297$	21.4036	+	17.0688i	1.24196	+	0.990434i
$298$	8.07321	−	1.84266i	0.467669	−	0.106742i
$299$	−2.88793	−	12.6528i	−0.167013	−	0.731733i
$300$		0			0
$301$	0.270479	−	1.18505i	0.0155901	−	0.0683049i
$302$			3.35019i			0.192782i
$303$	−3.92618	−	0.896125i	−0.225553	−	0.0514810i
$304$	−6.05376	+	2.91534i	−0.347207	+	0.167206i
$305$		0			0
$306$	−0.643104	+	2.81762i	−0.0367638	+	0.161073i
$307$			4.51812i			0.257863i	0.991654	+	0.128931i	$0.0411547\pi$
$307$			4.51812i			0.257863i	−0.991654	+	0.128931i	$0.958845\pi$
$308$	−3.09666	−	0.706791i	−0.176448	−	0.0402732i
$309$	−10.6148	−	13.3105i	−0.603853	−	0.757207i
$310$		0			0
$311$	2.80745	+	12.3002i	0.159196	+	0.697482i	0.990018	+	0.140944i	$0.0450136\pi$
$311$	2.80745	+	12.3002i	0.159196	+	0.697482i	−0.830822	+	0.556538i	$0.812129\pi$
$312$	9.32484	+	7.43631i	0.527915	+	0.420998i
$313$	8.34804	+	17.3349i	0.471859	+	0.979826i	0.992058	+	0.125781i	$0.0401436\pi$
$313$	8.34804	+	17.3349i	0.471859	+	0.979826i	−0.520199	+	0.854045i	$0.674142\pi$
$314$	7.31336	+	3.52193i	0.412717	+	0.198754i
$315$		0			0
$316$	5.24094	−	6.57193i	0.294826	−	0.369700i
$317$	1.24451	−	2.58426i	0.0698989	−	0.145147i	−0.863092	−	0.505047i	$-0.831475\pi$
$317$	1.24451	−	2.58426i	0.0698989	−	0.145147i	0.932991	+	0.359901i	$0.117189\pi$
$318$			2.60388i			0.146018i
$319$	−13.9596	+	22.6395i	−0.781586	+	1.26757i
$320$		0			0
$321$	18.2506	+	8.78904i	1.01865	+	0.490556i
$322$	−0.285107	−	0.227365i	−0.0158884	−	0.0126706i
$323$	−8.28100	+	6.60388i	−0.460767	+	0.367449i
$324$	4.18329	+	2.01457i	0.232405	+	0.111920i
$325$		0			0
$326$	−3.50753	+	4.39831i	−0.194264	+	0.243600i
$327$	−6.64609	+	1.51693i	−0.367529	+	0.0838862i
$328$	−5.13011	+	1.17092i	−0.283263	+	0.0646530i
$329$	1.43416	+	1.79838i	0.0790676	+	0.0991477i
$330$		0			0
$331$	3.13408			0.172265			0.0861323	−	0.996284i	$-0.472549\pi$
$331$	3.13408			0.172265			0.0861323	+	0.996284i	$0.472549\pi$
$332$	7.82589	+	1.78621i	0.429501	+	0.0980309i
$333$	3.09666	+	6.43027i	0.169696	+	0.352377i
$334$	0.319396	−	0.153813i	0.0174766	−	0.00841628i
$335$		0			0
$336$	−1.26875			−0.0692160
$337$	−4.85762	−	1.10872i	−0.264611	−	0.0603958i	0.0881567	−	0.996107i	$-0.471902\pi$
$337$	−4.85762	−	1.10872i	−0.264611	−	0.0603958i	−0.352768	+	0.935711i	$0.614760\pi$
$338$	−6.59502	+	5.25936i	−0.358722	+	0.286071i
$339$	2.96197	+	12.9772i	0.160872	+	0.704826i
$340$		0			0
$341$	−20.6075	+	25.8410i	−1.11596	+	1.39937i
$342$	0.657650	+	1.36563i	0.0355617	+	0.0738445i
$343$	2.14819	−	4.46077i	0.115992	−	0.240859i
$344$	3.59299	+	4.50547i	0.193721	+	0.242919i
$345$		0			0
$346$	−3.67025	−	1.76750i	−0.197314	−	0.0950214i
$347$			20.1172i			1.07995i	0.841682	+	0.539974i	$0.181566\pi$
$347$			20.1172i			1.07995i	−0.841682	+	0.539974i	$0.818434\pi$
$348$	−3.89971	+	11.4547i	−0.209046	+	0.614038i
$349$	−20.4892			−1.09676			−0.548380	−	0.836229i	$-0.684755\pi$
$349$	−20.4892			−1.09676			−0.548380	+	0.836229i	$0.684755\pi$
$350$		0			0
$351$	−19.5356	+	24.4969i	−1.04274	+	1.30755i
$352$	17.9666	−	14.3279i	0.957623	−	0.763679i
$353$	−7.80887	+	16.2153i	−0.415624	+	0.863052i	0.583092	+	0.812406i	$0.301843\pi$
$353$	−7.80887	+	16.2153i	−0.415624	+	0.863052i	−0.998717	+	0.0506467i	$0.983872\pi$
$354$	−6.24698	+	3.00839i	−0.332023	+	0.159894i
$355$		0			0
$356$	−2.27748	−	9.97829i	−0.120706	−	0.528848i
$357$	−1.94986	+	0.445042i	−0.103197	+	0.0235541i
$358$	−1.18505	+	0.945042i	−0.0626316	+	0.0499470i
$359$	5.25786	−	23.0362i	0.277499	−	1.21580i	−0.623444	−	0.781868i	$-0.714267\pi$
$359$	5.25786	−	23.0362i	0.277499	−	1.21580i	0.900943	−	0.433937i	$-0.142876\pi$
$360$		0			0
$361$	2.99180	−	13.1079i	0.157463	−	0.689892i
$362$	2.44741	+	5.08211i	0.128633	+	0.267110i
$363$	−7.24660	−	15.0477i	−0.380348	−	0.789801i
$364$	0.808938	−	3.54419i	0.0423999	−	0.185766i
$365$		0			0
$366$	0.202907	−	0.888992i	0.0106061	−	0.0464684i
$367$	23.1759	−	18.4822i	1.20977	−	0.964762i	0.209857	−	0.977732i	$-0.432700\pi$
$367$	23.1759	−	18.4822i	1.20977	−	0.964762i	0.999916	+	0.0129705i	$0.00412876\pi$
$368$	−6.38117	+	1.45646i	−0.332641	+	0.0759232i
$369$	−1.00000	−	4.38129i	−0.0520579	−	0.228081i
$370$		0			0
$371$	1.50873	−	0.726566i	0.0783293	−	0.0377214i
$372$	−6.52424	+	13.5477i	−0.338266	+	0.702417i
$373$	−19.6927	+	15.7044i	−1.01965	+	0.813143i	−0.982518	−	0.186167i	$-0.940393\pi$
$373$	−19.6927	+	15.7044i	−1.01965	+	0.813143i	−0.0371310	+	0.999310i	$0.511822\pi$
$374$	6.15883	−	7.72293i	0.318466	−	0.399343i
$375$		0			0
$376$	−10.9051			−0.562390
$377$	−25.9114	−	15.9770i	−1.33451	−	0.822859i
$378$			0.880395i			0.0452826i
$379$	−24.2424	−	11.6745i	−1.24525	−	0.599681i	−0.309016	−	0.951057i	$-0.600000\pi$
$379$	−24.2424	−	11.6745i	−1.24525	−	0.599681i	−0.936234	+	0.351376i	$0.885714\pi$
$380$		0			0
$381$	0.806118	+	1.01084i	0.0412987	+	0.0517869i
$382$	2.06039	−	4.27844i	0.105419	−	0.218904i
$383$	−8.53414	−	17.7213i	−0.436074	−	0.905517i	−0.996982	−	0.0776388i	$-0.975262\pi$
$383$	−8.53414	−	17.7213i	−0.436074	−	0.905517i	0.560907	−	0.827879i	$-0.310452\pi$
$384$	8.49127	−	10.6477i	0.433318	−	0.543364i
$385$		0			0
$386$	2.25086	+	9.86168i	0.114566	+	0.501946i
$387$	−3.84782	+	3.06853i	−0.195596	+	0.155982i
$388$	0.317278	+	0.0724165i	0.0161073	+	0.00367639i
$389$	−24.8552			−1.26021			−0.630103	−	0.776511i	$-0.716988\pi$
$389$	−24.8552			−1.26021			−0.630103	+	0.776511i	$0.716988\pi$
$390$		0			0
$391$	−9.29590	+	4.47667i	−0.470114	+	0.226395i
$392$	5.04547	+	10.4770i	0.254835	+	0.529170i
$393$	−9.75219	−	2.22587i	−0.491933	−	0.112280i
$394$	−8.70410			−0.438506
$395$		0			0
$396$	8.01842	+	10.0548i	0.402941	+	0.505272i
$397$	−3.89447	+	0.888887i	−0.195458	+	0.0446120i	−0.319129	−	0.947711i	$-0.603390\pi$
$397$	−3.89447	+	0.888887i	−0.195458	+	0.0446120i	0.123671	+	0.992323i	$0.460533\pi$
$398$	−0.379656	+	0.0866540i	−0.0190304	+	0.00434357i
