LMFDB - Embedded newform 700.2.p.e.451.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(451,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("700.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.p (of order $6$, degree $2$, 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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.12
Character	$\chi$	$=$	700.451
Dual form			700.2.p.e.551.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.843578 - 1.13507i) q^{2} +(-0.940044 + 1.62820i) q^{3} +(-0.576753 - 1.91503i) q^{4} +(1.05512 + 2.44053i) q^{6} +(-2.57589 + 0.603960i) q^{7} +(-2.66023 - 0.960828i) q^{8} +(-0.267367 - 0.463092i) q^{9} +O(q^{10})$	\(q+(0.843578 - 1.13507i) q^{2} +(-0.940044 + 1.62820i) q^{3} +(-0.576753 - 1.91503i) q^{4} +(1.05512 + 2.44053i) q^{6} +(-2.57589 + 0.603960i) q^{7} +(-2.66023 - 0.960828i) q^{8} +(-0.267367 - 0.463092i) q^{9} +(1.20016 + 0.692910i) q^{11} +(3.66024 + 0.861146i) q^{12} -5.79701i q^{13} +(-1.48743 + 3.43330i) q^{14} +(-3.33471 + 2.20900i) q^{16} +(-4.04066 - 2.33288i) q^{17} +(-0.751185 - 0.0871757i) q^{18} +(-2.74619 - 4.75654i) q^{19} +(1.43808 - 4.76183i) q^{21} +(1.79892 - 0.777733i) q^{22} +(-4.02241 + 2.32234i) q^{23} +(4.06516 - 3.42817i) q^{24} +(-6.57999 - 4.89023i) q^{26} -4.63492 q^{27} +(2.64226 + 4.58459i) q^{28} -2.04334 q^{29} +(-0.832529 + 1.44198i) q^{31} +(-0.305726 + 5.64859i) q^{32} +(-2.25640 + 1.30273i) q^{33} +(-6.05658 + 2.61846i) q^{34} +(-0.732633 + 0.779106i) q^{36} +(0.142718 + 0.247194i) q^{37} +(-7.71561 - 0.895403i) q^{38} +(9.43872 + 5.44945i) q^{39} -8.21024i q^{41} +(-4.19186 - 5.64930i) q^{42} -3.30992i q^{43} +(0.634754 - 2.69798i) q^{44} +(-0.757206 + 6.52477i) q^{46} +(0.0690967 + 0.119679i) q^{47} +(-0.461929 - 7.50615i) q^{48} +(6.27046 - 3.11147i) q^{49} +(7.59680 - 4.38601i) q^{51} +(-11.1015 + 3.34344i) q^{52} +(-3.36415 + 5.82688i) q^{53} +(-3.90992 + 5.26094i) q^{54} +(7.43277 + 0.868321i) q^{56} +10.3262 q^{57} +(-1.72372 + 2.31933i) q^{58} +(-0.832529 + 1.44198i) q^{59} +(-2.49596 + 1.44104i) q^{61} +(0.934444 + 2.16140i) q^{62} +(0.968397 + 1.03140i) q^{63} +(6.15362 + 5.11204i) q^{64} +(-0.424760 + 3.66012i) q^{66} +(10.0859 + 5.82309i) q^{67} +(-2.13708 + 9.08350i) q^{68} -8.73240i q^{69} -2.29926i q^{71} +(0.266304 + 1.48882i) q^{72} +(-4.04066 - 2.33288i) q^{73} +(0.400976 + 0.0465336i) q^{74} +(-7.52506 + 8.00239i) q^{76} +(-3.50996 - 1.06002i) q^{77} +(14.1478 - 6.11654i) q^{78} +(-8.88033 + 5.12706i) q^{79} +(5.15913 - 8.93587i) q^{81} +(-9.31917 - 6.92598i) q^{82} +0.0814876 q^{83} +(-9.94849 - 0.00758271i) q^{84} +(-3.75698 - 2.79218i) q^{86} +(1.92083 - 3.32698i) q^{87} +(-2.52692 - 2.99644i) q^{88} +(3.22105 - 1.85967i) q^{89} +(3.50116 + 14.9325i) q^{91} +(6.76729 + 6.36363i) q^{92} +(-1.56523 - 2.71106i) q^{93} +(0.194132 + 0.0225292i) q^{94} +(-8.90966 - 5.80771i) q^{96} -3.88816i q^{97} +(1.75790 - 9.74217i) q^{98} -0.741044i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 6 q^{4} - 4 q^{9}+O(q^{10}) $ 32 * q - 6 * q^4 - 4 * q^9	$ 32 q - 6 q^{4} - 4 q^{9} - 22 q^{14} + 18 q^{16} - 52 q^{21} + 48 q^{24} - 18 q^{26} - 28 q^{36} + 26 q^{44} - 22 q^{46} - 48 q^{54} - 16 q^{56} + 36 q^{61} - 36 q^{64} - 24 q^{66} - 14 q^{74} + 72 q^{81} - 56 q^{84} + 8 q^{86} + 108 q^{89} - 30 q^{94} + 60 q^{96}+O(q^{100}) $ 32 * q - 6 * q^4 - 4 * q^9 - 22 * q^14 + 18 * q^16 - 52 * q^21 + 48 * q^24 - 18 * q^26 - 28 * q^36 + 26 * q^44 - 22 * q^46 - 48 * q^54 - 16 * q^56 + 36 * q^61 - 36 * q^64 - 24 * q^66 - 14 * q^74 + 72 * q^81 - 56 * q^84 + 8 * q^86 + 108 * q^89 - 30 * q^94 + 60 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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 $

$2$	0.843578	−	1.13507i	0.596500	−	0.802613i
$2$	0.843578	−	1.13507i	0.596500	−	0.802613i
$3$	−0.940044	+	1.62820i	−0.542735	+	0.940044i	0.456011	+	0.889974i	$0.349278\pi$
$3$	−0.940044	+	1.62820i	−0.542735	+	0.940044i	−0.998746	+	0.0500701i	$0.984056\pi$
$4$	−0.576753	−	1.91503i	−0.288376	−	0.957517i
$5$		0			0
$5$		0			0
$6$	1.05512	+	2.44053i	0.430751	+	0.996342i
$7$	−2.57589	+	0.603960i	−0.973597	+	0.228275i
$7$	−2.57589	+	0.603960i	−0.973597	+	0.228275i
$8$	−2.66023	−	0.960828i	−0.940532	−	0.339704i
$9$	−0.267367	−	0.463092i	−0.0891222	−	0.154364i
$10$		0			0
$11$	1.20016	+	0.692910i	0.361860	+	0.208920i	0.669897	−	0.742454i	$-0.266338\pi$
$11$	1.20016	+	0.692910i	0.361860	+	0.208920i	−0.308036	+	0.951375i	$0.599672\pi$
$12$	3.66024	+	0.861146i	1.05662	+	0.248591i
$13$		−	5.79701i		−	1.60780i	−0.594764	−	0.803901i	$-0.702754\pi$
$13$		−	5.79701i		−	1.60780i	0.594764	−	0.803901i	$-0.297246\pi$
$14$	−1.48743	+	3.43330i	−0.397533	+	0.917588i
$15$		0			0
$16$	−3.33471	+	2.20900i	−0.833678	+	0.552250i
$17$	−4.04066	−	2.33288i	−0.980004	−	0.565806i	−0.0777328	−	0.996974i	$-0.524768\pi$
$17$	−4.04066	−	2.33288i	−0.980004	−	0.565806i	−0.902271	+	0.431169i	$0.858101\pi$
$18$	−0.751185	−	0.0871757i	−0.177056	−	0.0205475i
$19$	−2.74619	−	4.75654i	−0.630019	−	1.09122i	−0.987547	−	0.157322i	$-0.949714\pi$
$19$	−2.74619	−	4.75654i	−0.630019	−	1.09122i	0.357529	−	0.933902i	$-0.383619\pi$
$20$		0			0
$21$	1.43808	−	4.76183i	0.313816	−	1.03912i
$22$	1.79892	−	0.777733i	0.383532	−	0.165813i
$23$	−4.02241	+	2.32234i	−0.838730	+	0.484241i	−0.856832	−	0.515595i	$-0.827571\pi$
$23$	−4.02241	+	2.32234i	−0.838730	+	0.484241i	0.0181024	+	0.999836i	$0.494238\pi$
$24$	4.06516	−	3.42817i	0.829797	−	0.699773i
$25$		0			0
$26$	−6.57999	−	4.89023i	−1.29044	−	0.959053i
$27$	−4.63492			−0.891991
$28$	2.64226	+	4.58459i	0.499340	+	0.866406i
$29$	−2.04334			−0.379439			−0.189720	−	0.981838i	$-0.560758\pi$
$29$	−2.04334			−0.379439			−0.189720	+	0.981838i	$0.560758\pi$
$30$		0			0
$31$	−0.832529	+	1.44198i	−0.149527	+	0.258988i	−0.931053	−	0.364885i	$-0.881108\pi$
$31$	−0.832529	+	1.44198i	−0.149527	+	0.258988i	0.781526	+	0.623873i	$0.214442\pi$
$32$	−0.305726	+	5.64859i	−0.0540452	+	0.998538i
$33$	−2.25640	+	1.30273i	−0.392789	+	0.226777i
$34$	−6.05658	+	2.61846i	−1.03870	+	0.449062i
$35$		0			0
$36$	−0.732633	+	0.779106i	−0.122106	+	0.129851i
$37$	0.142718	+	0.247194i	0.0234627	+	0.0406385i	0.877518	−	0.479543i	$-0.159198\pi$
$37$	0.142718	+	0.247194i	0.0234627	+	0.0406385i	−0.854056	+	0.520182i	$0.825864\pi$
$38$	−7.71561	−	0.895403i	−1.25164	−	0.145254i
$39$	9.43872	+	5.44945i	1.51140	+	0.872610i
$40$		0			0
$41$		−	8.21024i		−	1.28222i	−0.767447	−	0.641112i	$-0.778473\pi$
$41$		−	8.21024i		−	1.28222i	0.767447	−	0.641112i	$-0.221527\pi$
$42$	−4.19186	−	5.64930i	−0.646818	−	0.871706i
$43$		−	3.30992i		−	0.504758i	−0.967628	−	0.252379i	$-0.918787\pi$
$43$		−	3.30992i		−	0.504758i	0.967628	−	0.252379i	$-0.0812130\pi$
$44$	0.634754	−	2.69798i	0.0956927	−	0.406735i
$45$		0			0
$46$	−0.757206	+	6.52477i	−0.111644	+	0.962025i
$47$	0.0690967	+	0.119679i	0.0100788	+	0.0174570i	0.871021	−	0.491246i	$-0.163458\pi$
$47$	0.0690967	+	0.119679i	0.0100788	+	0.0174570i	−0.860942	+	0.508703i	$0.830125\pi$
$48$	−0.461929	−	7.50615i	−0.0666737	−	1.08342i
$49$	6.27046	−	3.11147i	0.895781	−	0.444496i
$50$		0			0
$51$	7.59680	−	4.38601i	1.06376	−	0.614165i
$52$	−11.1015	+	3.34344i	−1.53950	+	0.463652i
$53$	−3.36415	+	5.82688i	−0.462102	+	0.800384i	−0.999066	−	0.0432214i	$-0.986238\pi$
$53$	−3.36415	+	5.82688i	−0.462102	+	0.800384i	0.536964	+	0.843605i	$0.319571\pi$
$54$	−3.90992	+	5.26094i	−0.532072	+	0.715924i
$55$		0			0
$56$	7.43277	+	0.868321i	0.993245	+	0.116034i
$57$	10.3262			1.36773
$58$	−1.72372	+	2.31933i	−0.226335	+	0.304543i
$59$	−0.832529	+	1.44198i	−0.108386	+	0.187730i	−0.915117	−	0.403189i	$-0.867902\pi$
$59$	−0.832529	+	1.44198i	−0.108386	+	0.187730i	0.806730	+	0.590920i	$0.201235\pi$
$60$		0			0
$61$	−2.49596	+	1.44104i	−0.319575	+	0.184507i	−0.651203	−	0.758903i	$-0.725735\pi$
$61$	−2.49596	+	1.44104i	−0.319575	+	0.184507i	0.331628	+	0.943410i	$0.392402\pi$
$62$	0.934444	+	2.16140i	0.118674	+	0.274498i
$63$	0.968397	+	1.03140i	0.122007	+	0.129944i
$64$	6.15362	+	5.11204i	0.769202	+	0.639005i
$65$		0			0
$66$	−0.424760	+	3.66012i	−0.0522843	+	0.450529i
$67$	10.0859	+	5.82309i	1.23219	+	0.711404i	0.967485	−	0.252927i	$-0.0813931\pi$
$67$	10.0859	+	5.82309i	1.23219	+	0.711404i	0.264702	+	0.964330i	$0.414726\pi$
$68$	−2.13708	+	9.08350i	−0.259159	+	1.10154i
$69$		−	8.73240i		−	1.05126i
$70$		0			0
$71$		−	2.29926i		−	0.272871i	−0.990649	−	0.136436i	$-0.956435\pi$