$399$	−0.653989	+	0.820077i	−0.0327404	+	0.0410552i
$400$		0			0
$401$	22.4405	+	10.8068i	1.12062	+	0.539664i	0.900085	−	0.435714i	$-0.143504\pi$
$401$	22.4405	+	10.8068i	1.12062	+	0.539664i	0.220539	+	0.975378i	$0.429218\pi$
$402$	1.00793	−	0.803798i	0.0502710	−	0.0400898i
$403$	−29.5756	−	23.5858i	−1.47327	−	1.17489i
$404$	−5.24309	−	2.52494i	−0.260854	−	0.125621i
$405$		0			0
$406$	−0.849126	+	0.102957i	−0.0421414	+	0.00510965i
$407$		−	24.3937i		−	1.20915i
$408$	4.11403	−	8.54288i	0.203675	−	0.422935i
$409$	−0.176587	+	0.221434i	−0.00873169	+	0.0109492i	−0.786178	−	0.618000i	$-0.787943\pi$
$409$	−0.176587	+	0.221434i	−0.00873169	+	0.0109492i	0.777446	+	0.628949i	$0.216515\pi$
$410$		0			0
$411$	19.3605	+	9.32355i	0.954985	+	0.459897i
$412$	−10.6742	−	22.1652i	−0.525879	−	1.09200i
$413$	3.48622	+	2.78017i	0.171546	+	0.136803i
$414$	0.328552	+	1.43948i	0.0161475	+	0.0707467i
$415$		0			0
$416$	16.3986	+	20.5632i	0.804006	+	1.00819i
$417$	−20.2634	−	4.62498i	−0.992301	−	0.226486i
$418$		−	5.18060i		−	0.253392i
$419$	−5.89426	+	25.8245i	−0.287954	+	1.26161i	0.599374	+	0.800469i	$0.295416\pi$
$419$	−5.89426	+	25.8245i	−0.287954	+	1.26161i	−0.887328	+	0.461139i	$0.847441\pi$
$420$		0			0
$421$	15.8409	−	7.62859i	0.772040	−	0.371795i	−0.00602261	−	0.999982i	$-0.501917\pi$
$421$	15.8409	−	7.62859i	0.772040	−	0.371795i	0.778062	+	0.628187i	$0.216203\pi$
$422$	−7.92651	−	1.80917i	−0.385857	−	0.0880693i
$423$		−	9.31336i		−	0.452831i
$424$	−1.76659	+	7.73995i	−0.0857934	+	0.375885i
$425$		0			0
$426$	0.905813	+	3.96863i	0.0438868	+	0.192281i
$427$	−0.571714	+	0.130490i	−0.0276672	+	0.00631486i
$428$	22.8856	+	18.2506i	1.10622	+	0.882177i
$429$	31.3669	−	15.1055i	1.51441	−	0.729300i
$430$		0			0
$431$	−17.3300	−	21.7312i	−0.834759	−	1.04675i	−0.998186	−	0.0601992i	$-0.980826\pi$
$431$	−17.3300	−	21.7312i	−0.834759	−	1.04675i	0.163428	−	0.986555i	$-0.447745\pi$
$432$	12.3545	+	9.85235i	0.594404	+	0.474021i
$433$	−2.54933	+	5.29374i	−0.122513	+	0.254401i	−0.953201	−	0.302337i	$-0.902233\pi$
$433$	−2.54933	+	5.29374i	−0.122513	+	0.254401i	0.830688	+	0.556738i	$0.187947\pi$
$434$	−1.06292			−0.0510217
$435$		0			0
$436$	−9.85086			−0.471770
$437$	−2.34783	+	4.87531i	−0.112312	+	0.233218i
$438$	−2.44088	−	1.94653i	−0.116630	−	0.0930090i
$439$	9.81431	+	12.3068i	0.468412	+	0.587370i	0.958781	−	0.284145i	$-0.0917097\pi$
$439$	9.81431	+	12.3068i	0.468412	+	0.587370i	−0.490370	+	0.871515i	$0.663138\pi$
$440$		0			0
$441$	−8.94773	+	4.30900i	−0.426082	+	0.205190i
$442$	8.83906	+	7.04892i	0.420431	+	0.335283i
$443$	−6.56960	+	1.49947i	−0.312131	+	0.0712419i	−0.375717	−	0.926735i	$-0.622603\pi$
$443$	−6.56960	+	1.49947i	−0.312131	+	0.0712419i	0.0635859	+	0.997976i	$0.479746\pi$
$444$	−2.46950	−	10.8196i	−0.117197	−	0.513475i
$445$		0			0
$446$	−0.180071	+	0.788944i	−0.00852663	+	0.0373576i
$447$		−	23.2024i		−	1.09743i
$448$	−1.26341	−	0.288364i	−0.0596903	−	0.0136239i
$449$	11.1000	−	5.34547i	0.523841	−	0.252269i	−0.153224	−	0.988191i	$-0.548966\pi$
$449$	11.1000	−	5.34547i	0.523841	−	0.252269i	0.677065	+	0.735923i	$0.263251\pi$
$450$		0			0
$451$	−3.41789	+	14.9748i	−0.160942	+	0.705135i
$452$			19.2349i			0.904733i
$453$	9.15167	+	2.08881i	0.429983	+	0.0981409i
$454$	−3.84481	−	4.82124i	−0.180446	−	0.226272i
$455$		0			0
$456$	−1.10656	−	4.84817i	−0.0518196	−	0.227037i
$457$	10.6818	+	8.51842i	0.499672	+	0.398475i	0.840635	−	0.541602i	$-0.182182\pi$
$457$	10.6818	+	8.51842i	0.499672	+	0.398475i	−0.340964	+	0.940076i	$0.610753\pi$
$458$	2.46630	+	5.12133i	0.115243	+	0.239304i
$459$	22.4426	+	10.8078i	1.04753	+	0.504465i
$460$		0			0
$461$	7.23759	−	9.07565i	0.337088	−	0.422695i	−0.584180	−	0.811624i	$-0.698584\pi$
$461$	7.23759	−	9.07565i	0.337088	−	0.422695i	0.921268	+	0.388929i	$0.127155\pi$
$462$	0.424438	−	0.881355i	0.0197466	−	0.0410043i
$463$			7.24267i			0.336595i	0.985736	+	0.168298i	$0.0538270\pi$
$463$			7.24267i			0.336595i	−0.985736	+	0.168298i	$0.946173\pi$
$464$	−8.05765	+	13.0678i	−0.374067	+	0.606659i
$465$		0			0
$466$	−3.55496	−	1.71198i	−0.164680	−	0.0793058i
$467$	−1.61322	−	1.28650i	−0.0746511	−	0.0595323i	0.585453	−	0.810706i	$-0.300917\pi$
$467$	−1.61322	−	1.28650i	−0.0746511	−	0.0595323i	−0.660104	+	0.751174i	$0.729488\pi$
$468$	−11.5079	+	9.17725i	−0.531953	+	0.424219i
$469$	−0.746980	−	0.359726i	−0.0344923	−	0.0166106i
$470$		0			0
$471$	14.1806	−	17.7819i	0.653408	−	0.819347i
$472$	−20.6100	+	4.70410i	−0.948653	+	0.216524i
$473$	16.3996	−	3.74309i	0.754053	−	0.172108i
$474$	1.61410	+	2.02401i	0.0741379	+	0.0929660i
$475$		0			0
$476$	−2.89008			−0.132467
$477$	−6.61017	−	1.50873i	−0.302659	−	0.0690800i
$478$	4.93644	+	10.2506i	0.225788	+	0.468853i
$479$	−3.50388	+	1.68738i	−0.160097	+	0.0770985i	−0.512216	−	0.858857i	$-0.671175\pi$
$479$	−3.50388	+	1.68738i	−0.160097	+	0.0770985i	0.352120	+	0.935955i	$0.385461\pi$
$480$		0			0
$481$	27.9191			1.27300
$482$	4.22223	+	0.963697i	0.192317	+	0.0438952i
$483$	−0.798852	+	0.637063i	−0.0363490	+	0.0289874i
$484$	−5.37047	−	23.5296i	−0.244112	−	1.06953i
$485$		0			0
$486$	3.72252	−	4.66789i	0.168857	−	0.211740i
$487$	−4.27179	−	8.87047i	−0.193573	−	0.401959i	0.781480	−	0.623931i	$-0.214465\pi$
$487$	−4.27179	−	8.87047i	−0.193573	−	0.401959i	−0.975053	+	0.221971i	$0.928751\pi$
$488$	1.20627	−	2.50484i	0.0546053	−	0.113389i
$489$	9.82789	+	12.3238i	0.444432	+	0.557301i
$490$		0			0
$491$	−7.01961	−	3.38047i	−0.316791	−	0.152558i	0.268731	−	0.963215i	$-0.413396\pi$
$491$	−7.01961	−	3.38047i	−0.316791	−	0.152558i	−0.585521	+	0.810657i	$0.699110\pi$
$492$			6.98792i			0.315040i
$493$	−7.79942	+	22.9095i	−0.351268	+	1.03179i
$494$	5.92931			0.266772
$495$		0			0
$496$	−11.8949	+	14.9158i	−0.534098	+	0.669738i
$497$	2.04674	−	1.63222i	0.0918087	−	0.0732150i
$498$	−1.07264	+	2.22737i	−0.0480663	+	0.0998106i
$499$	−18.5286	+	8.92292i	−0.829456	+	0.399445i	−0.799911	−	0.600119i	$-0.795120\pi$
$499$	−18.5286	+	8.92292i	−0.829456	+	0.399445i	−0.0295448	+	0.999563i	$0.509406\pi$
$500$		0			0
$501$	−0.221029	−	0.968391i	−0.00987485	−	0.0432645i
$502$	4.23484	−	0.966575i	0.189010	−	0.0431404i
$503$	6.43830	−	5.13437i	0.287070	−	0.228930i	−0.469358	−	0.883008i	$-0.655514\pi$
$503$	6.43830	−	5.13437i	0.287070	−	0.228930i	0.756427	+	0.654078i	$0.226943\pi$
$504$	−0.194177	+	0.850747i	−0.00864935	+	0.0378953i
$505$		0			0
$506$	1.12296	−	4.92000i	0.0499215	−	0.218721i
$507$	10.2550	+	21.2947i	0.455440	+	0.945731i
$508$	0.810631	+	1.68329i	0.0359659	+	0.0746840i
$509$	1.76151	−	7.71769i	0.0780777	−	0.342081i	−0.920768	−	0.390110i	$-0.872437\pi$
$509$	1.76151	−	7.71769i	0.0780777	−	0.342081i	0.998846	+	0.0480294i	$0.0152941\pi$
$510$		0			0
$511$	−0.446771	+	1.95743i	−0.0197640	+	0.0865916i
$512$	17.9132	−	14.2853i	0.791659	−	0.631327i
$513$	12.7364	−	2.90701i	0.562328	−	0.128348i
$514$	−1.61984	−	7.09699i	−0.0714482	−	0.313035i
$515$		0			0
$516$	6.89493	−	3.32042i	0.303532	−	0.146173i
$517$	−13.8114	+	28.6797i	−0.607425	+	1.26133i
$518$	0.613331	−	0.489115i	0.0269482	−	0.0214905i
$519$	−7.11662	+	8.92396i	−0.312385	+	0.391718i
$520$		0			0
$521$	−3.52542			−0.154451			−0.0772257	−	0.997014i	$-0.524606\pi$
$521$	−3.52542			−0.154451			−0.0772257	+	0.997014i	$0.524606\pi$
$522$	2.94788	+	1.81767i	0.129025	+	0.0795571i
$523$		−	10.0301i		−	0.438587i	−0.975659	−	0.219294i	$-0.929625\pi$
$523$		−	10.0301i		−	0.438587i	0.975659	−	0.219294i	$-0.0703752\pi$
$524$	−13.0233	−	6.27167i	−0.568924	−	0.273979i
$525$		0			0
$526$	−6.58277	−	8.25453i	−0.287022	−	0.359915i
$527$	−13.0485	+	27.0954i	−0.568401	+	1.18030i
$528$	−7.61811	−	15.8192i	−0.331535	−	0.688441i
$529$	11.0538	−	13.8610i	0.480598	−	0.602651i
$530$		0			0
$531$	−4.01746	−	17.6016i	−0.174343	−	0.763846i
$532$	−1.18505	+	0.945042i	−0.0513782	+	0.0409728i
$533$	−17.1390	−	3.91185i	−0.742370	−	0.169441i
$534$	3.15213			0.136406
$535$		0			0
$536$	3.54138	−	1.70544i	0.152965	−	0.0736638i
$537$	1.84270	+	3.82640i	0.0795182	+	0.165121i
$538$	−11.0009	−	2.51089i	−0.474283	−	0.108252i
$539$	33.9439			1.46207
$540$		0			0
$541$	5.12767	+	6.42990i	0.220456	+	0.276443i	0.879744	−	0.475447i	$-0.157714\pi$
$541$	5.12767	+	6.42990i	0.220456	+	0.276443i	−0.659288	+	0.751890i	$0.729142\pi$
$542$	0.522153	−	0.119178i	0.0224284	−	0.00511913i
$543$	15.4087	−	3.51693i	0.661249	−	0.150926i
$544$	13.0368	−	16.3477i	0.558950	−	0.700901i
$545$		0			0
$546$	1.00873	+	0.485778i	0.0431696	+	0.0207894i
$547$	−20.2205	+	16.1253i	−0.864564	+	0.689467i	−0.951800	−	0.306721i	$-0.900768\pi$
$547$	−20.2205	+	16.1253i	−0.864564	+	0.689467i	0.0872352	+	0.996188i	$0.472197\pi$
$548$	24.2774	+	19.3605i	1.03708	+	0.827041i
$549$	2.13922	+	1.03019i	0.0912997	+	0.0439676i
$550$		0			0
$551$	4.29321	+	11.9441i	0.182897	+	0.508837i
$552$		−	4.84415i		−	0.206181i
$553$	0.722362	−	1.50000i	0.0307180	−	0.0637865i
$554$	2.95928	−	3.71082i	0.125728	−	0.157658i
$555$		0			0
$556$	−27.0601	−	13.0315i	−1.14760	−	0.552657i
$557$	−9.98353	−	20.7310i	−0.423016	−	0.878401i	−0.998177	−	0.0603609i	$-0.980775\pi$
$557$	−9.98353	−	20.7310i	−0.423016	−	0.878401i	0.575161	−	0.818040i	$-0.304939\pi$
$558$	3.36474	+	2.68329i	0.142441	+	0.113593i
$559$	4.28405	+	18.7697i	0.181196	+	0.793872i
$560$		0			0
$561$	−17.2567	−	21.6392i	−0.728577	−	0.913607i
$562$	−7.06341	−	1.61218i	−0.297952	−	0.0680056i
$563$		−	43.1159i		−	1.81712i	−0.417757	−	0.908559i	$-0.637184\pi$
$563$		−	43.1159i		−	1.81712i	0.417757	−	0.908559i	$-0.362816\pi$
$564$	−3.22252	+	14.1188i	−0.135693	+	0.594508i
$565$		0			0
$566$	−2.10388	+	1.01317i	−0.0884325	+	0.0425868i
$567$	0.896567	+	0.204636i	0.0376523	+	0.00859388i
$568$			12.4112i			0.520762i
$569$	−5.40999	+	23.7027i	−0.226799	+	0.993670i	0.725433	+	0.688293i	$0.241640\pi$
$569$	−5.40999	+	23.7027i	−0.226799	+	0.993670i	−0.952231	+	0.305377i	$0.901217\pi$
$570$		0			0
$571$	−4.11410	−	18.0250i	−0.172170	−	0.754324i	−0.985103	−	0.171967i	$-0.944988\pi$
$571$	−4.11410	−	18.0250i	−0.172170	−	0.754324i	0.812933	−	0.582357i	$-0.197869\pi$
$572$	49.0472	−	11.1947i	2.05077	−	0.468074i
$573$	−10.4027	−	8.29590i	−0.434580	−	0.346566i
$574$	−0.445042	+	0.214321i	−0.0185757	+	0.00894558i
$575$		0			0
$576$	3.27144	+	4.10225i	0.136310	+	0.170927i
$577$	−29.5987	−	23.6042i	−1.23221	−	0.982654i	−0.999950	−	0.0100007i	$-0.996817\pi$
$577$	−29.5987	−	23.6042i	−1.23221	−	0.982654i	−0.232260	−	0.972654i	$-0.574612\pi$
$578$	0.617072	−	1.28136i	0.0256668	−	0.0532977i
$579$	28.3424			1.17787
$580$		0			0
$581$	1.58987			0.0659591
$582$	−0.0434871	+	0.0903019i	−0.00180260	+	0.00374314i
$583$	18.1181	+	14.4487i	0.750374	+	0.598404i
$584$	−5.93482	−	7.44203i	−0.245585	−	0.307953i
$585$		0			0
$586$	2.71206	−	1.30606i	0.112034	−	0.0539529i
$587$	−11.2860	−	9.00030i	−0.465824	−	0.371482i	0.362269	−	0.932074i	$-0.382002\pi$
$587$	−11.2860	−	9.00030i	−0.465824	−	0.371482i	−0.828092	+	0.560592i	$0.810574\pi$
$588$	15.0555	−	3.43631i	0.620877	−	0.141711i
$589$	3.50969	+	15.3770i	0.144614	+	0.633596i
$590$		0			0
$591$	−5.42692	+	23.7769i	−0.223234	+	0.978050i
$592$		−	14.0804i		−	0.578700i
$593$	−12.6759	−	2.89320i	−0.520538	−	0.118809i	−0.0458241	−	0.998950i	$-0.514591\pi$
$593$	−12.6759	−	2.89320i	−0.520538	−	0.118809i	−0.474714	+	0.880140i	$0.657449\pi$
$594$	−10.9770	+	5.28626i	−0.450393	+	0.216898i
$595$		0			0
$596$	7.46077	−	32.6878i	0.305605	−	1.33894i
$597$			1.09113i			0.0446570i
$598$	5.63104	+	1.28525i	0.230270	+	0.0525577i
$599$	−7.54019	−	9.45510i	−0.308084	−	0.386325i	0.603552	−	0.797323i	$-0.293751\pi$
$599$	−7.54019	−	9.45510i	−0.308084	−	0.386325i	−0.911636	+	0.410999i	$0.865180\pi$
$600$		0			0
$601$	4.97272	+	21.7869i	0.202842	+	0.888707i	0.969196	+	0.246289i	$0.0792113\pi$