$71$		−	2.29926i		−	0.272871i	0.990649	−	0.136436i	$-0.0435647\pi$
$72$	0.266304	+	1.48882i	0.0313842	+	0.175460i
$73$	−4.04066	−	2.33288i	−0.472924	−	0.273043i	0.244539	−	0.969639i	$-0.421363\pi$
$73$	−4.04066	−	2.33288i	−0.472924	−	0.273043i	−0.717463	+	0.696597i	$0.754697\pi$
$74$	0.400976	+	0.0465336i	0.0466125	+	0.00540942i
$75$		0			0
$76$	−7.52506	+	8.00239i	−0.863184	+	0.917937i
$77$	−3.50996	−	1.06002i	−0.399997	−	0.120800i
$78$	14.1478	−	6.11654i	1.60192	−	0.692562i
$79$	−8.88033	+	5.12706i	−0.999115	+	0.576839i	−0.907986	−	0.419000i	$-0.862381\pi$
$79$	−8.88033	+	5.12706i	−0.999115	+	0.576839i	−0.0911285	+	0.995839i	$0.529047\pi$
$80$		0			0
$81$	5.15913	−	8.93587i	0.573237	−	0.992875i
$82$	−9.31917	−	6.92598i	−1.02913	−	0.764846i
$83$	0.0814876			0.00894443			0.00447221	−	0.999990i	$-0.498576\pi$
$83$	0.0814876			0.00894443			0.00447221	+	0.999990i	$0.498576\pi$
$84$	−9.94849	−	0.00758271i	−1.08547	−	0.000827341i
$85$		0			0
$86$	−3.75698	−	2.79218i	−0.405126	−	0.301088i
$87$	1.92083	−	3.32698i	0.205935	−	0.356690i
$88$	−2.52692	−	2.99644i	−0.269370	−	0.319422i
$89$	3.22105	−	1.85967i	0.341430	−	0.197125i	−0.319474	−	0.947595i	$-0.603506\pi$
$89$	3.22105	−	1.85967i	0.341430	−	0.197125i	0.660904	+	0.750470i	$0.270173\pi$
$90$		0			0
$91$	3.50116	+	14.9325i	0.367022	+	1.56535i
$92$	6.76729	+	6.36363i	0.705539	+	0.663455i
$93$	−1.56523	−	2.71106i	−0.162307	−	0.281123i
$94$	0.194132	+	0.0225292i	0.0200232	+	0.00232371i
$95$		0			0
$96$	−8.90966	−	5.80771i	−0.909338	−	0.592746i
$97$		−	3.88816i		−	0.394783i	−0.980325	−	0.197391i	$-0.936753\pi$
$97$		−	3.88816i		−	0.394783i	0.980325	−	0.197391i	$-0.0632470\pi$
$98$	1.75790	−	9.74217i	0.177574	−	0.984107i
$99$		−	0.741044i		−	0.0744777i
$100$		0			0
$101$	8.91845	+	5.14907i	0.887419	+	0.512352i	0.873097	−	0.487546i	$-0.162108\pi$
$101$	8.91845	+	5.14907i	0.887419	+	0.512352i	0.0143218	+	0.999897i	$0.495441\pi$
$102$	1.43007	−	12.3228i	0.141598	−	1.22014i
$103$	−2.02688	−	3.51065i	−0.199714	−	0.345915i	0.748722	−	0.662885i	$-0.230668\pi$
$103$	−2.02688	−	3.51065i	−0.199714	−	0.345915i	−0.948436	+	0.316970i	$0.897335\pi$
$104$	−5.56993	+	15.4214i	−0.546177	+	1.51219i
$105$		0			0
$106$	3.77598	+	8.73397i	0.366755	+	0.848318i
$107$	6.73270	−	3.88713i	0.650875	−	0.375783i	−0.137917	−	0.990444i	$-0.544041\pi$
$107$	6.73270	−	3.88713i	0.650875	−	0.375783i	0.788791	+	0.614661i	$0.210707\pi$
$108$	2.67320	+	8.87603i	0.257229	+	0.854097i
$109$	−4.42650	+	7.66692i	−0.423981	+	0.734357i	−0.996325	−	0.0856567i	$-0.972701\pi$
$109$	−4.42650	+	7.66692i	−0.423981	+	0.734357i	0.572343	+	0.820014i	$0.306034\pi$
$110$		0			0
$111$	−0.536644			−0.0509360
$112$	7.25572	−	7.70419i	0.685601	−	0.727977i
$113$	14.8389			1.39593			0.697965	−	0.716131i	$-0.254089\pi$
$113$	14.8389			1.39593			0.697965	+	0.716131i	$0.254089\pi$
$114$	8.71091	−	11.7209i	0.815852	−	1.09776i
$115$		0			0
$116$	1.17850	+	3.91307i	0.109421	+	0.363320i
$117$	−2.68455	+	1.54993i	−0.248187	+	0.143291i
$118$	0.934444	+	2.16140i	0.0860225	+	0.198973i
$119$	11.8173	+	3.56885i	1.08329	+	0.327156i
$120$		0			0
$121$	−4.53975	−	7.86308i	−0.412705	−	0.714825i
$122$	−0.469857	+	4.04872i	−0.0425389	+	0.366554i
$123$	13.3679	+	7.71799i	1.20535	+	0.695908i
$124$	3.24161	+	0.762655i	0.291105	+	0.0684884i
$125$		0			0
$126$	1.98762	−	0.229130i	0.177072	−	0.0204126i
$127$		−	12.8398i		−	1.13935i	−0.821871	−	0.569674i	$-0.807070\pi$
$127$		−	12.8398i		−	1.13935i	0.821871	−	0.569674i	$-0.192930\pi$
$128$	10.9936	−	2.67236i	0.971703	−	0.236206i
$129$	5.38923	+	3.11147i	0.474495	+	0.273950i
$130$		0			0
$131$	1.64534	+	2.84981i	0.143754	+	0.248989i	0.928907	−	0.370312i	$-0.120749\pi$
$131$	1.64534	+	2.84981i	0.143754	+	0.248989i	−0.785154	+	0.619301i	$0.787416\pi$
$132$	3.79616	+	3.56973i	0.330413	+	0.310705i
$133$	9.94665	+	10.5937i	0.862484	+	0.918595i
$134$	15.1178	−	6.53592i	1.30598	−	0.564618i
$135$		0			0
$136$	8.50758	+	10.0884i	0.729519	+	0.865070i
$137$	−10.6293	+	18.4106i	−0.908126	+	1.57292i	−0.0914606	+	0.995809i	$0.529154\pi$
$137$	−10.6293	+	18.4106i	−0.908126	+	1.57292i	−0.816665	+	0.577112i	$0.804180\pi$
$138$	−9.91186	−	7.36646i	−0.843753	−	0.627075i
$139$	8.44096			0.715953			0.357976	−	0.933731i	$-0.383467\pi$
$139$	8.44096			0.715953			0.357976	+	0.933731i	$0.383467\pi$
$140$		0			0
$141$	−0.259816			−0.0218804
$142$	−2.60981	−	1.93960i	−0.219010	−	0.162768i
$143$	4.01681	−	6.95731i	0.335902	−	0.581800i
$144$	1.91456	+	0.953667i	0.159547	+	0.0794723i
$145$		0			0
$146$	−6.05658	+	2.61846i	−0.501246	+	0.216705i
$147$	−0.828399	+	13.1345i	−0.0683252	+	1.08332i
$148$	0.391073	−	0.415879i	0.0321460	−	0.0341851i
$149$	1.28756	+	2.23013i	0.105481	+	0.182699i	0.913935	−	0.405861i	$-0.133028\pi$
$149$	1.28756	+	2.23013i	0.105481	+	0.182699i	−0.808453	+	0.588560i	$0.799695\pi$
$150$		0			0
$151$	−16.3278	−	9.42688i	−1.32874	−	0.767148i	−0.343635	−	0.939103i	$-0.611658\pi$
$151$	−16.3278	−	9.42688i	−1.32874	−	0.767148i	−0.985105	+	0.171955i	$0.944992\pi$
$152$	2.73527	+	15.2921i	0.221860	+	1.24035i
$153$			2.49493i			0.201703i
$154$	−4.16412	+	3.08983i	−0.335554	+	0.248986i
$155$		0			0
$156$	4.99207	−	21.2185i	0.399686	−	1.69884i
$157$	15.7955	+	9.11954i	1.26062	+	0.727819i	0.973194	−	0.229985i	$-0.0738676\pi$
$157$	15.7955	+	9.11954i	1.26062	+	0.727819i	0.287425	+	0.957803i	$0.407201\pi$
$158$	−1.67169	+	14.4048i	−0.132993	+	1.14599i
$159$	−6.32490	−	10.9551i	−0.501598	−	0.868793i
$160$		0			0
$161$	8.95870	−	8.41147i	0.706044	−	0.662917i
$162$	−5.79069	−	13.3941i	−0.454959	−	1.05234i
$163$	8.67532	−	5.00870i	0.679503	−	0.392311i	−0.120165	−	0.992754i	$-0.538342\pi$
$163$	8.67532	−	5.00870i	0.679503	−	0.392311i	0.799668	+	0.600443i	$0.205009\pi$
$164$	−15.7229	+	4.73528i	−1.22775	+	0.369763i
$165$		0			0
$166$	0.0687412	−	0.0924939i	0.00533535	−	0.00717892i
$167$	−5.53046			−0.427960			−0.213980	−	0.976838i	$-0.568643\pi$
$167$	−5.53046			−0.427960			−0.213980	+	0.976838i	$0.568643\pi$
$168$	−8.40093	+	11.2858i	−0.648146	+	0.870719i
$169$	−20.6053			−1.58503
$170$		0			0
$171$	−1.46848	+	2.54348i	−0.112297	+	0.194505i
$172$	−6.33862	+	1.90901i	−0.483315	+	0.145560i
$173$	−1.73252	+	1.00027i	−0.131721	+	0.0760493i	−0.564413	−	0.825493i	$-0.690897\pi$
$173$	−1.73252	+	1.00027i	−0.131721	+	0.0760493i	0.432691	+	0.901542i	$0.357564\pi$
$174$	−2.15597	−	4.98684i	−0.163444	−	0.378051i
$175$		0			0
$176$	−5.53281	+	0.340489i	−0.417051	+	0.0256654i
$177$	−1.56523	−	2.71106i	−0.117650	−	0.203775i
$178$	0.606352	−	5.22488i	0.0454480	−	0.391621i
$179$	−22.0168	−	12.7114i	−1.64561	−	0.950095i	−0.978787	−	0.204880i	$-0.934320\pi$
$179$	−22.0168	−	12.7114i	−1.64561	−	0.950095i	−0.666825	−	0.745214i	$-0.732347\pi$
$180$		0			0
$181$			12.0441i			0.895227i	0.894227	+	0.447614i	$0.147726\pi$
$181$			12.0441i			0.895227i	−0.894227	+	0.447614i	$0.852274\pi$
$182$	19.9029	+	8.62266i	1.47530	+	0.639154i
$183$		−	5.41858i		−	0.400553i
$184$	12.9319	−	2.31310i	0.953351	−	0.170524i
$185$		0			0
$186$	−4.39762	−	0.510348i	−0.322449	−	0.0374205i
$187$	−3.23295	−	5.59963i	−0.236417	−	0.409485i
$188$	0.189338	−	0.201348i	0.0138089	−	0.0146848i
$189$	11.9391	−	2.79931i	0.868439	−	0.203620i
$190$		0			0
$191$	16.9835	−	9.80543i	1.22888	−	0.709496i	0.262087	−	0.965044i	$-0.415589\pi$
$191$	16.9835	−	9.80543i	1.22888	−	0.709496i	0.966796	+	0.255548i	$0.0822560\pi$
$192$	−14.1081	+	5.21380i	−1.01817	+	0.376274i
$193$	1.41942	−	2.45851i	0.102172	−	0.176967i	−0.810407	−	0.585867i	$-0.800754\pi$
$193$	1.41942	−	2.45851i	0.102172	−	0.176967i	0.912579	+	0.408900i	$0.134087\pi$
$194$	−4.41332	−	3.27997i	−0.316858	−	0.235488i
$195$		0			0
$196$	−9.57509	−	10.2136i	−0.683935	−	0.729543i
$197$	−10.7935			−0.769008			−0.384504	−	0.923123i	$-0.625628\pi$
$197$	−10.7935			−0.769008			−0.384504	+	0.923123i	$0.625628\pi$
$198$	−0.841134	−	0.625128i	−0.0597768	−	0.0444259i
$199$	−0.713503	+	1.23582i	−0.0505789	+	0.0876052i	−0.890206	−	0.455557i	$-0.849440\pi$
$199$	−0.713503	+	1.23582i	−0.0505789	+	0.0876052i	0.839628	+	0.543163i	$0.182773\pi$
$200$		0			0
$201$	−18.9624	+	10.9479i	−1.33750	+	0.772207i
$202$	13.3679	−	5.77940i	0.940566	−	0.406637i
$203$	5.26343	−	1.23410i	0.369421	−	0.0866166i
$204$	−12.7808	−	12.0185i	−0.894838	−	0.841463i
$205$		0			0
$206$	−5.69466	−	0.660870i	−0.396765	−	0.0460450i
$207$	2.15091	+	1.24183i	0.149499	+	0.0863132i
$208$	12.8056	+	19.3314i	0.887909	+	1.34039i