$601$	4.97272	+	21.7869i	0.202842	+	0.888707i	−0.766355	+	0.642418i	$0.777932\pi$
$602$	0.422938	+	0.337282i	0.0172377	+	0.0137466i
$603$	1.45650	+	3.02446i	0.0593134	+	0.123165i
$604$	12.2213	+	5.88548i	0.497279	+	0.239477i
$605$		0			0
$606$	1.11745	−	1.40124i	0.0453933	−	0.0569214i
$607$	17.9926	−	37.3620i	0.730297	−	1.51648i	−0.121491	−	0.992593i	$-0.538768\pi$
$607$	17.9926	−	37.3620i	0.730297	−	1.51648i	0.851789	−	0.523886i	$-0.175518\pi$
$608$		−	10.9661i		−	0.444736i
$609$	−0.248176	+	2.38374i	−0.0100566	+	0.0965940i
$610$		0			0
$611$	−32.8245	−	15.8075i	−1.32794	−	0.639502i
$612$	9.14877	+	7.29590i	0.369817	+	0.294919i
$613$	20.1591	−	16.0764i	0.814219	−	0.649318i	−0.125184	−	0.992134i	$-0.539952\pi$
$613$	20.1591	−	16.0764i	0.814219	−	0.649318i	0.939403	+	0.342816i	$0.111381\pi$
$614$	−1.81163	−	0.872433i	−0.0731113	−	0.0352085i
$615$		0			0
$616$	1.85958	−	2.33184i	0.0749248	−	0.0939527i
$617$	8.64306	−	1.97272i	0.347956	−	0.0794188i	−0.0449710	−	0.998988i	$-0.514320\pi$
$617$	8.64306	−	1.97272i	0.347956	−	0.0794188i	0.392927	+	0.919570i	$0.371462\pi$
$618$	7.38676	−	1.68598i	0.297139	−	0.0678201i
$619$	−18.3626	−	23.0259i	−0.738054	−	0.925490i	0.261153	−	0.965297i	$-0.415897\pi$
$619$	−18.3626	−	23.0259i	−0.738054	−	0.925490i	−0.999207	+	0.0398069i	$0.987326\pi$
$620$		0			0
$621$	12.7259			0.510672
$622$	−5.47412	−	1.24943i	−0.219492	−	0.0500976i
$623$	−0.879546	−	1.82640i	−0.0352383	−	0.0731730i
$624$	18.1054	−	8.71909i	0.724795	−	0.349043i
$625$		0			0
$626$	−8.56273			−0.342235
$627$	−14.1518	−	3.23005i	−0.565168	−	0.128996i
$628$	25.6956	−	20.4916i	1.02537	−	0.817703i
$629$	−4.93900	−	21.6392i	−0.196931	−	0.862811i
$630$		0			0
$631$	14.8210	−	18.5850i	0.590015	−	0.739856i	−0.393769	−	0.919209i	$-0.628829\pi$
$631$	14.8210	−	18.5850i	0.590015	−	0.739856i	0.983785	+	0.179353i	$0.0574005\pi$
$632$	3.42467	+	7.11141i	0.136226	+	0.282877i
$633$	−9.88420	+	20.5248i	−0.392862	+	0.815786i
$634$	0.795897	+	0.998023i	0.0316091	+	0.0396366i
$635$		0			0
$636$	9.49880	+	4.57438i	0.376652	+	0.181386i
$637$			38.8495i			1.53927i
$638$	−6.38220	−	9.96897i	−0.252674	−	0.394675i
$639$	−10.5996			−0.419312
$640$		0			0
$641$	17.7479	−	22.2552i	0.701001	−	0.879028i	−0.296096	−	0.955158i	$-0.595685\pi$
$641$	17.7479	−	22.2552i	0.701001	−	0.879028i	0.997098	+	0.0761300i	$0.0242564\pi$
$642$	−7.04826	+	5.62080i	−0.278173	+	0.221835i
$643$	8.39423	−	17.4308i	0.331036	−	0.687404i	−0.667317	−	0.744774i	$-0.732557\pi$
$643$	8.39423	−	17.4308i	0.331036	−	0.687404i	0.998353	+	0.0573702i	$0.0182715\pi$
$644$	−1.33028	+	0.640630i	−0.0524204	+	0.0252443i
$645$		0			0
$646$	−1.04892	−	4.59561i	−0.0412691	−	0.180812i
$647$	22.1449	−	5.05443i	0.870605	−	0.198710i	0.236194	−	0.971706i	$-0.424100\pi$
$647$	22.1449	−	5.05443i	0.870605	−	0.198710i	0.634411	+	0.772996i	$0.281243\pi$
$648$	−3.40869	+	2.71834i	−0.133906	+	0.106787i
$649$	−13.7313	+	60.1605i	−0.538999	+	2.36151i
$650$		0			0
$651$	−0.662718	+	2.90356i	−0.0259740	+	0.113799i
$652$	9.88291	+	20.5221i	0.387044	+	0.803706i
$653$	9.94949	+	20.6603i	0.389354	+	0.808501i	0.999864	+	0.0164928i	$0.00525006\pi$
$653$	9.94949	+	20.6603i	0.389354	+	0.808501i	−0.610510	+	0.792008i	$0.709036\pi$
$654$	0.675096	−	2.95779i	0.0263983	−	0.115659i
$655$		0			0
$656$	−1.97285	+	8.64363i	−0.0770270	+	0.337477i
$657$	6.35574	−	5.06853i	0.247961	−	0.197742i
$658$	−0.998023	+	0.227792i	−0.0389070	+	0.00888027i
$659$	−4.26755	−	18.6974i	−0.166240	−	0.728346i	−0.987478	−	0.157759i	$-0.949573\pi$
$659$	−4.26755	−	18.6974i	−0.166240	−	0.728346i	0.821237	−	0.570587i	$-0.193284\pi$
$660$		0			0
$661$	3.05107	−	1.46932i	0.118673	−	0.0571499i	−0.373605	−	0.927588i	$-0.621879\pi$
$661$	3.05107	−	1.46932i	0.118673	−	0.0571499i	0.492278	+	0.870438i	$0.336164\pi$
$662$	−0.605180	+	1.25667i	−0.0235210	+	0.0488418i
$663$	24.7665	−	19.7506i	0.961851	−	0.767051i
$664$	−4.69955	+	5.89305i	−0.182378	+	0.228695i
$665$		0			0
$666$	−3.17629			−0.123079
$667$	1.48821	+	12.2739i	0.0576238	+	0.475247i
$668$		−	1.43535i		−	0.0555355i
$669$	2.04288	+	0.983797i	0.0789822	+	0.0380358i
$670$		0			0
$671$	−5.05980	−	6.34479i	−0.195332	−	0.244938i
$672$	0.898438	−	1.86563i	0.0346580	−	0.0719680i
$673$	2.06983	+	4.29805i	0.0797862	+	0.165678i	0.937046	−	0.349207i	$-0.113549\pi$
$673$	2.06983	+	4.29805i	0.0797862	+	0.165678i	−0.857259	+	0.514885i	$0.827835\pi$
$674$	1.38255	−	1.73366i	0.0532539	−	0.0667782i
$675$		0			0
$676$	7.59999	+	33.2977i	0.292307	+	1.28068i
$677$	33.6892	−	26.8662i	1.29478	−	1.03255i	0.297821	−	0.954622i	$-0.403740\pi$
$677$	33.6892	−	26.8662i	1.29478	−	1.03255i	0.996959	−	0.0779309i	$-0.0248314\pi$
$678$	−5.77541	−	1.31820i	−0.221803	−	0.0506252i
$679$	0.0644568			0.00247362
$680$		0			0
$681$	−15.5673	+	7.49683i	−0.596542	+	0.287279i
$682$	−6.38220	−	13.2528i	−0.244387	−	0.507475i
$683$	22.8454	+	5.21432i	0.874157	+	0.199521i	0.635984	−	0.771702i	$-0.280594\pi$
$683$	22.8454	+	5.21432i	0.874157	+	0.199521i	0.238173	+	0.971223i	$0.423452\pi$
$684$	6.13706			0.234656
$685$		0			0
$686$	1.37382	+	1.72272i	0.0524528	+	0.0657737i
$687$	15.5276	−	3.54407i	0.592415	−	0.135215i
$688$	9.46604	−	2.16056i	0.360890	−	0.0823707i
$689$	−16.5368	+	20.7365i	−0.630003	+	0.789999i
$690$		0			0
$691$	−38.8657	−	18.7167i	−1.47852	−	0.712018i	−0.491243	−	0.871023i	$-0.663457\pi$
$691$	−38.8657	−	18.7167i	−1.47852	−	0.712018i	−0.987278	+	0.159005i	$0.949171\pi$
$692$	−12.8955	+	10.2838i	−0.490213	+	0.390932i
$693$	1.99147	+	1.58815i	0.0756498	+	0.0603287i
$694$	−8.06638	−	3.88456i	−0.306195	−	0.147456i
$695$		0			0
$696$	−8.10202	−	7.96605i	−0.307106	−	0.301952i
$697$			13.9758i			0.529373i
$698$	3.95639	−	8.21552i	0.149751	−	0.310962i
$699$	−6.89307	+	8.64363i	−0.260720	+	0.326932i
$700$		0			0
$701$	−3.81186	−	1.83570i	−0.143972	−	0.0693333i	0.360511	−	0.932755i	$-0.382602\pi$