$209$		−	7.61144i		−	0.526495i
$210$		0			0
$211$		−	1.21343i		−	0.0835359i	−0.999127	−	0.0417679i	$-0.986701\pi$
$211$		−	1.21343i		−	0.0835359i	0.999127	−	0.0417679i	$-0.0132990\pi$
$212$	13.0990	+	3.08180i	0.899641	+	0.211659i
$213$	3.74366	+	2.16140i	0.256511	+	0.148097i
$214$	1.26741	−	10.9212i	0.0866383	−	0.746555i
$215$		0			0
$216$	12.3299	+	4.45336i	0.838946	+	0.303013i
$217$	1.27361	−	4.21721i	0.0864581	−	0.286283i
$218$	4.96837	+	11.4920i	0.336500	+	0.778337i
$219$	7.59680	−	4.38601i	0.513344	−	0.296379i
$220$		0			0
$221$	−13.5237	+	23.4238i	−0.909703	+	1.57565i
$222$	−0.452701	+	0.609127i	−0.0303833	+	0.0408819i
$223$	−25.1115			−1.68159			−0.840794	−	0.541355i	$-0.817912\pi$
$223$	−25.1115			−1.68159			−0.840794	+	0.541355i	$0.817912\pi$
$224$	−2.62400	−	14.7348i	−0.175324	−	0.984511i
$225$		0			0
$226$	12.5178	−	16.8432i	0.832672	−	1.12039i
$227$	9.97424	−	17.2759i	0.662014	−	1.14664i	−0.318072	−	0.948067i	$-0.603035\pi$
$227$	9.97424	−	17.2759i	0.662014	−	1.14664i	0.980086	−	0.198575i	$-0.0636313\pi$
$228$	−5.95563	−	19.7749i	−0.394422	−	1.30963i
$229$	−17.7498	+	10.2478i	−1.17294	+	0.677196i	−0.954370	−	0.298626i	$-0.903472\pi$
$229$	−17.7498	+	10.2478i	−1.17294	+	0.677196i	−0.218568	+	0.975822i	$0.570138\pi$
$230$		0			0
$231$	5.02545	−	4.71847i	0.330650	−	0.310453i
$232$	5.43576	+	1.96330i	0.356875	+	0.128897i
$233$	2.16542	+	3.75062i	0.141861	+	0.245711i	0.928198	−	0.372088i	$-0.121358\pi$
$233$	2.16542	+	3.75062i	0.141861	+	0.245711i	−0.786336	+	0.617799i	$0.788025\pi$
$234$	−0.505358	+	4.35463i	−0.0330363	+	0.284671i
$235$		0			0
$236$	3.24161	+	0.762655i	0.211011	+	0.0496446i
$237$		−	19.2786i		−	1.25228i
$238$	14.0197	−	10.4028i	0.908761	−	0.674313i
$239$			3.58881i			0.232141i	0.993241	+	0.116070i	$0.0370298\pi$
$239$			3.58881i			0.232141i	−0.993241	+	0.116070i	$0.962970\pi$
$240$		0			0
$241$	−0.749733	−	0.432858i	−0.0482945	−	0.0278829i	0.475658	−	0.879630i	$-0.342210\pi$
$241$	−0.749733	−	0.432858i	−0.0482945	−	0.0278829i	−0.523953	+	0.851747i	$0.675543\pi$
$242$	−12.7548	−	1.48020i	−0.819907	−	0.0951509i
$243$	2.74724	+	4.75836i	0.176236	+	0.305249i
$244$	4.19920	+	3.94873i	0.268826	+	0.252791i
$245$		0			0
$246$	20.0373	−	8.66279i	1.27753	−	0.552319i
$247$	−27.5737	+	15.9197i	−1.75447	+	1.01294i
$248$	3.60022	−	3.03609i	0.228614	−	0.192792i
$249$	−0.0766020	+	0.132679i	−0.00485445	+	0.00840816i
$250$		0			0
$251$	−19.8507			−1.25297			−0.626484	−	0.779434i	$-0.715507\pi$
$251$	−19.8507			−1.25297			−0.626484	+	0.779434i	$0.715507\pi$
$252$	1.41664	−	2.44938i	0.0892398	−	0.154296i
$253$	−6.43668			−0.404671
$254$	−14.5740	−	10.8314i	−0.914455	−	0.679620i
$255$		0			0
$256$	6.24062	−	14.7328i	0.390039	−	0.920798i
$257$	14.3600	−	8.29075i	0.895752	−	0.517162i	0.0199322	−	0.999801i	$-0.493655\pi$
$257$	14.3600	−	8.29075i	0.895752	−	0.517162i	0.875819	+	0.482639i	$0.160322\pi$
$258$	8.07797	−	3.49237i	0.502912	−	0.217425i
$259$	−0.516921	−	0.550551i	−0.0321199	−	0.0342096i
$260$		0			0
$261$	0.546321	+	0.946256i	0.0338164	+	0.0585718i
$262$	4.62269	+	0.536467i	0.285591	+	0.0331431i
$263$	−6.87750	−	3.97073i	−0.424085	−	0.244845i	0.272739	−	0.962088i	$-0.412071\pi$
$263$	−6.87750	−	3.97073i	−0.424085	−	0.244845i	−0.696823	+	0.717243i	$0.745404\pi$
$264$	7.25423	−	1.29755i	0.446467	−	0.0798589i
$265$		0			0
$266$	20.4154	−	2.35345i	1.25175	−	0.144300i
$267$			6.99269i			0.427946i
$268$	5.33436	−	22.6733i	0.325848	−	1.38499i
$269$	15.7337	+	9.08388i	0.959303	+	0.553854i	0.895958	−	0.444138i	$-0.146490\pi$
$269$	15.7337	+	9.08388i	0.959303	+	0.553854i	0.0633443	+	0.997992i	$0.479823\pi$
$270$		0			0
$271$	−11.6622	−	20.1995i	−0.708426	−	1.22703i	−0.965441	−	0.260623i	$-0.916072\pi$
$271$	−11.6622	−	20.1995i	−0.708426	−	1.22703i	0.257014	−	0.966408i	$-0.417261\pi$
$272$	18.6278	−	1.14635i	1.12947	−	0.0695079i
$273$	−27.6044	−	8.33659i	−1.67069	−	0.504553i
$274$	11.9305	+	27.5958i	0.720750	+	1.66712i
$275$		0			0
$276$	−16.7228	+	5.03643i	−1.00660	+	0.303158i
$277$	11.5998	−	20.0914i	0.696962	−	1.20717i	−0.272553	−	0.962141i	$-0.587868\pi$
$277$	11.5998	−	20.0914i	0.696962	−	1.20717i	0.969515	−	0.245033i	$-0.0787987\pi$
$278$	7.12061	−	9.58105i	0.427066	−	0.574633i
$279$	0.890362			0.0533046
$280$		0			0
$281$	−1.57513			−0.0939643			−0.0469821	−	0.998896i	$-0.514960\pi$
$281$	−1.57513			−0.0939643			−0.0469821	+	0.998896i	$0.514960\pi$
$282$	−0.219175	+	0.294908i	−0.0130517	+	0.0175615i
$283$	3.82072	−	6.61768i	0.227118	−	0.393380i	−0.729835	−	0.683624i	$-0.760403\pi$
$283$	3.82072	−	6.61768i	0.227118	−	0.393380i	0.956953	+	0.290244i	$0.0937363\pi$
$284$	−4.40315	+	1.32610i	−0.261279	+	0.0786896i
$285$		0			0
$286$	−4.50852	−	10.4284i	−0.266595	−	0.616643i
$287$	4.95866	+	21.1487i	0.292700	+	1.24837i
$288$	2.69756	−	1.36866i	0.158955	−	0.0806493i
$289$	2.38463	+	4.13030i	0.140272	+	0.242959i
$290$		0			0
$291$	6.33072	+	3.65504i	0.371113	+	0.214262i
$292$	−2.13708	+	9.08350i	−0.125063	+	0.531571i
$293$		−	9.48295i		−	0.554000i	−0.960870	−	0.277000i	$-0.910660\pi$
$293$		−	9.48295i		−	0.554000i	0.960870	−	0.277000i	$-0.0893401\pi$
$294$	14.2097	+	12.0203i	0.828729	+	0.701037i
$295$		0			0
$296$	−0.142150	−	0.794720i	−0.00826232	−	0.0461922i
$297$	−5.56262	−	3.21158i	−0.322776	−	0.186355i
$298$	3.61750	+	0.419814i	0.209556	+	0.0243192i
$299$	13.4626	+	23.3179i	0.778563	+	1.34851i
$300$		0			0
$301$	1.99906	+	8.52601i	0.115224	+	0.491431i
$302$	−24.4739	+	10.5809i	−1.40832	+	0.608861i
$303$	−16.7675	+	9.68071i	−0.963267	+	0.556142i
$304$	19.6649	+	9.79535i	1.12786	+	0.561802i
$305$		0			0
$306$	2.83191	+	2.10467i	0.161890	+	0.120316i
$307$	−26.2893			−1.50041			−0.750205	−	0.661205i	$-0.770045\pi$
$307$	−26.2893			−1.50041			−0.750205	+	0.661205i	$0.770045\pi$
$308$	−0.00558924	+	7.33307i	−0.000318477	+	0.417840i
$309$	7.62142			0.433567
$310$		0			0
$311$	−15.1994	+	26.3262i	−0.861880	+	1.49282i	0.00823251	+	0.999966i	$0.497379\pi$
$311$	−15.1994	+	26.3262i	−0.861880	+	1.49282i	−0.870112	+	0.492853i	$0.835954\pi$
$312$	−19.8732	−	23.5658i	−1.12510	−	1.33415i
$313$	−2.35988	+	1.36248i	−0.133388	+	0.0770118i	−0.565209	−	0.824948i	$-0.691205\pi$
$313$	−2.35988	+	1.36248i	−0.133388	+	0.0770118i	0.431821	+	0.901959i	$0.357871\pi$
$314$	23.6760	−	10.2359i	1.33612	−	0.577646i
$315$		0			0
$316$	14.9402	+	14.0491i	0.840454	+	0.790323i
$317$	5.24105	+	9.07776i	0.294366	+	0.509858i	0.974837	−	0.222917i	$-0.0715580\pi$
$317$	5.24105	+	9.07776i	0.294366	+	0.509858i	−0.680471	+	0.732775i	$0.738225\pi$
$318$	−17.7703	−	2.06226i	−0.996507	−	0.115646i
$319$	−2.45233	−	1.41585i	−0.137304	−	0.0792725i
$320$		0			0
$321$			14.6163i			0.815801i
$322$	−1.99022	−	17.2644i	−0.110911	−	0.962110i
$323$			25.6261i			1.42587i
$324$	−20.0880	−	4.72612i	−1.11600	−	0.262562i
$325$		0			0
$326$	1.63310	−	14.0723i	0.0904491	−	0.779392i
$327$	−8.32221	−	14.4145i	−0.460219	−	0.797123i
$328$	−7.88863	+	21.8411i	−0.435577	+	1.20597i
$329$	−0.250267	−	0.266549i	−0.0137977	−	0.0146953i
$330$		0			0
$331$	−10.6909	+	6.17239i	−0.587625	+	0.339265i	−0.764158	−	0.645030i	$-0.776845\pi$
$331$	−10.6909	+	6.17239i	−0.587625	+	0.339265i	0.176533	+	0.984295i	$0.443512\pi$
$332$	−0.0469982	−	0.156052i	−0.00257936	−	0.00856445i
$333$	0.0763159	−	0.132183i	0.00418208	−	0.00724358i
$334$	−4.66538	+	6.27745i	−0.255278	+	0.343487i
$335$		0			0
$336$	5.72330	+	19.0561i	0.312231	+	1.03959i
$337$	−6.54017			−0.356266			−0.178133	−	0.984006i	$-0.557006\pi$
$337$	−6.54017			−0.356266			−0.178133	+	0.984006i	$0.557006\pi$
$338$	−17.3822	+	23.3884i	−0.945467	+	1.27216i
$339$	−13.9493	+	24.1608i	−0.757620	+	1.31224i
$340$		0			0
$341$	−1.99833	+	1.15374i	−0.108216	+	0.0624783i
$342$	1.64824	+	3.81244i	0.0891267	+	0.206153i
$343$	−14.2729	+	11.8019i	−0.770661	+	0.637245i
$344$	−3.18027	+	8.80515i	−0.171468	+	0.474742i
$345$		0			0
$346$	−0.326142	+	2.81033i	−0.0175335	+	0.151085i
$347$	30.4869	+	17.6016i	1.63662	+	0.944903i	0.981985	+	0.188959i	$0.0605113\pi$
$347$	30.4869	+	17.6016i	1.63662	+	0.944903i	0.654636	+	0.755945i	$0.272822\pi$
$348$	−7.47912	−	1.75962i	−0.400923	−	0.0943253i
$349$			11.2696i			0.603247i	0.953427	+	0.301623i	$0.0975285\pi$
$349$			11.2696i			0.603247i	−0.953427	+	0.301623i	$0.902472\pi$
$350$		0			0
$351$			26.8687i			1.43414i
$352$	−4.28088	+	6.56734i	−0.228172	+	0.350040i
$353$	10.2236	+	5.90260i	0.544148	+	0.314164i	0.746758	−	0.665096i	$-0.231609\pi$