$701$	−3.81186	−	1.83570i	−0.143972	−	0.0693333i	−0.504483	+	0.863422i	$0.668317\pi$
$702$	−6.05024	−	12.5635i	−0.228352	−	0.474177i
$703$	−9.10107	−	7.25786i	−0.343254	−	0.273736i
$704$	−3.99061	−	17.4840i	−0.150402	−	0.658953i
$705$		0			0
$706$	−4.99396	−	6.26223i	−0.187950	−	0.235682i
$707$	−1.12370	−	0.256478i	−0.0422613	−	0.00964586i
$708$			28.0737i			1.05507i
$709$	3.18287	−	13.9450i	0.119535	−	0.523717i	−0.879336	−	0.476203i	$-0.842013\pi$
$709$	3.18287	−	13.9450i	0.119535	−	0.523717i	0.998871	−	0.0475144i	$-0.0151300\pi$
$710$		0			0
$711$	−6.07338	+	2.92478i	−0.227769	+	0.109688i
$712$	9.36962	+	2.13856i	0.351141	+	0.0801457i
$713$			15.3642i			0.575393i
$714$	0.198062	−	0.867767i	0.00741229	−	0.0324754i
$715$		0			0
$716$	1.36563	+	5.98319i	0.0510358	+	0.223602i
$717$	31.0793	−	7.09365i	1.16068	−	0.264917i
$718$	8.22153	+	6.55645i	0.306825	+	0.244685i
$719$	−21.1194	+	10.1706i	−0.787620	+	0.379298i	−0.784051	−	0.620696i	$-0.786850\pi$
$719$	−21.1194	+	10.1706i	−0.787620	+	0.379298i	−0.00356825	+	0.999994i	$0.501136\pi$
$720$		0			0
$721$	−3.03803	−	3.80957i	−0.113142	−	0.141876i
$722$	4.67817	+	3.73072i	0.174104	+	0.138843i
$723$	5.26504	−	10.9330i	0.195809	−	0.406601i
$724$	22.8388			0.848796
$725$		0			0
$726$	7.43296			0.275863
$727$	22.5609	−	46.8482i	0.836738	−	1.73750i	0.179592	−	0.983741i	$-0.442522\pi$
$727$	22.5609	−	46.8482i	0.836738	−	1.73750i	0.657146	−	0.753763i	$-0.271763\pi$
$728$	2.66885	+	2.12833i	0.0989140	+	0.0788813i
$729$	−15.2500	−	19.1228i	−0.564813	−	0.708254i
$730$		0			0
$731$	13.7899	−	6.64084i	0.510036	−	0.245621i
$732$	−2.88654	−	2.30194i	−0.106690	−	0.0850821i
$733$	−33.3331	+	7.60806i	−1.23119	+	0.281010i	−0.788144	−	0.615491i	$-0.788958\pi$
$733$	−33.3331	+	7.60806i	−1.23119	+	0.281010i	−0.443041	+	0.896501i	$0.646101\pi$
$734$	2.93559	+	12.8617i	0.108355	+	0.474733i
$735$		0			0
$736$	2.37704	−	10.4145i	0.0876190	−	0.383884i
$737$		−	11.4735i		−	0.422632i
$738$	1.94986	+	0.445042i	0.0717752	+	0.0163822i
$739$	35.8342	−	17.2569i	1.31818	−	0.634804i	0.363269	−	0.931684i	$-0.381661\pi$
$739$	35.8342	−	17.2569i	1.31818	−	0.634804i	0.954915	+	0.296881i	$0.0959464\pi$
$740$		0			0
$741$	3.69687	−	16.1970i	0.135808	−	0.595013i
$742$			0.745251i			0.0273590i
$743$	6.99824	+	1.59730i	0.256740	+	0.0585993i	0.348954	−	0.937140i	$-0.386537\pi$
$743$	6.99824	+	1.59730i	0.256740	+	0.0585993i	−0.0922133	+	0.995739i	$0.529394\pi$
$744$	−8.80343	−	11.0392i	−0.322749	−	0.404715i
$745$		0			0
$746$	−2.49439	−	10.9286i	−0.0913260	−	0.400125i
$747$	−5.03286	−	4.01357i	−0.184143	−	0.146849i
$748$	−17.3533	−	36.0344i	−0.634499	−	1.31755i
$749$	5.22348	+	2.51550i	0.190862	+	0.0919142i
$750$		0			0
$751$	−16.9393	+	21.2412i	−0.618124	+	0.775103i	−0.988079	−	0.153947i	$-0.950802\pi$
$751$	−16.9393	+	21.2412i	−0.618124	+	0.775103i	0.369955	+	0.929050i	$0.379373\pi$
$752$	−7.97213	+	16.5543i	−0.290714	+	0.603673i
$753$		−	12.1709i		−	0.443533i
$754$	11.4097	−	7.30457i	0.415517	−	0.266017i
$755$		0			0
$756$	3.21164	+	1.54664i	0.116806	+	0.0562508i
$757$	18.5236	+	14.7721i	0.673253	+	0.536901i	0.899364	−	0.437200i	$-0.144030\pi$
$757$	18.5236	+	14.7721i	0.673253	+	0.536901i	−0.226111	+	0.974101i	$0.572601\pi$
$758$	9.36225	−	7.46615i	0.340052	−	0.271183i
$759$	−12.7397	−	6.13514i	−0.462423	−	0.222691i
$760$		0			0
$761$	−8.88740	+	11.1444i	−0.322168	+	0.403986i	−0.916372	−	0.400329i	$-0.868896\pi$
$761$	−8.88740	+	11.1444i	−0.322168	+	0.403986i	0.594204	+	0.804315i	$0.297467\pi$
$762$	−0.560974	+	0.128039i	−0.0203219	+	0.00463835i
$763$	−1.90216	+	0.434157i	−0.0688630	+	0.0157175i
$764$	−11.9879	−	15.0324i	−0.433708	−	0.543852i
$765$		0			0
$766$	8.75361			0.316281
$767$	−68.8550	−	15.7157i	−2.48621	−	0.567461i
$768$	−1.29932	−	2.69806i	−0.0468851	−	0.0973579i
$769$	−40.2793	+	19.3975i	−1.45251	+	0.699491i	−0.983029	−	0.183453i	$-0.941273\pi$
$769$	−40.2793	+	19.3975i	−1.45251	+	0.699491i	−0.469479	+	0.882944i	$0.655558\pi$
$770$		0			0
$771$	−20.3967			−0.734570
$772$	39.9291	+	9.11356i	1.43708	+	0.328004i
$773$	17.9420	−	14.3083i	0.645329	−	0.514633i	−0.245251	−	0.969460i	$-0.578870\pi$
$773$	17.9420	−	14.3083i	0.645329	−	0.514633i	0.890580	+	0.454827i	$0.150299\pi$
$774$	−0.487386	−	2.13538i	−0.0175187	−	0.0767546i
$775$		0			0
$776$	−0.190530	+	0.238916i	−0.00683961	+	0.00857660i
$777$	−0.953703	−	1.98039i	−0.0342139	−	0.0710459i
$778$	4.79944	−	9.96615i	0.172068	−	0.357304i
$779$	4.57002	+	5.73063i	0.163738	+	0.205321i
$780$		0			0
$781$	32.6405	+	15.7188i	1.16797	+	0.562464i
$782$		−	4.59179i		−	0.164202i
$783$	20.9273	−	21.2845i	0.747881	−	0.760645i
$784$	19.5929			0.699745
$785$		0			0
$786$	2.77562	−	3.48052i	0.0990030	−	0.124146i
$787$	−11.2058	+	8.93631i	−0.399443	+	0.318545i	−0.802525	−	0.596619i	$-0.796510\pi$
$787$	−11.2058	+	8.93631i	−0.399443	+	0.318545i	0.403082	+	0.915164i	$0.367939\pi$
$788$	−15.2910	+	31.7521i	−0.544720	+	1.13112i
$789$	−26.6531	+	12.8355i	−0.948875	+	0.456954i
$790$		0			0
$791$	0.847740	+	3.71419i	0.0301422	+	0.132061i
$792$	−11.7733	+	2.68718i	−0.418346	+	0.0954847i
$793$	7.26175	−	5.79105i	0.257872	−	0.205646i
$794$	0.395592	−	1.73320i	0.0140390	−	0.0615090i
$795$		0			0
$796$	−0.350855	+	1.53720i	−0.0124357	+	0.0544845i
$797$	−4.42270	−	9.18382i	−0.156660	−	0.325308i	0.807835	−	0.589409i	$-0.200639\pi$
$797$	−4.42270	−	9.18382i	−0.156660	−	0.325308i	−0.964495	+	0.264101i	$0.914925\pi$
$798$	−0.202542	−	0.420583i	−0.00716992	−	0.0148885i
$799$	−6.44504	+	28.2376i	−0.228009	+	0.998974i
$800$		0			0
$801$	−1.82640	+	8.00197i	−0.0645325	+	0.282736i
$802$	−8.66636	+	6.91119i	−0.306020	+	0.244043i
$803$	−27.0884	+	6.18276i	−0.955930	+	0.218185i
$804$	−1.16152	−	5.08896i	−0.0409637	−	0.179474i
$805$		0			0
$806$	15.1681	−	7.30457i	0.534273	−	0.257292i
$807$	−13.7179	+	28.4855i	−0.482893	+	1.00274i
$808$	4.27225	−	3.40701i	0.150297	−	0.119858i