$353$	10.2236	+	5.90260i	0.544148	+	0.314164i	−0.202611	+	0.979259i	$0.564943\pi$
$354$	−4.39762	−	0.510348i	−0.233731	−	0.0271247i
$355$		0			0
$356$	−5.41908	−	5.09584i	−0.287211	−	0.270079i
$357$	−16.9196	+	15.8861i	−0.895479	+	0.840780i
$358$	−33.0012	+	14.2675i	−1.74417	+	0.754059i
$359$	13.9275	−	8.04106i	0.735066	−	0.424391i	−0.0852064	−	0.996363i	$-0.527155\pi$
$359$	13.9275	−	8.04106i	0.735066	−	0.424391i	0.820273	+	0.571973i	$0.193822\pi$
$360$		0			0
$361$	−5.58309	+	9.67020i	−0.293847	+	0.508958i
$362$	13.6708	+	10.1601i	0.718521	+	0.534003i
$363$	17.0703			0.895957
$364$	26.5769	−	15.3172i	1.39301	−	0.802839i
$365$		0			0
$366$	−6.15045	−	4.57100i	−0.321489	−	0.238930i
$367$	15.1931	−	26.3153i	0.793075	−	1.37365i	−0.130979	−	0.991385i	$-0.541812\pi$
$367$	15.1931	−	26.3153i	0.793075	−	1.37365i	0.924054	−	0.382262i	$-0.124855\pi$
$368$	8.28352	−	16.6298i	0.431809	−	0.866890i
$369$	−3.80210	+	2.19514i	−0.197929	+	0.114275i
$370$		0			0
$371$	5.14650	−	17.0412i	0.267193	−	0.884738i
$372$	−4.28902	+	4.56108i	−0.222375	+	0.236481i
$373$	−9.82168	−	17.0117i	−0.508547	−	0.880830i	−0.999951	−	0.00989806i	$-0.996849\pi$
$373$	−9.82168	−	17.0117i	−0.508547	−	0.880830i	0.491404	−	0.870932i	$-0.336484\pi$
$374$	−9.08319	−	1.05411i	−0.469681	−	0.0545069i
$375$		0			0
$376$	−0.0688220	−	0.384763i	−0.00354922	−	0.0198427i
$377$			11.8453i			0.610063i
$378$	6.89413	−	15.9131i	0.354596	−	0.818480i
$379$		−	18.7575i		−	0.963507i	−0.876307	−	0.481754i	$-0.840000\pi$
$379$		−	18.7575i		−	0.963507i	0.876307	−	0.481754i	$-0.160000\pi$
$380$		0			0
$381$	20.9058	+	12.0700i	1.07104	+	0.618363i
$382$	3.19709	−	27.5490i	0.163577	−	1.40953i
$383$	−8.81632	−	15.2703i	−0.450493	−	0.780277i	0.547924	−	0.836528i	$-0.315418\pi$
$383$	−8.81632	−	15.2703i	−0.450493	−	0.780277i	−0.998417	+	0.0562516i	$0.982085\pi$
$384$	−5.98329	+	20.4119i	−0.305333	+	1.04164i
$385$		0			0
$386$	−1.59318	−	3.68508i	−0.0810906	−	0.187565i
$387$	−1.53280	+	0.884963i	−0.0779166	+	0.0449852i
$388$	−7.44596	+	2.24251i	−0.378011	+	0.113846i
$389$	0.464820	−	0.805092i	0.0235673	−	0.0408198i	−0.854001	−	0.520271i	$-0.825831\pi$
$389$	0.464820	−	0.805092i	0.0235673	−	0.0408198i	0.877569	+	0.479451i	$0.159164\pi$
$390$		0			0
$391$	21.6709			1.09595
$392$	−19.6705	+	2.25239i	−0.993508	+	0.113763i
$393$	−6.18676			−0.312081
$394$	−9.10519	+	12.2514i	−0.458713	+	0.617216i
$395$		0			0
$396$	−1.41912	+	0.427399i	−0.0713137	+	0.0214776i
$397$	−22.1790	+	12.8051i	−1.11313	+	0.642668i	−0.939639	−	0.342167i	$-0.888839\pi$
$397$	−22.1790	+	12.8051i	−1.11313	+	0.642668i	−0.173494	+	0.984835i	$0.555506\pi$
$398$	0.800847	+	1.85239i	0.0401428	+	0.0928518i
$399$	−26.5991	+	6.23658i	−1.33162	+	0.312220i
$400$		0			0
$401$	1.45666	+	2.52300i	0.0727420	+	0.125993i	0.900102	−	0.435679i	$-0.143492\pi$
$401$	1.45666	+	2.52300i	0.0727420	+	0.125993i	−0.827360	+	0.561672i	$0.810158\pi$
$402$	−3.56961	+	30.7590i	−0.178036	+	1.53412i
$403$	8.35919	+	4.82618i	0.416401	+	0.240409i
$404$	4.71691	−	20.0489i	0.234675	−	0.997469i
$405$		0			0
$406$	3.03933	−	7.01541i	0.150840	−	0.348169i
$407$			0.395562i			0.0196073i
$408$	−24.4234	+	4.36858i	−1.20914	+	0.216277i
$409$	−29.1390	−	16.8234i	−1.44083	−	0.831864i	−0.442926	−	0.896558i	$-0.646060\pi$
$409$	−29.1390	−	16.8234i	−1.44083	−	0.831864i	−0.997905	+	0.0646940i	$0.979393\pi$
$410$		0			0
$411$	−19.9841	−	34.6135i	−0.985743	−	1.70736i
$412$	−5.55402	+	5.90632i	−0.273627	+	0.290983i
$413$	1.27361	−	4.21721i	0.0626701	−	0.207515i
$414$	3.22402	−	1.39385i	0.158452	−	0.0685040i
$415$		0			0
$416$	32.7449	+	1.77230i	1.60545	+	0.0868940i
$417$	−7.93488	+	13.7436i	−0.388573	+	0.673027i
$418$	−8.63950	−	6.42085i	−0.422572	−	0.314054i
$419$	−12.2683			−0.599345			−0.299672	−	0.954042i	$-0.596877\pi$
$419$	−12.2683			−0.599345			−0.299672	+	0.954042i	$0.596877\pi$
$420$		0			0
$421$	−9.36160			−0.456257			−0.228128	−	0.973631i	$-0.573261\pi$
$421$	−9.36160			−0.456257			−0.228128	+	0.973631i	$0.573261\pi$
$422$	−1.37732	−	1.02362i	−0.0670470	−	0.0498291i
$423$	0.0369483	−	0.0639963i	0.00179649	−	0.00311161i
$424$	14.5480	−	12.2685i	0.706515	−	0.595809i
$425$		0			0
$426$	5.61140	−	2.42599i	0.271873	−	0.117540i
$427$	5.55900	−	5.21944i	0.269019	−	0.252586i
$428$	−11.3271	−	10.6514i	−0.547515	−	0.514857i
$429$	7.55195	+	13.0804i	0.364612	+	0.631526i
$430$		0			0
$431$	21.0179	+	12.1347i	1.01240	+	0.584509i	0.911893	−	0.410428i	$-0.134621\pi$
$431$	21.0179	+	12.1347i	1.01240	+	0.584509i	0.100506	+	0.994936i	$0.467954\pi$
$432$	15.4561	−	10.2385i	0.743633	−	0.492602i
$433$		−	3.00004i		−	0.144172i	−0.997398	−	0.0720862i	$-0.977034\pi$
$433$		−	3.00004i		−	0.144172i	0.997398	−	0.0720862i	$-0.0229657\pi$
$434$	−3.71243	−	5.00318i	−0.178202	−	0.240160i
$435$		0			0
$436$	17.2354	+	4.05498i	0.825426	+	0.194198i
$437$	22.0926	+	12.7552i	1.05683	+	0.610162i
$438$	1.43007	−	12.3228i	0.0683316	−	0.588807i
$439$	−7.17918	−	12.4347i	−0.342644	−	0.593476i	0.642279	−	0.766471i	$-0.277989\pi$
$439$	−7.17918	−	12.4347i	−0.342644	−	0.593476i	−0.984923	+	0.172995i	$0.944656\pi$
$440$		0			0
$441$	−3.11741	−	2.07190i	−0.148448	−	0.0986619i
$442$	15.1792	+	35.1101i	0.722002	+	1.67002i
$443$	13.3394	−	7.70151i	0.633775	−	0.365910i	−0.148438	−	0.988922i	$-0.547424\pi$
$443$	13.3394	−	7.70151i	0.633775	−	0.365910i	0.782212	+	0.623012i	$0.214091\pi$
$444$	0.309511	+	1.02769i	0.0146887	+	0.0487721i
$445$		0			0
$446$	−21.1835	+	28.5032i	−1.00307	+	1.34967i
$447$	−4.84147			−0.228994
$448$	−18.9385	−	9.45154i	−0.894762	−	0.446543i
$449$	26.4360			1.24759			0.623797	−	0.781586i	$-0.285589\pi$
$449$	26.4360			1.24759			0.623797	+	0.781586i	$0.285589\pi$
$450$		0			0
$451$	5.68896	−	9.85356i	0.267883	−	0.463986i
$452$	−8.55840	−	28.4171i	−0.402553	−	1.33663i
$453$	30.6978	−	17.7234i	1.44231	−	0.832716i
$454$	−11.1952	−	25.8950i	−0.525419	−	1.21531i
$455$		0			0
$456$	−27.4699	−	9.92166i	−1.28640	−	0.464624i
$457$	−18.8435	−	32.6378i	−0.881460	−	1.52673i	−0.849718	−	0.527238i	$-0.823228\pi$
$457$	−18.8435	−	32.6378i	−0.881460	−	1.52673i	−0.0317424	−	0.999496i	$-0.510106\pi$
$458$	−3.34134	+	28.7920i	−0.156131	+	1.34536i
$459$	18.7281	+	10.8127i	0.874155	+	0.504693i
$460$		0			0
$461$		−	3.61152i		−	0.168205i	−0.996457	−	0.0841027i	$-0.973198\pi$
$461$		−	3.61152i		−	0.168205i	0.996457	−	0.0841027i	$-0.0268024\pi$
$462$	−1.11643	−	9.68462i	−0.0519409	−	0.450569i
$463$		−	27.6093i		−	1.28311i	−0.767076	−	0.641556i	$-0.778289\pi$
$463$		−	27.6093i		−	1.28311i	0.767076	−	0.641556i	$-0.221711\pi$
$464$	6.81396	−	4.51375i	0.316330	−	0.209545i
$465$		0			0
$466$	6.08391	+	0.706043i	0.281831	+	0.0327068i
$467$	0.657053	+	1.13805i	0.0304048	+	0.0526626i	0.880827	−	0.473438i	$-0.156987\pi$
$467$	0.657053	+	1.13805i	0.0304048	+	0.0526626i	−0.850423	+	0.526100i	$0.823654\pi$
$468$	4.51648	+	4.24708i	0.208775	+	0.196322i
$469$	−29.4971	−	8.90819i	−1.36205	−	0.411342i
$470$		0			0
$471$	−29.6970	+	17.1455i	−1.36836	+	0.790025i
$472$	3.60022	−	3.03609i	0.165713	−	0.139747i
$473$	2.29348	−	3.97242i	0.105454	−	0.182652i
$474$	−21.8826	−	16.2630i	−1.00510	−	0.746986i
$475$		0			0
$476$	0.0188178	−	24.6888i	0.000862511	−	1.13161i
$477$	3.59785			0.164734
$478$	4.07354	+	3.02744i	0.186319	+	0.138472i
$479$	9.32551	−	16.1523i	0.426093	−	0.738015i	−0.570429	−	0.821347i	$-0.693223\pi$
$479$	9.32551	−	16.1523i	0.426093	−	0.738015i	0.996522	+	0.0833320i	$0.0265562\pi$
$480$		0			0
$481$	1.43299	−	0.827336i	0.0653386	−	0.0377233i
$482$	−1.12378	+	0.485847i	−0.0511868	+	0.0221297i
$483$	5.27402	+	22.4937i	0.239976	+	1.02350i
$484$	−12.4398	+	13.2288i	−0.565443	+	0.601311i
$485$		0			0
$486$	7.71857	+	0.895747i	0.350121	+	0.0406319i
$487$	8.89500	+	5.13553i	0.403071	+	0.232713i	0.687808	−	0.725892i	$-0.258573\pi$
$487$	8.89500	+	5.13553i	0.403071	+	0.232713i	−0.284737	+	0.958606i	$0.591906\pi$
$488$	8.02442	−	1.43532i	0.363249	−	0.0649737i
$489$			18.8336i			0.851684i
$490$		0			0
$491$		−	21.0407i		−	0.949553i	−0.880106	−	0.474776i	$-0.842529\pi$
$491$		−	21.0407i		−	0.949553i	0.880106	−	0.474776i	$-0.157471\pi$
$492$	7.07022	−	30.0515i	0.318750	−	1.35482i
$493$	8.25645	+	4.76687i	0.371852	+	0.214689i
$494$	−5.19066	+	44.7275i	−0.233539	+	2.01238i
$495$		0			0
$496$	−0.409097	−	6.64766i	−0.0183690	−	0.298489i
$497$	1.38866	+	5.92264i	0.0622898	+	0.265667i
$498$	0.0859792	+	0.198873i	0.00385282	+	0.00891171i
$499$	18.2670	−	10.5465i	0.817744	−	0.472125i	−0.0318936	−	0.999491i	$-0.510154\pi$
$499$	18.2670	−	10.5465i	0.817744	−	0.472125i	0.849638	+	0.527366i	$0.176820\pi$
$500$		0			0
$501$	5.19888	−	9.00473i	0.232269	−	0.402302i
$502$	−16.7456	+	22.5319i	−0.747395	+	1.00565i
$503$	−3.01250			−0.134321			−0.0671605	−	0.997742i	$-0.521394\pi$
$503$	−3.01250			−0.134321			−0.0671605	+	0.997742i	$0.521394\pi$
$504$	−1.58516	−	3.67422i	−0.0706086	−	0.163663i
$505$		0			0
$506$	−5.42984	+	7.30607i	−0.241386	+	0.324794i
$507$	19.3699	−	33.5497i	0.860249	−	1.48999i
$508$	−24.5886	+	7.40538i	−1.09094	+	0.328561i
$509$	11.2920	−	6.51942i	0.500508	−	0.288968i	−0.228415	−	0.973564i	$-0.573354\pi$
$509$	11.2920	−	6.51942i	0.500508	−	0.288968i	0.728923	+	0.684595i	$0.240021\pi$
$510$		0			0
$511$	11.8173	+	3.56885i	0.522766	+	0.157876i
$512$	−11.4582	−	19.5118i	−0.506387	−	0.862306i
$513$	12.7284	+	22.0462i	0.561971	+	0.973362i
$514$	2.70322	−	23.2934i	0.119234	−	1.02743i
$515$		0			0
$516$	2.85033	−	12.1151i	0.125479	−	0.533338i
$517$			0.191511i			0.00842265i
$518$	−1.06098	+	0.122308i	−0.0466166	+	0.00537389i
$519$		−	3.76120i		−	0.165098i
$520$		0			0
$521$	−17.6924	−	10.2147i	−0.775116	−	0.447514i	0.0595804	−	0.998224i	$-0.481024\pi$
$521$	−17.6924	−	10.2147i	−0.775116	−	0.447514i	−0.834697	+	0.550710i	$0.814357\pi$
$522$	1.53493	+	0.178130i	0.0671820	+	0.00779653i
$523$	17.0061	+	29.4555i	0.743626	+	1.28800i	0.950834	+	0.309701i	$0.100229\pi$
$523$	17.0061	+	29.4555i	0.743626	+	1.28800i	−0.207208	+	0.978297i	$0.566438\pi$
$524$	4.50852	−	4.79451i	0.196956	−	0.209449i
$525$		0			0
$526$	−10.3087	+	4.45680i	−0.449483	+	0.194326i
$527$	6.72794	−	3.88438i	0.293074	−	0.169206i
$528$	4.64670	−	9.32863i	0.202222	−	0.405976i
$529$	−0.713494	+	1.23581i	−0.0310215	+	0.0537308i
$530$		0			0
$531$	0.890362			0.0386384
$532$	14.5506	−	25.1581i	0.630850	−	1.09074i
$533$	−47.5948			−2.06156
$534$	7.93717	+	5.89888i	0.343475	+	0.255270i
$535$		0			0
$536$	−21.2358	−	25.1815i	−0.917245	−	1.08768i
$537$	41.3935	−	23.8986i	1.78626	−	1.03130i
$538$	23.5834	−	10.1959i	1.01675	−	0.439576i
$539$	9.68150	+	0.610616i	0.417012	+	0.0263011i
$540$		0			0
$541$	−20.5137	−	35.5309i	−0.881955	−	1.52759i	−0.849165	−	0.528128i	$-0.822894\pi$
$541$	−20.5137	−	35.5309i	−0.881955	−	1.52759i	−0.0327904	−	0.999462i	$-0.510439\pi$
$542$	−32.7657	−	3.80249i	−1.40741	−	0.163331i
$543$	−19.6102	−	11.3219i	−0.841553	−	0.485871i
$544$	14.4128	−	22.1108i	0.617943	−	0.947993i
$545$		0			0
$546$	−32.7490	+	24.3003i	−1.40153	+	1.03996i
$547$			32.3049i			1.38126i	0.723209	+	0.690629i	$0.242666\pi$
$547$			32.3049i			1.38126i	−0.723209	+	0.690629i	$0.757334\pi$
$548$	41.3874	+	9.73722i	1.76798	+	0.415953i
$549$	1.33467	+	0.770574i	0.0569625	+	0.0328873i
$550$		0			0
$551$	5.61140	+	9.71923i	0.239054	+	0.414053i
$552$	−8.39034	+	23.2302i	−0.357116	+	0.988742i
$553$	19.7782	−	18.5701i	0.841057	−	0.789682i
$554$	−13.0197	−	30.1151i	−0.553156	−	1.27947i
$555$		0			0
$556$	−4.86835	−	16.1647i	−0.206464	−	0.685537i
$557$	−2.59501	+	4.49470i	−0.109954	+	0.190446i	−0.915752	−	0.401745i	$-0.868404\pi$
$557$	−2.59501	+	4.49470i	−0.109954	+	0.190446i	0.805797	+	0.592192i	$0.201737\pi$
$558$	0.751090	−	1.01062i	0.0317962	−	0.0427830i
$559$	−19.1877			−0.811551
$560$		0			0
$561$	12.1565			0.513246
$562$	−1.32874	+	1.78788i	−0.0560497	+	0.0754170i
$563$	14.1225	−	24.4608i	0.595190	−	1.03090i	−0.398330	−	0.917242i	$-0.630410\pi$
$563$	14.1225	−	24.4608i	0.595190	−	1.03090i	0.993520	−	0.113658i	$-0.0362567\pi$
$564$	0.149849	+	0.497556i	0.00630980	+	0.0209509i
$565$		0			0
$566$	−4.28843	−	9.91930i	−0.180256	−	0.416939i
$567$	−7.89246	+	26.1338i	−0.331452	+	1.09752i
$568$	−2.20919	+	6.11654i	−0.0926955	+	0.256644i
$569$	−15.3058	−	26.5104i	−0.641651	−	1.11137i	−0.985064	−	0.172188i	$-0.944916\pi$
$569$	−15.3058	−	26.5104i	−0.641651	−	1.11137i	0.343413	−	0.939184i	$-0.388417\pi$
$570$		0			0
$571$	−1.43282	−	0.827239i	−0.0599617	−	0.0346189i	0.469719	−	0.882816i	$-0.344355\pi$
$571$	−1.43282	−	0.827239i	−0.0599617	−	0.0346189i	−0.529681	+	0.848197i	$0.677688\pi$
$572$	−15.6402	−	3.67967i	−0.653949	−	0.153855i
$573$			36.8702i			1.54027i
$574$	28.1882	+	12.2122i	1.17655	+	0.509727i
$575$		0			0
$576$	0.722076	−	4.21648i	0.0300865	−	0.175687i
$577$	18.4801	+	10.6695i	0.769335	+	0.444176i	0.832637	−	0.553819i	$-0.186830\pi$
$577$	18.4801	+	10.6695i	0.769335	+	0.444176i	−0.0633023	+	0.997994i	$0.520163\pi$
$578$	6.69978	+	0.777515i	0.278674	+	0.0323404i
$579$	2.66863	+	4.62221i	0.110905	+	0.192092i
$580$		0			0
$581$	−0.209904	+	0.0492153i	−0.00870827	+	0.00204179i
$582$	9.48917	−	4.10248i	0.393339	−	0.170053i
$583$	−8.07501	+	4.66211i	−0.334433	+	0.193085i
$584$	8.50758	+	10.0884i	0.352046	+	0.417459i
$585$		0			0
$586$	−10.7638	−	7.99960i	−0.444647	−	0.330461i
$587$	−19.5450			−0.806710			−0.403355	−	0.915044i	$-0.632156\pi$
$587$	−19.5450			−0.806710			−0.403355	+	0.915044i	$0.632156\pi$
$588$	25.6308	−	5.98896i	1.05700	−	0.246980i
$589$	9.14513			0.376818
$590$		0			0
$591$	10.1464	−	17.5741i	0.417367	−	0.722902i
$592$	−1.02198	−	0.509059i	−0.0420029	−	0.0209222i
$593$	−22.2662	+	12.8554i	−0.914362	+	0.527907i	−0.881832	−	0.471563i	$-0.843690\pi$
$593$	−22.2662	+	12.8554i	−0.914362	+	0.527907i	−0.0325303	+	0.999471i	$0.510357\pi$
$594$	−8.33787	+	3.60473i	−0.342107	+	0.147904i
$595$		0			0
$596$	3.52816	−	3.75196i	0.144519	−	0.153686i
$597$	−1.34145	−	2.32346i	−0.0549018	−	0.0950928i
$598$	37.8242	+	4.38953i	1.54675	+	0.179501i
$599$	−22.2773	−	12.8618i	−0.910225	−	0.525518i	−0.0297211	−	0.999558i	$-0.509462\pi$
$599$	−22.2773	−	12.8618i	−0.910225	−	0.525518i	−0.880503	+	0.474040i	$0.842795\pi$
$600$		0			0
$601$			12.5087i			0.510239i	0.966909	+	0.255120i	$0.0821149\pi$
$601$			12.5087i			0.510239i	−0.966909	+	0.255120i	$0.917885\pi$
$602$	11.3640	+	4.92329i	0.463160	+	0.200658i
$603$		−	6.22760i		−	0.253607i
$604$	−8.63568	+	36.7053i	−0.351381	+	1.49352i
$605$		0			0
$606$	−3.15643	+	27.1986i	−0.128221	+	1.10487i
$607$	−11.1358	−	19.2877i	−0.451987	−	0.782865i	0.546522	−	0.837445i	$-0.315951\pi$
$607$	−11.1358	−	19.2877i	−0.451987	−	0.782865i	−0.998509	+	0.0545800i	$0.982618\pi$
$608$	27.7073	−	14.0579i	1.12368	−	0.570122i
$609$	−2.93850	+	9.73005i	−0.119074	+	0.394282i
$610$		0			0
$611$	0.693780	−	0.400554i	0.0280673	−	0.0162047i
$612$	4.77788	−	1.43896i	0.193134	−	0.0581665i
$613$	−12.3373	+	21.3688i	−0.498298	+	0.863078i	−0.999998	−	0.00196375i	$-0.999375\pi$
$613$	−12.3373	+	21.3688i	−0.498298	+	0.863078i	0.501700	+	0.865042i	$0.332708\pi$
$614$	−22.1771	+	29.8401i	−0.894994	+	1.20425i
$615$		0			0
$616$	8.31881	+	6.19236i	0.335174	+	0.249497i
$617$	0.570871			0.0229824			0.0114912	−	0.999934i	$-0.496342\pi$
$617$	0.570871			0.0229824			0.0114912	+	0.999934i	$0.496342\pi$
$618$	6.42926	−	8.65082i	0.258623	−	0.347987i
$619$	18.6506	−	32.3038i	0.749630	−	1.29840i	−0.198370	−	0.980127i	$-0.563565\pi$
$619$	18.6506	−	32.3038i	0.749630	−	1.29840i	0.948000	−	0.318271i	$-0.103102\pi$
$620$		0			0
$621$	18.6435	−	10.7639i	0.748139	−	0.431938i
$622$	17.0601	+	39.4605i	0.684046	+	1.58222i
$623$	−7.17391	+	6.73570i	−0.287416	+	0.269860i
$624$	−43.5133	+	2.67781i	−1.74192	+	0.107198i
$625$		0			0
$626$	−0.444240	+	3.82798i	−0.0177554	+	0.152997i
$627$	12.3930	+	7.15509i	0.494928	+	0.285747i
$628$	8.35414	−	35.5087i	0.333366	−	1.41695i
$629$		−	1.33177i		−	0.0531012i
$630$		0			0
$631$		−	3.05636i		−	0.121672i	−0.998148	−	0.0608359i	$-0.980623\pi$
$631$		−	3.05636i		−	0.121672i	0.998148	−	0.0608359i	$-0.0193766\pi$
$632$	28.5499	−	5.10667i	1.13565	−	0.203133i
$633$	1.97571	+	1.14068i	0.0785274	+	0.0453378i
$634$	14.7251	+	1.70886i	0.584808	+	0.0678675i
$635$		0			0
$636$	−17.3314	+	18.4308i	−0.687235	+	0.730827i
$637$	−18.0372	−	36.3500i	−0.714662	−	1.44024i
$638$	−3.67582	+	1.58917i	−0.145527	+	0.0629160i
$639$	−1.06477	+	0.614744i	−0.0421216	+	0.0243189i
$640$		0			0
$641$	15.8964	−	27.5333i	0.627869	−	1.08750i	−0.360110	−	0.932910i	$-0.617261\pi$
$641$	15.8964	−	27.5333i	0.627869	−	1.08750i	0.987979	−	0.154591i	$-0.0494059\pi$
$642$	16.5905	+	12.3300i	0.654773	+	0.486625i
$643$	−2.73243			−0.107756			−0.0538782	−	0.998548i	$-0.517158\pi$
$643$	−2.73243			−0.107756			−0.0538782	+	0.998548i	$0.517158\pi$
$644$	−21.2752	−	12.3049i	−0.838361	−	0.484880i
$645$		0			0
$646$	29.0873	+	21.6176i	1.14442	+	0.850533i