$809$	−5.59448	+	7.01526i	−0.196692	+	0.246643i	−0.870390	−	0.492363i	$-0.836133\pi$
$809$	−5.59448	+	7.01526i	−0.196692	+	0.246643i	0.673698	+	0.739006i	$0.264705\pi$
$810$		0			0
$811$	−28.5628			−1.00298			−0.501489	−	0.865164i	$-0.667214\pi$
$811$	−28.5628			−1.00298			−0.501489	+	0.865164i	$0.667214\pi$
$812$	−1.11613	+	3.27844i	−0.0391685	+	0.115051i
$813$		−	1.50066i		−	0.0526306i
$814$	9.78113	+	4.71034i	0.342828	+	0.165097i
$815$		0			0
$816$	−9.96077	−	12.4904i	−0.348697	−	0.437252i
$817$	3.48285	−	7.23221i	0.121849	−	0.253023i
$818$	−0.0546896	−	0.113564i	−0.00191218	−	0.00397068i
$819$	−1.81767	+	2.27928i	−0.0635144	+	0.0796446i
$820$		0			0
$821$	−2.52230	−	11.0509i	−0.0880290	−	0.385680i	0.911651	−	0.410965i	$-0.134808\pi$
$821$	−2.52230	−	11.0509i	−0.0880290	−	0.385680i	−0.999680	+	0.0252844i	$0.991951\pi$
$822$	−7.47690	+	5.96263i	−0.260787	+	0.207971i
$823$	5.52996	+	1.26218i	0.192762	+	0.0439967i	0.317812	−	0.948154i	$-0.397052\pi$
$823$	5.52996	+	1.26218i	0.192762	+	0.0439967i	−0.125050	+	0.992150i	$0.539909\pi$
$824$	23.1008			0.804755
$825$		0			0
$826$	−1.78794	+	0.861025i	−0.0622103	+	0.0299589i
$827$	1.25966	+	2.61572i	0.0438028	+	0.0909575i	0.921722	−	0.387852i	$-0.126783\pi$
$827$	1.25966	+	2.61572i	0.0438028	+	0.0909575i	−0.877919	+	0.478809i	$0.841069\pi$
$828$	5.82834	+	1.33028i	0.202549	+	0.0462305i
$829$	45.2137			1.57034			0.785169	−	0.619282i	$-0.212576\pi$
$829$	45.2137			1.57034			0.785169	+	0.619282i	$0.212576\pi$
$830$		0			0
$831$	−8.29172	−	10.3975i	−0.287636	−	0.360685i
$832$	20.0108	−	4.56734i	0.693750	−	0.158344i
$833$	30.1109	−	6.87263i	1.04328	−	0.238122i
$834$	5.76726	−	7.23191i	0.199704	−	0.250421i
$835$		0			0
$836$	−18.8986	−	9.10107i	−0.653621	−	0.314767i
$837$	29.0005	−	23.1271i	1.00240	−	0.799391i
$838$	−9.21664	−	7.35003i	−0.318384	−	0.253902i
$839$	−41.1073	−	19.7962i	−1.41918	−	0.683442i	−0.442229	−	0.896902i	$-0.645812\pi$
$839$	−41.1073	−	19.7962i	−1.41918	−	0.683442i	−0.976952	+	0.213460i	$0.931527\pi$
$840$		0			0
$841$	22.9758	+	17.6949i	0.792270	+	0.610170i
$842$			7.82477i			0.269659i
$843$	−8.80793	+	18.2899i	−0.303361	+	0.629936i
$844$	−20.5248	+	25.7372i	−0.706491	+	0.885912i
$845$		0			0
$846$	3.73437	+	1.79838i	0.128390	+	0.0618294i
$847$	−2.07404	−	4.30678i	−0.0712648	−	0.147983i
$848$	10.4580	+	8.33997i	0.359129	+	0.286396i
$849$	1.45593	+	6.37883i	0.0499673	+	0.218921i
$850$		0			0
$851$	−7.07002	−	8.86553i	−0.242357	−	0.303906i
$852$	16.0686	+	3.66756i	0.550503	+	0.125649i
$853$			36.9288i			1.26442i	0.774797	+	0.632210i	$0.217852\pi$
$853$			36.9288i			1.26442i	−0.774797	+	0.632210i	$0.782148\pi$
$854$	0.0580735	−	0.254437i	0.00198724	−	0.00870665i
$855$		0			0
$856$	−24.7642	+	11.9258i	−0.846423	+	0.407616i
$857$	−34.6589	−	7.91066i	−1.18392	−	0.270223i	−0.415156	−	0.909750i	$-0.636273\pi$
$857$	−34.6589	−	7.91066i	−1.18392	−	0.270223i	−0.768768	+	0.639527i	$0.779130\pi$
$858$			15.4940i			0.528955i
$859$	9.43070	−	41.3186i	0.321771	−	1.40977i	−0.512628	−	0.858611i	$-0.671328\pi$
$859$	9.43070	−	41.3186i	0.321771	−	1.40977i	0.834399	−	0.551161i	$-0.185815\pi$
$860$		0			0
$861$	0.307979	+	1.34934i	0.0104959	+	0.0459855i
$862$	12.0599	−	2.75259i	0.410762	−	0.0937537i
$863$	−38.9193	−	31.0371i	−1.32483	−	1.05652i	−0.993599	−	0.112966i	$-0.963965\pi$
$863$	−38.9193	−	31.0371i	−1.32483	−	1.05652i	−0.331231	−	0.943550i	$-0.607464\pi$
$864$	−23.2359	+	11.1898i	−0.790500	+	0.380685i
$865$		0			0
$866$	−1.63036	−	2.04440i	−0.0554018	−	0.0694717i
$867$	−3.11555	−	2.48457i	−0.105810	−	0.0843803i
$868$	−1.86729	+	3.87747i	−0.0633800	+	0.131610i
$869$	23.0398			0.781572
$870$		0			0
$871$	13.1317			0.444950
$872$	4.01341	−	8.33393i	0.135911	−	0.282222i
$873$	−0.204042	−	0.162718i	−0.00690579	−	0.00550719i
$874$	−1.50149	−	1.88281i	−0.0507887	−	0.0636870i
$875$		0			0
$876$	−11.3889	+	5.48460i	−0.384795	+	0.185307i
$877$	17.1167	+	13.6501i	0.577990	+	0.460931i	0.868326	−	0.495993i	$-0.165196\pi$
$877$	17.1167	+	13.6501i	0.577990	+	0.460931i	−0.290337	+	0.956925i	$0.593767\pi$
$878$	−6.82974	+	1.55884i	−0.230492	+	0.0526084i
$879$	−1.87681	−	8.22282i	−0.0633031	−	0.277349i
$880$		0			0
$881$	7.46130	−	32.6901i	0.251378	−	1.10136i	−0.678822	−	0.734303i	$-0.737509\pi$
$881$	7.46130	−	32.6901i	0.251378	−	1.10136i	0.930199	−	0.367055i	$-0.119634\pi$
$882$		−	4.41981i		−	0.148823i
$883$	−15.7230	−	3.58868i	−0.529122	−	0.120769i	−0.0503898	−	0.998730i	$-0.516046\pi$
$883$	−15.7230	−	3.58868i	−0.529122	−	0.120769i	−0.478732	+	0.877961i	$0.658904\pi$
$884$	41.2422	−	19.8612i	1.38713	−	0.668004i
$885$		0			0
$886$	0.667326	−	2.92375i	0.0224192	−	0.0982252i
$887$			52.7391i			1.77081i	0.464823	+	0.885403i	$0.346118\pi$
$887$			52.7391i			1.77081i	−0.464823	+	0.885403i	$0.653882\pi$
$888$	10.1596	+	2.31886i	0.340934	+	0.0778160i
$889$	0.230718	+	0.289311i	0.00773802	+	0.00970317i
$890$		0			0
$891$	2.83190	+	12.4074i	0.0948724	+	0.415663i
$892$	2.56169	+	2.04288i	0.0857716	+	0.0684006i
$893$	6.59082	+	13.6860i	0.220553	+	0.457984i
$894$	9.30343	+	4.48030i	0.311153	+	0.149844i
$895$		0			0
$896$	2.43027	−	3.04746i	0.0811897	−	0.101809i
$897$	7.02180	−	14.5809i	0.234451	−	0.486842i
$898$			5.48294i			0.182968i
$899$	25.6972	+	25.2659i	0.857048	+	0.842666i
$900$		0			0
$901$	18.9976	+	9.14877i	0.632902	+	0.304790i
$902$	−5.34444	−	4.26205i	−0.177950	−	0.141911i
$903$	1.18505	−	0.945042i	0.0394358	−	0.0314490i
$904$	−16.2729	−	7.83663i	−0.541230	−	0.260642i
$905$		0			0
$906$	−2.60470	+	3.26619i	−0.0865355	+	0.108512i
$907$	−29.0954	+	6.64084i	−0.966098	+	0.220506i	−0.676336	−	0.736593i	$-0.736433\pi$
$907$	−29.0954	+	6.64084i	−0.966098	+	0.220506i	−0.289762	+	0.957099i	$0.593576\pi$
$908$	−24.3421	+	5.55592i	−0.807820	+	0.184380i
$909$	2.90970	+	3.64865i	0.0965086	+	0.121018i
$910$		0			0