$647$	−14.1630	+	24.5311i	−0.556805	+	0.964415i	0.440955	+	0.897529i	$0.354640\pi$
$647$	−14.1630	+	24.5311i	−0.556805	+	0.964415i	−0.997761	+	0.0668861i	$0.978694\pi$
$648$	−22.3103	+	18.8144i	−0.876431	+	0.739100i
$649$	−1.99833	+	1.15374i	−0.0784413	+	0.0452881i
$650$		0			0
$651$	5.66923	+	6.03806i	0.222195	+	0.236650i
$652$	−14.5953	−	13.7248i	−0.571598	−	0.537503i
$653$	4.06833	+	7.04655i	0.159206	+	0.275753i	0.934583	−	0.355746i	$-0.115773\pi$
$653$	4.06833	+	7.04655i	0.159206	+	0.275753i	−0.775377	+	0.631499i	$0.782440\pi$
$654$	−23.3818	−	2.71348i	−0.914302	−	0.106106i
$655$		0			0
$656$	18.1364	+	27.3788i	0.708109	+	1.06896i
$657$			2.49493i			0.0973366i
$658$	−0.513670	+	0.0592152i	−0.0200250	+	0.00230845i
$659$			45.7747i			1.78313i	0.452894	+	0.891565i	$0.350392\pi$
$659$			45.7747i			1.78313i	−0.452894	+	0.891565i	$0.649608\pi$
$660$		0			0
$661$	−21.6199	−	12.4823i	−0.840918	−	0.485504i	0.0166580	−	0.999861i	$-0.494697\pi$
$661$	−21.6199	−	12.4823i	−0.840918	−	0.485504i	−0.857576	+	0.514357i	$0.828031\pi$
$662$	−2.01253	+	17.3418i	−0.0782191	+	0.674007i
$663$	−25.4258	−	44.0387i	−0.987455	−	1.71032i
$664$	−0.216776	−	0.0782956i	−0.00841253	−	0.00303846i
$665$		0			0
$666$	−0.0856581	−	0.198130i	−0.00331918	−	0.00767739i
$667$	8.21916	−	4.74533i	0.318247	−	0.183740i
$668$	3.18971	+	10.5910i	0.123414	+	0.409779i
$669$	23.6059	−	40.8866i	0.912657	−	1.58077i
$670$		0			0
$671$	−3.99406			−0.154189
$672$	26.4580	+	9.57896i	1.02064	+	0.369516i
$673$	16.4406			0.633739			0.316870	−	0.948469i	$-0.397368\pi$
$673$	16.4406			0.633739			0.316870	+	0.948469i	$0.397368\pi$
$674$	−5.51714	+	7.42352i	−0.212512	+	0.285943i
$675$		0			0
$676$	11.8842	+	39.4599i	0.457084	+	1.51769i
$677$	−4.01299	+	2.31690i	−0.154232	+	0.0890458i	−0.575130	−	0.818062i	$-0.695048\pi$
$677$	−4.01299	+	2.31690i	−0.154232	+	0.0890458i	0.420898	+	0.907108i	$0.361715\pi$
$678$	15.6569	+	36.2149i	0.601299	+	1.39082i
$679$	2.34829	+	10.0155i	0.0901192	+	0.384359i
$680$		0			0
$681$	18.7525	+	32.4802i	0.718596	+	1.24464i
$682$	−0.376179	+	3.24150i	−0.0144046	+	0.124124i
$683$	37.1863	+	21.4695i	1.42289	+	0.821508i	0.996545	−	0.0830518i	$-0.0264667\pi$
$683$	37.1863	+	21.4695i	1.42289	+	0.821508i	0.426348	+	0.904559i	$0.359800\pi$
$684$	5.71779	+	1.34523i	0.218625	+	0.0514361i
$685$		0			0
$686$	1.35573	+	26.1565i	0.0517618	+	0.998659i
$687$		−	38.5337i		−	1.47015i
$688$	7.31163	+	11.0376i	0.278753	+	0.420806i
$689$	33.7785	+	19.5020i	1.28686	+	0.742968i
$690$		0			0
$691$	20.2222	+	35.0258i	0.769287	+	1.33244i	0.937950	+	0.346771i	$0.112722\pi$
$691$	20.2222	+	35.0258i	0.769287	+	1.33244i	−0.168663	+	0.985674i	$0.553945\pi$
$692$	2.91479	+	2.74093i	0.110804	+	0.104194i
$693$	0.447561	+	1.90885i	0.0170014	+	0.0725112i
$694$	45.6970	−	19.7563i	1.73464	−	0.749939i
$695$		0			0
$696$	−8.30651	+	7.00493i	−0.314857	+	0.265521i
$697$	−19.1535	+	33.1748i	−0.725490	+	1.25658i
$698$	12.7917	+	9.50676i	0.484174	+	0.359836i
$699$	−8.14237			−0.307973
$700$		0			0
$701$	30.8942			1.16686			0.583429	−	0.812164i	$-0.301711\pi$
$701$	30.8942			1.16686			0.583429	+	0.812164i	$0.301711\pi$
$702$	30.4977	+	22.6658i	1.15106	+	0.855467i
$703$	0.783859	−	1.35768i	0.0295638	−	0.0512060i
$704$	3.84311	+	10.3991i	0.144843	+	0.391933i
$705$		0			0
$706$	15.3243	−	6.62517i	0.576736	−	0.249342i
$707$	−26.0828	−	7.87708i	−0.980946	−	0.296248i
$708$	−4.28902	+	4.56108i	−0.161191	+	0.171416i
$709$	−21.6586	−	37.5139i	−0.813407	−	1.40886i	−0.910466	−	0.413584i	$-0.864277\pi$
$709$	−21.6586	−	37.5139i	−0.813407	−	1.40886i	0.0970588	−	0.995279i	$-0.469057\pi$
$710$		0			0
$711$	4.74860	+	2.74161i	0.178087	+	0.102818i
$712$	−10.3555	+	1.85228i	−0.388090	+	0.0694170i
$713$		−	7.73366i		−	0.289628i
$714$	3.75877	+	32.6060i	0.140668	+	1.22025i
$715$		0			0
$716$	−11.6445	+	49.4942i	−0.435176	+	1.84969i
$717$	−5.84331	−	3.37364i	−0.218223	−	0.125991i
$718$	2.62181	−	22.5919i	0.0978452	−	0.843123i
$719$	21.4941	+	37.2288i	0.801593	+	1.38840i	0.918567	+	0.395265i	$0.129347\pi$
$719$	21.4941	+	37.2288i	0.801593	+	1.38840i	−0.116974	+	0.993135i	$0.537320\pi$
$720$		0			0
$721$	7.34132	+	7.81892i	0.273405	+	0.291192i
$722$	6.26655	+	14.4948i	0.233217	+	0.539439i
$723$	1.40956	−	0.813812i	0.0524223	−	0.0302660i
$724$	23.0648	−	6.94644i	0.857196	−	0.258162i
$725$		0			0
$726$	14.4001	−	19.3759i	0.534438	−	0.719107i
$727$	−1.38049			−0.0511995			−0.0255997	−	0.999672i	$-0.508150\pi$
$727$	−1.38049			−0.0511995			−0.0255997	+	0.999672i	$0.508150\pi$
$728$	5.03367	−	43.0878i	0.186560	−	1.59694i
$729$	20.6247			0.763877
$730$		0			0
$731$	−7.72164	+	13.3743i	−0.285595	+	0.494665i
$732$	−10.3768	+	3.12518i	−0.383537	+	0.115510i
$733$	13.1258	−	7.57816i	0.484811	−	0.279906i	−0.237608	−	0.971361i	$-0.576363\pi$
$733$	13.1258	−	7.57816i	0.484811	−	0.279906i	0.722419	+	0.691455i	$0.243030\pi$
$734$	−17.0530	−	39.4442i	−0.629438	−	1.45591i
$735$		0			0
$736$	−11.8882	−	23.4309i	−0.438204	−	0.863675i
$737$	8.06975	+	13.9772i	0.297253	+	0.514858i
$738$	−0.715733	+	6.16741i	−0.0263465	+	0.227026i
$739$	24.2546	+	14.0034i	0.892219	+	0.515123i	0.874668	−	0.484723i	$-0.161080\pi$
$739$	24.2546	+	14.0034i	0.892219	+	0.515123i	0.0175513	+	0.999846i	$0.494413\pi$
$740$		0			0
$741$		−	59.8608i		−	2.19904i
$742$	−15.0015	−	20.2172i	−0.550722	−	0.742198i
$743$			8.25628i			0.302894i	0.988465	+	0.151447i	$0.0483932\pi$
$743$			8.25628i			0.302894i	−0.988465	+	0.151447i	$0.951607\pi$
$744$	1.55901	+	8.71594i	0.0571559	+	0.319542i
$745$		0			0
$746$	−27.5947	−	3.20239i	−1.01031	−	0.117248i
$747$	−0.0217871	−	0.0377363i	−0.000797147	−	0.00138070i
$748$	−8.85887	+	9.42080i	−0.323912	+	0.344459i
$749$	−14.9951	+	14.0791i	−0.547907	+	0.514439i
$750$		0			0
$751$	30.7859	−	17.7743i	1.12339	−	0.648592i	0.181129	−	0.983459i	$-0.442025\pi$
$751$	30.7859	−	17.7743i	1.12339	−	0.648592i	0.942265	+	0.334867i	$0.108691\pi$
$752$	−0.494789	−	0.246460i	−0.0180431	−	0.00898748i
$753$	18.6606	−	32.3211i	0.680029	−	1.17785i
$754$	13.4452	+	9.99241i	0.489645	+	0.363902i
$755$		0			0
$756$	−12.2467	−	21.2492i	−0.445406	−	0.772826i
$757$	36.8013			1.33757			0.668783	−	0.743458i	$-0.266815\pi$
$757$	36.8013			1.33757			0.668783	+	0.743458i	$0.266815\pi$
$758$	−21.2910	−	15.8234i	−0.773324	−	0.574732i
$759$	6.05077	−	10.4802i	0.219629	−	0.380409i
$760$		0			0
$761$	33.8606	−	19.5494i	1.22744	−	0.708666i	0.260950	−	0.965352i	$-0.415964\pi$
$761$	33.8606	−	19.5494i	1.22744	−	0.708666i	0.966495	+	0.256687i	$0.0826309\pi$
$762$	31.3359	−	13.5475i	1.13518	−	0.490775i
$763$	6.77168	−	22.4226i	0.245151	−	0.811752i
$764$	−28.5730	−	26.8687i	−1.03374	−	0.972075i
$765$		0			0
$766$	−24.7701	−	2.87459i	−0.894979	−	0.103863i
$767$	8.35919	+	4.82618i	0.301833	+	0.174263i
$768$	18.1215	+	24.0105i	0.653904	+	0.866403i
$769$			17.0090i			0.613359i	0.951813	+	0.306679i	$0.0992179\pi$
$769$			17.0090i			0.613359i	−0.951813	+	0.306679i	$0.900782\pi$
$770$		0			0
$771$			31.1747i			1.12273i
$772$	−5.52677	−	1.30029i	−0.198913	−	0.0467983i
$773$	7.53906	+	4.35268i	0.271161	+	0.156555i	0.629415	−	0.777069i	$-0.283295\pi$
$773$	7.53906	+	4.35268i	0.271161	+	0.156555i	−0.358254	+	0.933624i	$0.616628\pi$
$774$	−0.288545	+	2.48637i	−0.0103715	+	0.0893705i
$775$		0			0
$776$	−3.73585	+	10.3434i	−0.134109	+	0.371306i
$777$	1.38234	−	0.324111i	0.0495911	−	0.0116274i
$778$	−0.521721	−	1.20676i	−0.0187046	−	0.0432644i
$779$	−39.0523	+	22.5469i	−1.39919	+	0.807825i
$780$		0			0
$781$	1.59318	−	2.75946i	0.0570084	−	0.0987414i
$782$	18.2811	−	24.5979i	0.653731	−	0.879620i
$783$	9.47073			0.338456
$784$	−14.0369	+	24.2273i	−0.501320	+	0.865262i
$785$		0			0
$786$	−5.21901	+	7.02238i	−0.186156	+	0.250480i
$787$	1.12075	−	1.94119i	0.0399503	−	0.0691960i	−0.845359	−	0.534199i	$-0.820613\pi$
$787$	1.12075	−	1.94119i	0.0399503	−	0.0691960i	0.885309	+	0.465003i	$0.153947\pi$
$788$	6.22520	+	20.6700i	0.221764	+	0.736338i
$789$	12.9303	−	7.46531i	0.460331	−	0.265772i
$790$		0			0
$791$	−38.2236	+	8.96213i	−1.35907	+	0.318657i
$792$	−0.712016	+	1.97134i	−0.0253004	+	0.0700487i
$793$	8.35375	+	14.4691i	0.296650	+	0.513814i
$794$	−4.17513	+	35.9767i	−0.148170	+	1.27677i
$795$		0			0
$796$	2.77816	+	0.653618i	0.0984692	+	0.0231669i
$797$		−	20.8126i		−	0.737220i	−0.929584	−	0.368610i	$-0.879834\pi$
$797$		−	20.8126i		−	0.737220i	0.929584	−	0.368610i	$-0.120166\pi$
$798$	−15.3595	+	35.4528i	−0.543719	+	1.25501i
$799$		−	0.644776i		−	0.0228105i
$800$		0			0
$801$	−1.72240	−	0.994428i	−0.0608580	−	0.0351364i
$802$	4.09258	+	0.474948i	0.144514	+	0.0167710i
$803$	−3.23295	−	5.59963i	−0.114088	−	0.197607i
$804$	31.9022	+	29.9993i	1.12511	+	1.05799i
$805$		0			0
$806$	12.5297	−	5.41698i	0.441339	−	0.190805i
$807$	−29.5808	+	17.0785i	−1.04129	+	0.601191i
$808$	−18.7777	−	22.2668i	−0.660599	−	0.783343i
$809$	2.55436	−	4.42429i	0.0898067	−	0.155550i	−0.817623	−	0.575754i	$-0.804708\pi$
$809$	2.55436	−	4.42429i	0.0898067	−	0.155550i	0.907429	+	0.420205i	$0.138042\pi$
$810$		0			0
$811$	2.38868			0.0838779			0.0419390	−	0.999120i	$-0.486646\pi$
$811$	2.38868			0.0838779			0.0419390	+	0.999120i	$0.486646\pi$
$812$	−5.39904	−	9.36789i	−0.189469	−	0.328748i
$813$	43.8518			1.53795
$814$	0.448989	+	0.333688i	0.0157371	+	0.0116957i
$815$		0			0
$816$	−15.6444	+	31.4074i	−0.547665	+	1.09948i
$817$	−15.7438	+	9.08967i	−0.550805	+	0.318007i
$818$	−43.6767	+	18.8829i	−1.52712	+	0.660223i
$819$	5.97903	−	5.61381i	0.208924	−	0.196162i
$820$		0			0
$821$	−14.7840	−	25.6066i	−0.515964	−	0.893676i	−0.999828	−	0.0185331i	$-0.994100\pi$
$821$	−14.7840	−	25.6066i	−0.515964	−	0.893676i	0.483864	−	0.875143i	$-0.339233\pi$
$822$	−56.1468	−	6.51588i	−1.95834	−	0.227267i
$823$	11.4243	+	6.59584i	0.398227	+	0.229916i	0.685719	−	0.727867i	$-0.259488\pi$
$823$	11.4243	+	6.59584i	0.398227	+	0.229916i	−0.287492	+	0.957783i	$0.592821\pi$
$824$	2.01882	+	11.2866i	0.0703289	+	0.393188i
$825$		0			0
$826$	−3.71243	−	5.00318i	−0.129172	−	0.174083i
$827$		−	18.3687i		−	0.638743i	−0.947630	−	0.319371i	$-0.896528\pi$
$827$		−	18.3687i		−	0.638743i	0.947630	−	0.319371i	$-0.103472\pi$
$828$	1.13760	−	4.83530i	0.0395344	−	0.168038i
$829$	−30.4962	−	17.6070i	−1.05918	−	0.611515i	−0.133971	−	0.990985i	$-0.542773\pi$
$829$	−30.4962	−	17.6070i	−1.05918	−	0.611515i	−0.925204	+	0.379470i	$0.876106\pi$
$830$		0			0
$831$	21.8086	+	37.7736i	0.756531	+	1.31035i
$832$	29.6346	−	35.6726i	1.02739	−	1.23672i
$833$	−32.5955	−	2.05581i	−1.12937	−	0.0712296i
$834$	8.90623	+	20.6004i	0.308397	+	0.713334i
$835$		0			0
$836$	−14.5762	+	4.38992i	−0.504128	+	0.151829i
$837$	3.85871	−	6.68348i	0.133376	−	0.231015i
$838$	−10.3492	+	13.9253i	−0.357509	+	0.481042i
$839$	7.83756			0.270583			0.135291	−	0.990806i	$-0.456803\pi$
$839$	7.83756			0.270583			0.135291	+	0.990806i	$0.456803\pi$
$840$		0			0
$841$	−24.8248			−0.856026
$842$	−7.89724	+	10.6260i	−0.272157	+	0.366198i
$843$	1.48069	−	2.56463i	0.0509977	−	0.0883306i
$844$	−2.32376	+	0.699848i	−0.0799870	+	0.0240898i
$845$		0			0
$846$	−0.0414713	−	0.0959246i	−0.00142581	−	0.00329796i
$847$	16.4429	+	17.5126i	0.564985	+	0.601741i
$848$	−1.65311	−	26.8624i	−0.0567681	−	0.922459i
$849$	7.18329	+	12.4418i	0.246530	+	0.427002i
$850$		0			0
$851$	−1.14814	−	0.662878i	−0.0393577	−	0.0227232i
$852$	1.97999	−	8.41583i	0.0678335	−	0.288321i
$853$			10.4840i			0.358965i	0.983761	+	0.179483i	$0.0574424\pi$
$853$			10.4840i			0.358965i	−0.983761	+	0.179483i	$0.942558\pi$
$854$	−1.23496	−	10.7128i	−0.0422595	−	0.366586i
$855$		0			0
$856$	−21.6454	+	3.87167i	−0.739824	+	0.132331i
$857$	−23.8916	−	13.7938i	−0.816122	−	0.471189i	0.0329550	−	0.999457i	$-0.489508\pi$
$857$	−23.8916	−	13.7938i	−0.816122	−	0.471189i	−0.849077	+	0.528268i	$0.822842\pi$
$858$	21.2177	+	2.46234i	0.724362	+	0.0840628i
$859$	−20.8628	−	36.1355i	−0.711831	−	1.23293i	−0.964169	−	0.265288i	$-0.914533\pi$
$859$	−20.8628	−	36.1355i	−0.711831	−	1.23293i	0.252338	−	0.967639i	$-0.418800\pi$
$860$		0			0
$861$	−39.0958	−	11.8070i	−1.33238	−	0.402382i
$862$	31.5040	−	13.6202i	1.07303	−	0.463906i
$863$	−0.212051	+	0.122428i	−0.00721829	+	0.00416748i	−0.503605	−	0.863934i	$-0.667993\pi$
$863$	−0.212051	+	0.122428i	−0.00721829	+	0.00416748i	0.496387	+	0.868102i	$0.334660\pi$
$864$	1.41702	−	26.1807i	0.0482078	−	0.890687i
$865$		0			0
$866$	−3.40524	−	2.53076i	−0.115715	−	0.0859988i
$867$	−8.96662			−0.304522
$868$	−8.81066	−	0.00671546i	−0.299053	−	0.000227938i
$869$	−14.2104			−0.482053
$870$		0			0
$871$	33.7565	−	58.4680i	1.14380	−	1.98111i
$872$	19.1421	−	16.1426i	0.648232	−	0.546659i
$873$	−1.80058	+	1.03956i	−0.0609403	+	0.0351839i
$874$	33.1148	−	14.3166i	1.12012	−	0.484265i
$875$		0			0
$876$	−12.7808	−	12.0185i	−0.431825	−	0.406067i
$877$	25.7877	+	44.6656i	0.870789	+	1.50825i	0.861182	+	0.508297i	$0.169725\pi$
$877$	25.7877	+	44.6656i	0.870789	+	1.50825i	0.00960752	+	0.999954i	$0.496942\pi$
$878$	−20.1704	−	2.34080i	−0.680719	−	0.0789980i
$879$	15.4402	+	8.91439i	0.520784	+	0.300675i
$880$		0			0
$881$			35.8603i			1.20816i	0.796922	+	0.604082i	$0.206460\pi$
$881$			35.8603i			1.20816i	−0.796922	+	0.604082i	$0.793540\pi$
$882$	−4.98153	+	1.79066i	−0.167737	+	0.0602947i
$883$			24.5636i			0.826632i	0.910588	+	0.413316i	$0.135629\pi$
$883$			24.5636i			0.826632i	−0.910588	+	0.413316i	$0.864371\pi$
$884$	52.6571	+	12.3887i	1.77105	+	0.416676i
$885$		0			0
$886$	2.51110	−	21.6379i	0.0843621	−	0.726941i
$887$	−9.18275	−	15.9050i	−0.308327	−	0.534037i	0.669670	−	0.742659i	$-0.266436\pi$
$887$	−9.18275	−	15.9050i	−0.308327	−	0.534037i	−0.977996	+	0.208622i	$0.933102\pi$
$888$	1.42759	+	0.515623i	0.0479069	+	0.0173032i
$889$	7.75472	+	33.0739i	0.260085	+	1.10926i
$890$		0			0
$891$	12.3835	−	7.14963i	0.414863	−	0.239521i
$892$	14.4831	+	48.0893i	0.484930	+	1.61015i
$893$	0.379505	−	0.657322i	0.0126996	−	0.0219964i
$894$	−4.08416	+	5.49539i	−0.136595	+	0.183793i
$895$		0			0
$896$	−26.7043	+	13.5234i	−0.892127	+	0.451785i
$897$	−50.6218			−1.69021
$898$	22.3009	−	30.0067i	0.744189	−	1.00134i
$899$	1.70114	−	2.94647i	0.0567363	−	0.0982701i
$900$		0			0
$901$	27.1868	−	15.6963i	0.905724	−	0.522920i
$902$	−6.38537	−	14.7696i	−0.212610	−	0.491774i
$903$	−15.7613	−	4.75995i	−0.524503	−	0.158401i
$904$	−39.4750	−	14.2577i	−1.31292	−	0.474203i
$905$		0			0
$906$	5.77876	−	49.7951i	0.191986	−	1.65433i
$907$	29.8456	+	17.2314i	0.991008	+	0.572159i	0.905575	−	0.424185i	$-0.139439\pi$
$907$	29.8456	+	17.2314i	0.991008	+	0.572159i	0.0854324	+	0.996344i	$0.472773\pi$
$908$	−38.8366	−	9.13710i	−1.28884	−	0.303225i
$909$		−	5.50676i		−	0.182648i
$910$		0			0
$911$		−	33.5138i		−	1.11036i	−0.831729	−	0.555182i	$-0.812649\pi$
$911$		−	33.5138i		−	1.11036i	0.831729	−	0.555182i	$-0.187351\pi$
$912$	−34.4348	+	22.8105i	−1.14025	+	0.755331i
$913$	0.0977978	+	0.0564636i	0.00323664	+	0.00186867i
$914$	−52.9421	−	6.14397i	−1.75117	−	0.203225i
$915$		0			0
$916$	29.8622	+	28.0810i	0.986674	+	0.927821i
$917$	−5.95938	−	6.34708i	−0.196796	−	0.209599i
$918$	28.0718	−	12.1363i	0.926507	−	0.400559i
$919$	10.9820	−	6.34049i	0.362264	−	0.209153i	−0.307809	−	0.951448i	$-0.599596\pi$
$919$	10.9820	−	6.34049i	0.362264	−	0.209153i	0.670074	+	0.742295i	$0.266263\pi$
$920$		0			0
$921$	24.7131	−	42.8044i	0.814325	−	1.41045i
$922$	−4.09932	−	3.04660i	−0.135004	−	0.100334i
$923$	−13.3288			−0.438723
$924$	−11.9345	−	6.90251i	−0.392616	−	0.227076i
$925$		0			0
$926$	−31.3384	−	23.2906i	−1.02984	−	0.765376i
$927$	−1.08384	+	1.87726i	−0.0355979	+	0.0616574i
$928$	0.624703	−	11.5420i	0.0205069	−	0.378885i
$929$	35.8442	−	20.6947i	1.17601	−	0.678970i	0.220922	−	0.975291i	$-0.429093\pi$
$929$	35.8442	−	20.6947i	1.17601	−	0.678970i	0.955088	+	0.296322i	$0.0957601\pi$
$930$		0			0
$931$	−32.0197	−	21.2810i	−1.04940	−	0.697457i
$932$	5.93365	−	6.31004i	0.194363	−	0.206692i
$933$	−28.5762	−	49.4955i	−0.935544	−	1.62041i
$934$	1.84604	+	0.214234i	0.0604041	+	0.00700995i
$935$		0			0
$936$	8.63073	−	1.54376i	0.282104	−	0.0504595i
$937$		−	0.183387i		−	0.00599098i	−0.999996	−	0.00299549i	$-0.999047\pi$
$937$		−	0.183387i		−	0.00599098i	0.999996	−	0.00299549i	$-0.000953496\pi$
$938$	−34.9945	+	25.9664i	−1.14261	+	0.847833i
$939$		−	5.12316i		−	0.167188i
$940$		0			0
$941$	−6.13750	−	3.54349i	−0.200077	−	0.115514i	0.396615	−	0.917985i	$-0.370185\pi$
$941$	−6.13750	−	3.54349i	−0.200077	−	0.115514i	−0.596691	+	0.802471i	$0.703518\pi$
$942$	−5.59036	+	48.1716i	−0.182144	+	1.56952i
$943$	19.0670	+	33.0249i	0.620905	+	1.07544i
$944$	−0.409097	−	6.64766i	−0.0133150	−	0.216363i
$945$		0			0
$946$	−2.57424	−	5.95430i	−0.0836956	−	0.193591i
$947$	7.75877	−	4.47953i	0.252126	−	0.145565i	−0.368611	−	0.929584i	$-0.620167\pi$
$947$	7.75877	−	4.47953i	0.252126	−	0.145565i	0.620737	+	0.784019i	$0.286833\pi$
$948$	−36.9193	+	11.1190i	−1.19908	+	0.361129i