$911$	−9.34050			−0.309465			−0.154732	−	0.987956i	$-0.549452\pi$
$911$	−9.34050			−0.309465			−0.154732	+	0.987956i	$0.549452\pi$
$912$	−8.16860	−	1.86443i	−0.270489	−	0.0617374i
$913$	9.54627	+	19.8230i	0.315936	+	0.656047i
$914$	−5.47823	+	2.63818i	−0.181204	+	0.0872631i
$915$		0			0
$916$	23.0151			0.760439
$917$	−2.79116	−	0.637063i	−0.0921721	−	0.0210377i
$918$	−8.66719	+	6.91185i	−0.286060	+	0.228125i
$919$	−4.09903	−	17.9590i	−0.135215	−	0.592414i	−0.996448	−	0.0842049i	$-0.973165\pi$
$919$	−4.09903	−	17.9590i	−0.135215	−	0.592414i	0.861234	−	0.508209i	$-0.169692\pi$
$920$		0			0
$921$	−3.51275	+	4.40484i	−0.115749	+	0.145145i
$922$	2.24150	+	4.65452i	0.0738199	+	0.153289i
$923$	−17.9905	+	37.3577i	−0.592166	+	1.22964i
$924$	−2.46950	−	3.09666i	−0.0812406	−	0.101872i
$925$		0			0
$926$	−2.90408	−	1.39853i	−0.0954341	−	0.0459587i
$927$			19.7289i			0.647981i
$928$	−13.5097	−	21.1020i	−0.443476	−	0.692708i
$929$	4.84654			0.159010			0.0795050	−	0.996834i	$-0.474666\pi$
$929$	4.84654			0.159010			0.0795050	+	0.996834i	$0.474666\pi$
$930$		0			0
$931$	10.0993	−	12.6642i	0.330992	−	0.415051i
$932$	−12.4904	+	9.96077i	−0.409137	+	0.326276i
$933$	−6.82611	+	14.1746i	−0.223477	+	0.464054i
$934$	0.827356	−	0.398434i	0.0270719	−	0.0130371i
$935$		0			0
$936$	−3.07553	−	13.4748i	−0.100527	−	0.440437i
$937$	−43.5933	+	9.94989i	−1.42413	+	0.325049i	−0.864057	−	0.503394i	$-0.832084\pi$
$937$	−43.5933	+	9.94989i	−1.42413	+	0.325049i	−0.560074	+	0.828443i	$0.689227\pi$
$938$	0.288478	−	0.230054i	0.00941915	−	0.00751152i
$939$	−5.33877	+	23.3907i	−0.174224	+	0.763326i
$940$		0			0
$941$	−3.02297	+	13.2445i	−0.0985459	+	0.431758i	−0.999999	−	0.00111821i	$-0.999644\pi$
$941$	−3.02297	+	13.2445i	−0.0985459	+	0.431758i	0.901453	+	0.432876i	$0.142501\pi$
$942$	4.39177	+	9.11960i	0.143092	+	0.297133i
$943$	3.09795	+	6.43296i	0.100883	+	0.209486i
$944$	−7.92585	+	34.7254i	−0.257965	+	1.13022i
$945$		0			0
$946$	−1.66583	+	7.29850i	−0.0541609	+	0.237295i
$947$	−11.7365	+	9.35958i	−0.381387	+	0.304146i	−0.795353	−	0.606147i	$-0.792715\pi$
$947$	−11.7365	+	9.35958i	−0.381387	+	0.304146i	0.413966	+	0.910292i	$0.364143\pi$
$948$	10.2191	−	2.33244i	0.331900	−	0.0757540i
$949$	−7.07630	−	31.0033i	−0.229706	−	1.00641i
$950$		0			0
$951$	3.22252	−	1.55188i	0.104497	−	0.0503233i
$952$	1.17747	−	2.44504i	0.0381620	−	0.0792443i
$953$	40.5339	−	32.3247i	1.31302	−	1.04710i	0.317931	−	0.948114i	$-0.397012\pi$
$953$	40.5339	−	32.3247i	1.31302	−	1.04710i	0.995089	−	0.0989849i	$-0.0315596\pi$
$954$	1.88135	−	2.35914i	0.0609111	−	0.0763801i
$955$		0			0
$956$	46.0659			1.48988
$957$	−31.2113	+	11.2186i	−1.00892	+	0.362647i
$958$		−	1.73078i		−	0.0559188i
$959$	5.54115	+	2.66848i	0.178933	+	0.0861696i
$960$		0			0
$961$	8.59365	+	10.7761i	0.277215	+	0.347616i
$962$	−5.39109	+	11.1947i	−0.173816	+	0.360932i
$963$	−10.1850	−	21.1494i	−0.328208	−	0.681531i
$964$	10.9330	−	13.7095i	0.352127	−	0.441553i
$965$		0			0
$966$	−0.101187	−	0.443330i	−0.00325564	−	0.0142639i
$967$	32.5437	−	25.9527i	1.04653	−	0.834583i	0.0600094	−	0.998198i	$-0.480887\pi$
$967$	32.5437	−	25.9527i	1.04653	−	0.834583i	0.986524	+	0.163615i	$0.0523155\pi$
$968$	22.0943	+	5.04288i	0.710137	+	0.162084i
$969$	−13.2078			−0.424294
$970$		0			0
$971$	50.2497	−	24.1990i	1.61259	−	0.776583i	0.612685	−	0.790327i	$-0.290089\pi$
$971$	50.2497	−	24.1990i	1.61259	−	0.776583i	0.999906	+	0.0137446i	$0.00437519\pi$
$972$	−10.4887	−	21.7799i	−0.336424	−	0.698592i
$973$	−5.79954	−	1.32371i	−0.185925	−	0.0424361i
$974$	4.38165			0.140397
$975$		0			0
$976$	−2.92058	−	3.66230i	−0.0934856	−	0.117227i
$977$	47.7309	−	10.8943i	1.52705	−	0.348538i	0.625155	−	0.780501i	$-0.285036\pi$
$977$	47.7309	−	10.8943i	1.52705	−	0.348538i	0.901892	+	0.431962i	$0.142179\pi$
$978$	−6.83918	+	1.56100i	−0.218693	+	0.0499152i
$979$	17.4909	−	21.9329i	0.559012	−	0.700978i
$980$		0			0
$981$	7.11745	+	3.42758i	0.227243	+	0.109434i
$982$	2.71092	−	2.16189i	0.0865091	−	0.0689887i
$983$	−4.04466	−	3.22550i	−0.129004	−	0.102878i	0.556862	−	0.830605i	$-0.312005\pi$
$983$	−4.04466	−	3.22550i	−0.129004	−	0.102878i	−0.685867	+	0.727727i	$0.740577\pi$
$984$	−5.91185	−	2.84700i	−0.188463	−	0.0907590i
$985$		0			0
$986$	−7.67994	−	7.55106i	−0.244579	−	0.240475i
$987$			2.86831i			0.0912994i
$988$	10.4164	−	21.6298i	0.331389	−	0.688136i
$989$	4.87531	−	6.11345i	0.155026	−	0.194396i
$990$		0			0
$991$	15.1838	+	7.31214i	0.482330	+	0.232278i	0.659216	−	0.751953i	$-0.270888\pi$
$991$	15.1838	+	7.31214i	0.482330	+	0.232278i	−0.176886	+	0.984231i	$0.556602\pi$
$992$	−13.5097	−	28.0531i	−0.428932	−	0.890687i
$993$	3.05550	+	2.43668i	0.0969634	+	0.0773257i
$994$	0.259251	+	1.13585i	0.00822295	+	0.0360271i
$995$		0			0
$996$	6.24094	+	7.82589i	0.197752	+	0.247973i
$997$	−37.2517	−	8.50245i	−1.17977	−	0.269275i	−0.412719	−	0.910858i	$-0.635421\pi$
$997$	−37.2517	−	8.50245i	−1.17977	−	0.269275i	−0.767054	+	0.641583i	$0.778278\pi$
$998$		−	9.15239i		−	0.289714i
$999$	−6.09179	+	26.6899i	−0.192736	+	0.844431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.r.b.74.1		12
5.2	odd	4		725.2.l.b.451.1		6
5.3	odd	4		29.2.d.a.16.1	✓	6
5.4	even	2	inner	725.2.r.b.74.2		12
15.8	even	4		261.2.k.a.190.1		6
20.3	even	4		464.2.u.f.161.1		6
29.20	even	7	inner	725.2.r.b.49.2		12
145.3	even	28		841.2.b.c.840.4		6
145.8	even	28		841.2.e.d.270.2		12
145.13	odd	28		841.2.d.a.645.1		6
145.18	even	28		841.2.e.b.196.1		12
145.23	odd	28		841.2.d.e.605.1		6
145.28	odd	4		841.2.d.d.190.1		6
145.33	odd	28		841.2.d.c.778.1		6
145.38	odd	28		841.2.d.d.571.1		6
145.43	even	28		841.2.e.b.236.1		12
145.48	even	28		841.2.e.c.63.1		12
145.49	even	14	inner	725.2.r.b.49.1		12
145.53	odd	28		841.2.d.b.574.1		6
145.63	odd	28		841.2.d.c.574.1		6
145.68	even	28		841.2.e.c.63.2		12
145.73	even	28		841.2.e.b.236.2		12
145.78	odd	28		29.2.d.a.20.1	yes	6
145.83	odd	28		841.2.d.b.778.1		6
145.93	odd	28		841.2.d.a.605.1		6
145.98	even	28		841.2.e.b.196.2		12
145.103	odd	28		841.2.d.e.645.1		6
145.107	odd	28		725.2.l.b.426.1		6
145.108	even	28		841.2.e.d.270.1		12
145.113	even	28		841.2.b.c.840.3		6
145.118	even	28		841.2.e.c.267.2		12
145.123	odd	28		841.2.a.e.1.2		3
145.128	even	4		841.2.e.d.651.1		12
145.133	even	4		841.2.e.d.651.2		12
145.138	odd	28		841.2.a.f.1.2		3
145.143	even	28		841.2.e.c.267.1		12
435.368	even	28		261.2.k.a.136.1		6
435.413	even	28		7569.2.a.r.1.2		3
435.428	even	28		7569.2.a.p.1.2		3
580.223	even	28		464.2.u.f.49.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.16.1	✓	6	5.3	odd	4
29.2.d.a.20.1	yes	6	145.78	odd	28
261.2.k.a.136.1		6	435.368	even	28
261.2.k.a.190.1		6	15.8	even	4
464.2.u.f.49.1		6	580.223	even	28
464.2.u.f.161.1		6	20.3	even	4
725.2.l.b.426.1		6	145.107	odd	28
725.2.l.b.451.1		6	5.2	odd	4
725.2.r.b.49.1		12	145.49	even	14	inner
725.2.r.b.49.2		12	29.20	even	7	inner
725.2.r.b.74.1		12	1.1	even	1	trivial
725.2.r.b.74.2		12	5.4	even	2	inner
841.2.a.e.1.2		3	145.123	odd	28
841.2.a.f.1.2		3	145.138	odd	28
841.2.b.c.840.3		6	145.113	even	28
841.2.b.c.840.4		6	145.3	even	28
841.2.d.a.605.1		6	145.93	odd	28
841.2.d.a.645.1		6	145.13	odd	28
841.2.d.b.574.1		6	145.53	odd	28
841.2.d.b.778.1		6	145.83	odd	28
841.2.d.c.574.1		6	145.63	odd	28
841.2.d.c.778.1		6	145.33	odd	28
841.2.d.d.190.1		6	145.28	odd	4
841.2.d.d.571.1		6	145.38	odd	28
841.2.d.e.605.1		6	145.23	odd	28
841.2.d.e.645.1		6	145.103	odd	28
841.2.e.b.196.1		12	145.18	even	28
841.2.e.b.196.2		12	145.98	even	28
841.2.e.b.236.1		12	145.43	even	28
841.2.e.b.236.2		12	145.73	even	28
841.2.e.c.63.1		12	145.48	even	28
841.2.e.c.63.2		12	145.68	even	28
841.2.e.c.267.1		12	145.143	even	28
841.2.e.c.267.2		12	145.118	even	28
841.2.e.d.270.1		12	145.108	even	28
841.2.e.d.270.2		12	145.8	even	28
841.2.e.d.651.1		12	145.128	even	4
841.2.e.d.651.2		12	145.133	even	4
7569.2.a.p.1.2		3	435.428	even	28
7569.2.a.r.1.2		3	435.413	even	28

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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.r (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.193096 + 0.400969i) q^{2} +(0.974928 + 0.777479i) q^{3} +(1.12349 + 1.40881i) q^{4} +(-0.500000 + 0.240787i) q^{6} +(0.279032 + 0.222521i) q^{7} +(-1.64960 + 0.376510i) q^{8} +(-0.321552 - 1.40881i) q^{9} +O(q^{10})\)	\(q+(-0.193096 + 0.400969i) q^{2} +(0.974928 + 0.777479i) q^{3} +(1.12349 + 1.40881i) q^{4} +(-0.500000 + 0.240787i) q^{6} +(0.279032 + 0.222521i) q^{7} +(-1.64960 + 0.376510i) q^{8} +(-0.321552 - 1.40881i) q^{9} +(-1.09903 + 4.81517i) q^{11} +2.24698i q^{12} +(-5.51107 - 1.25786i) q^{13} +(-0.143104 + 0.0689153i) q^{14} +(-0.634375 + 2.77938i) q^{16} +4.49396i q^{17} +(0.626980 + 0.143104i) q^{18} +(1.46950 + 1.84270i) q^{19} +(0.0990311 + 0.433884i) q^{21} +(-1.71851 - 1.37047i) q^{22} +(0.996152 + 2.06853i) q^{23} +(-1.90097 - 0.915458i) q^{24} +(1.56853 - 1.96688i) q^{26} +(2.40496 - 4.99396i) q^{27} +0.643104i q^{28} +(5.09783 + 1.73553i) q^{29} +(6.02930 + 2.90356i) q^{31} +(-3.63770 - 2.90097i) q^{32} +(-4.81517 + 3.83997i) q^{33} +(-1.80194 - 0.867767i) q^{34} +(1.62349 - 2.03579i) q^{36} +(-4.81517 + 1.09903i) q^{37} +(-1.02262 + 0.233406i) q^{38} +(-4.39493 - 5.51107i) q^{39} +3.10992 q^{41} +(-0.193096 - 0.0440730i) q^{42} +(-1.47773 - 3.06853i) q^{43} +(-8.01842 + 3.86147i) q^{44} -1.02177 q^{46} +(6.28345 + 1.43416i) q^{47} +(-2.77938 + 2.21648i) q^{48} +(-1.52930 - 6.70031i) q^{49} +(-3.49396 + 4.38129i) q^{51} +(-4.41953 - 9.17725i) q^{52} +(2.03579 - 4.22737i) q^{53} +(1.53803 + 1.92863i) q^{54} +(-0.544073 - 0.262012i) q^{56} +2.93900i q^{57} +(-1.68027 + 1.70895i) q^{58} +12.4940 q^{59} +(-1.02446 + 1.28463i) q^{61} +(-2.32847 + 1.85690i) q^{62} +(0.223767 - 0.464656i) q^{63} +(-3.27144 + 1.57544i) q^{64} +(-0.609916 - 2.67222i) q^{66} +(-2.26480 + 0.516926i) q^{67} +(-6.33114 + 5.04892i) q^{68} +(-0.637063 + 2.79116i) q^{69} +(1.63222 - 7.15122i) q^{71} +(1.06086 + 2.20291i) q^{72} +(2.44088 + 5.06853i) q^{73} +(0.489115 - 2.14295i) q^{74} +(-0.945042 + 4.14050i) q^{76} +(-1.37814 + 1.09903i) q^{77} +(3.05841 - 0.698062i) q^{78} +(-1.03803 - 4.54792i) q^{79} +(2.32155 - 1.11800i) q^{81} +(-0.600514 + 1.24698i) q^{82} +(3.48285 - 2.77748i) q^{83} +(-0.500000 + 0.626980i) q^{84} +1.51573 q^{86} +(3.62068 + 5.65548i) q^{87} -8.35690i q^{88} +(-5.11745 - 2.46443i) q^{89} +(-1.25786 - 1.57731i) q^{91} +(-1.79500 + 3.72737i) q^{92} +(3.62068 + 7.51842i) q^{93} +(-1.78836 + 2.24254i) q^{94} +(-1.29105 - 5.65647i) q^{96} +(0.141202 - 0.112605i) q^{97} +(2.98192 + 0.680604i) q^{98} +7.13706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 6 q^{6} - 12 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 - 6 * q^6 - 12 * q^9	\( 12 q + 4 q^{4} - 6 q^{6} - 12 q^{9} - 22 q^{11} - 18 q^{14} + 8 q^{16} - 2 q^{19} + 10 q^{21} - 14 q^{24} + 8 q^{26} - 12 q^{29} + 10 q^{31} - 4 q^{34} + 10 q^{36} - 6 q^{39} + 40 q^{41} - 40 q^{44} + 44 q^{49} - 4 q^{51} - 12 q^{54} - 14 q^{56} + 112 q^{59} + 6 q^{61} - 2 q^{64} - 10 q^{66} + 14 q^{69} + 42 q^{71} + 12 q^{74} - 10 q^{76} + 18 q^{79} + 36 q^{81} - 6 q^{84} - 32 q^{86} - 14 q^{89} + 10 q^{91} - 16 q^{94} - 4 q^{96} + 64 q^{99}+O(q^{100}) \) 12 * q + 4 * q^4 - 6 * q^6 - 12 * q^9 - 22 * q^11 - 18 * q^14 + 8 * q^16 - 2 * q^19 + 10 * q^21 - 14 * q^24 + 8 * q^26 - 12 * q^29 + 10 * q^31 - 4 * q^34 + 10 * q^36 - 6 * q^39 + 40 * q^41 - 40 * q^44 + 44 * q^49 - 4 * q^51 - 12 * q^54 - 14 * q^56 + 112 * q^59 + 6 * q^61 - 2 * q^64 - 10 * q^66 + 14 * q^69 + 42 * q^71 + 12 * q^74 - 10 * q^76 + 18 * q^79 + 36 * q^81 - 6 * q^84 - 32 * q^86 - 14 * q^89 + 10 * q^91 - 16 * q^94 - 4 * q^96 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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