$949$	−13.5237	+	23.4238i	−0.438998	+	0.760367i
$950$		0			0
$951$	−19.7073			−0.639052
$952$	−28.0076	−	20.8483i	−0.907732	−	0.675698i
$953$	−18.0436			−0.584488			−0.292244	−	0.956344i	$-0.594402\pi$
$953$	−18.0436			−0.584488			−0.292244	+	0.956344i	$0.594402\pi$
$954$	3.03506	−	4.08380i	0.0982638	−	0.132218i
$955$		0			0
$956$	6.87269	−	2.06985i	0.222279	−	0.0669439i
$957$	4.61059	−	2.66193i	0.149039	−	0.0860479i
$958$	−10.4671	−	24.2108i	−0.338176	−	0.782214i
$959$	16.2608	−	53.8434i	0.525089	−	1.73869i
$960$		0			0
$961$	14.1138	+	24.4458i	0.455284	+	0.788574i
$962$	0.269756	−	2.32446i	0.00869727	−	0.0749436i
$963$	−3.60020	−	2.07857i	−0.116015	−	0.0669811i
$964$	−0.396529	+	1.68542i	−0.0127713	+	0.0542836i
$965$		0			0
$966$	29.9809	+	12.9889i	0.964621	+	0.417910i
$967$		−	41.2336i		−	1.32598i	−0.748627	−	0.662991i	$-0.769287\pi$
$967$		−	41.2336i		−	1.32598i	0.748627	−	0.662991i	$-0.230713\pi$
$968$	4.52170	+	25.2795i	0.145333	+	0.812514i
$969$	−41.7245	−	24.0896i	−1.34038	−	0.773871i
$970$		0			0
$971$	16.9420	+	29.3445i	0.543696	+	0.941708i	0.998688	+	0.0512130i	$0.0163087\pi$
$971$	16.9420	+	29.3445i	0.543696	+	0.941708i	−0.454992	+	0.890495i	$0.650358\pi$
$972$	7.52795	−	8.00546i	0.241459	−	0.256775i
$973$	−21.7430	+	5.09800i	−0.697049	+	0.163434i
$974$	13.3328	−	5.76420i	0.427210	−	0.184697i
$975$		0			0
$976$	5.14005	−	10.3191i	0.164529	−	0.330305i
$977$	14.6946	−	25.4518i	0.470121	−	0.814274i	−0.529295	−	0.848438i	$-0.677544\pi$
$977$	14.6946	−	25.4518i	0.470121	−	0.814274i	0.999416	+	0.0341641i	$0.0108769\pi$
$978$	21.3774	+	15.8876i	0.683573	+	0.508029i
$979$	5.15434			0.164733
$980$		0			0
$981$	4.73399			0.151145
$982$	−23.8826	−	17.7495i	−0.762124	−	0.566408i
$983$	−20.9083	+	36.2142i	−0.666871	+	1.15505i	0.311904	+	0.950114i	$0.399033\pi$
$983$	−20.9083	+	36.2142i	−0.666871	+	1.15505i	−0.978774	+	0.204940i	$0.934300\pi$
$984$	−28.1461	−	33.3759i	−0.897266	−	1.06399i
$985$		0			0
$986$	12.3757	−	5.35040i	0.394122	−	0.170392i
$987$	0.669258	−	0.156918i	0.0213027	−	0.00499477i
$988$	46.3899	+	43.6229i	1.47586	+	1.38783i
$989$	7.68676	+	13.3139i	0.244425	+	0.423356i
$990$		0			0
$991$	−19.0788	−	11.0151i	−0.606056	−	0.349907i	0.165364	−	0.986233i	$-0.447120\pi$
$991$	−19.0788	−	11.0151i	−0.606056	−	0.349907i	−0.771420	+	0.636326i	$0.780453\pi$
$992$	−7.89064	−	5.14347i	−0.250528	−	0.163305i
$993$		−	23.2093i		−	0.736524i
$994$	7.89403	+	3.41999i	0.250383	+	0.108475i
$995$		0			0
$996$	0.298264	+	0.0701727i	0.00945087	+	0.00222351i
$997$	−28.1444	−	16.2492i	−0.891341	−	0.514616i	−0.0169601	−	0.999856i	$-0.505399\pi$
$997$	−28.1444	−	16.2492i	−0.891341	−	0.514616i	−0.874381	+	0.485240i	$0.838732\pi$
$998$	3.43871	−	29.6311i	0.108850	−	0.937955i
$999$	−0.661485	−	1.14573i	−0.0209285	−	0.0362492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.p.e.451.12		32
4.3	odd	2	inner	700.2.p.e.451.1		32
5.2	odd	4		140.2.s.b.59.13	yes	32
5.3	odd	4		140.2.s.b.59.4	yes	32
5.4	even	2	inner	700.2.p.e.451.5		32
7.5	odd	6	inner	700.2.p.e.551.1		32
20.3	even	4		140.2.s.b.59.9	yes	32
20.7	even	4		140.2.s.b.59.8	yes	32
20.19	odd	2	inner	700.2.p.e.451.16		32
28.19	even	6	inner	700.2.p.e.551.12		32
35.2	odd	12		980.2.s.e.19.9		32
35.3	even	12		980.2.c.d.979.29		32
35.12	even	12		140.2.s.b.19.9	yes	32
35.13	even	4		980.2.s.e.619.4		32
35.17	even	12		980.2.c.d.979.4		32
35.18	odd	12		980.2.c.d.979.30		32
35.19	odd	6	inner	700.2.p.e.551.16		32
35.23	odd	12		980.2.s.e.19.8		32
35.27	even	4		980.2.s.e.619.13		32
35.32	odd	12		980.2.c.d.979.3		32
35.33	even	12		140.2.s.b.19.8	yes	32
140.3	odd	12		980.2.c.d.979.2		32
140.19	even	6	inner	700.2.p.e.551.5		32
140.23	even	12		980.2.s.e.19.13		32
140.27	odd	4		980.2.s.e.619.8		32
140.47	odd	12		140.2.s.b.19.4	✓	32
140.67	even	12		980.2.c.d.979.32		32
140.83	odd	4		980.2.s.e.619.9		32
140.87	odd	12		980.2.c.d.979.31		32
140.103	odd	12		140.2.s.b.19.13	yes	32
140.107	even	12		980.2.s.e.19.4		32
140.123	even	12		980.2.c.d.979.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.s.b.19.4	✓	32	140.47	odd	12
140.2.s.b.19.8	yes	32	35.33	even	12
140.2.s.b.19.9	yes	32	35.12	even	12
140.2.s.b.19.13	yes	32	140.103	odd	12
140.2.s.b.59.4	yes	32	5.3	odd	4
140.2.s.b.59.8	yes	32	20.7	even	4
140.2.s.b.59.9	yes	32	20.3	even	4
140.2.s.b.59.13	yes	32	5.2	odd	4
700.2.p.e.451.1		32	4.3	odd	2	inner
700.2.p.e.451.5		32	5.4	even	2	inner
700.2.p.e.451.12		32	1.1	even	1	trivial
700.2.p.e.451.16		32	20.19	odd	2	inner
700.2.p.e.551.1		32	7.5	odd	6	inner
700.2.p.e.551.5		32	140.19	even	6	inner
700.2.p.e.551.12		32	28.19	even	6	inner
700.2.p.e.551.16		32	35.19	odd	6	inner
980.2.c.d.979.1		32	140.123	even	12
980.2.c.d.979.2		32	140.3	odd	12
980.2.c.d.979.3		32	35.32	odd	12
980.2.c.d.979.4		32	35.17	even	12
980.2.c.d.979.29		32	35.3	even	12
980.2.c.d.979.30		32	35.18	odd	12
980.2.c.d.979.31		32	140.87	odd	12
980.2.c.d.979.32		32	140.67	even	12
980.2.s.e.19.4		32	140.107	even	12
980.2.s.e.19.8		32	35.23	odd	12
980.2.s.e.19.9		32	35.2	odd	12
980.2.s.e.19.13		32	140.23	even	12
980.2.s.e.619.4		32	35.13	even	4
980.2.s.e.619.8		32	140.27	odd	4
980.2.s.e.619.9		32	140.83	odd	4
980.2.s.e.619.13		32	35.27	even	4

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.843578 - 1.13507i) q^{2} +(-0.940044 + 1.62820i) q^{3} +(-0.576753 - 1.91503i) q^{4} +(1.05512 + 2.44053i) q^{6} +(-2.57589 + 0.603960i) q^{7} +(-2.66023 - 0.960828i) q^{8} +(-0.267367 - 0.463092i) q^{9} +O(q^{10})\)	\(q+(0.843578 - 1.13507i) q^{2} +(-0.940044 + 1.62820i) q^{3} +(-0.576753 - 1.91503i) q^{4} +(1.05512 + 2.44053i) q^{6} +(-2.57589 + 0.603960i) q^{7} +(-2.66023 - 0.960828i) q^{8} +(-0.267367 - 0.463092i) q^{9} +(1.20016 + 0.692910i) q^{11} +(3.66024 + 0.861146i) q^{12} -5.79701i q^{13} +(-1.48743 + 3.43330i) q^{14} +(-3.33471 + 2.20900i) q^{16} +(-4.04066 - 2.33288i) q^{17} +(-0.751185 - 0.0871757i) q^{18} +(-2.74619 - 4.75654i) q^{19} +(1.43808 - 4.76183i) q^{21} +(1.79892 - 0.777733i) q^{22} +(-4.02241 + 2.32234i) q^{23} +(4.06516 - 3.42817i) q^{24} +(-6.57999 - 4.89023i) q^{26} -4.63492 q^{27} +(2.64226 + 4.58459i) q^{28} -2.04334 q^{29} +(-0.832529 + 1.44198i) q^{31} +(-0.305726 + 5.64859i) q^{32} +(-2.25640 + 1.30273i) q^{33} +(-6.05658 + 2.61846i) q^{34} +(-0.732633 + 0.779106i) q^{36} +(0.142718 + 0.247194i) q^{37} +(-7.71561 - 0.895403i) q^{38} +(9.43872 + 5.44945i) q^{39} -8.21024i q^{41} +(-4.19186 - 5.64930i) q^{42} -3.30992i q^{43} +(0.634754 - 2.69798i) q^{44} +(-0.757206 + 6.52477i) q^{46} +(0.0690967 + 0.119679i) q^{47} +(-0.461929 - 7.50615i) q^{48} +(6.27046 - 3.11147i) q^{49} +(7.59680 - 4.38601i) q^{51} +(-11.1015 + 3.34344i) q^{52} +(-3.36415 + 5.82688i) q^{53} +(-3.90992 + 5.26094i) q^{54} +(7.43277 + 0.868321i) q^{56} +10.3262 q^{57} +(-1.72372 + 2.31933i) q^{58} +(-0.832529 + 1.44198i) q^{59} +(-2.49596 + 1.44104i) q^{61} +(0.934444 + 2.16140i) q^{62} +(0.968397 + 1.03140i) q^{63} +(6.15362 + 5.11204i) q^{64} +(-0.424760 + 3.66012i) q^{66} +(10.0859 + 5.82309i) q^{67} +(-2.13708 + 9.08350i) q^{68} -8.73240i q^{69} -2.29926i q^{71} +(0.266304 + 1.48882i) q^{72} +(-4.04066 - 2.33288i) q^{73} +(0.400976 + 0.0465336i) q^{74} +(-7.52506 + 8.00239i) q^{76} +(-3.50996 - 1.06002i) q^{77} +(14.1478 - 6.11654i) q^{78} +(-8.88033 + 5.12706i) q^{79} +(5.15913 - 8.93587i) q^{81} +(-9.31917 - 6.92598i) q^{82} +0.0814876 q^{83} +(-9.94849 - 0.00758271i) q^{84} +(-3.75698 - 2.79218i) q^{86} +(1.92083 - 3.32698i) q^{87} +(-2.52692 - 2.99644i) q^{88} +(3.22105 - 1.85967i) q^{89} +(3.50116 + 14.9325i) q^{91} +(6.76729 + 6.36363i) q^{92} +(-1.56523 - 2.71106i) q^{93} +(0.194132 + 0.0225292i) q^{94} +(-8.90966 - 5.80771i) q^{96} -3.88816i q^{97} +(1.75790 - 9.74217i) q^{98} -0.741044i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 6 q^{4} - 4 q^{9}+O(q^{10}) \) 32 * q - 6 * q^4 - 4 * q^9	\( 32 q - 6 q^{4} - 4 q^{9} - 22 q^{14} + 18 q^{16} - 52 q^{21} + 48 q^{24} - 18 q^{26} - 28 q^{36} + 26 q^{44} - 22 q^{46} - 48 q^{54} - 16 q^{56} + 36 q^{61} - 36 q^{64} - 24 q^{66} - 14 q^{74} + 72 q^{81} - 56 q^{84} + 8 q^{86} + 108 q^{89} - 30 q^{94} + 60 q^{96}+O(q^{100}) \) 32 * q - 6 * q^4 - 4 * q^9 - 22 * q^14 + 18 * q^16 - 52 * q^21 + 48 * q^24 - 18 * q^26 - 28 * q^36 + 26 * q^44 - 22 * q^46 - 48 * q^54 - 16 * q^56 + 36 * q^61 - 36 * q^64 - 24 * q^66 - 14 * q^74 + 72 * q^81 - 56 * q^84 + 8 * q^86 + 108 * q^89 - 30 * q^94 + 60 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more