LMFDB - Embedded newform 950.2.f.c.607.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(493,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("950.493");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.f (of order $4$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 212x^{12} + 880x^{10} + 1858x^{8} + 1960x^{6} + 892x^{4} + 96x^{2} + 1 $ x^16 + 24x^14 + 212x^12 + 880x^10 + 1858x^8 + 1960x^6 + 892x^4 + 96*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			607.7
Root			$1.52212i$ of defining polynomial
Character	$\chi$	$=$	950.607
Dual form			950.2.f.c.493.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.29807 + 1.29807i) q^{3} -1.00000i q^{4} +1.83575 q^{6} +(-2.12620 - 2.12620i) q^{7} +(-0.707107 - 0.707107i) q^{8} +0.369965i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.29807 + 1.29807i) q^{3} -1.00000i q^{4} +1.83575 q^{6} +(-2.12620 - 2.12620i) q^{7} +(-0.707107 - 0.707107i) q^{8} +0.369965i q^{9} +5.08815 q^{11} +(1.29807 - 1.29807i) q^{12} +(-3.71401 - 3.71401i) q^{13} -3.00690 q^{14} -1.00000 q^{16} +(1.18498 + 1.18498i) q^{17} +(0.261605 + 0.261605i) q^{18} +(4.18883 - 1.20571i) q^{19} -5.51991i q^{21} +(3.59786 - 3.59786i) q^{22} +(5.59198 - 5.59198i) q^{23} -1.83575i q^{24} -5.25240 q^{26} +(3.41397 - 3.41397i) q^{27} +(-2.12620 + 2.12620i) q^{28} -0.861689 q^{29} +7.04657i q^{31} +(-0.707107 + 0.707107i) q^{32} +(6.60477 + 6.60477i) q^{33} +1.67582 q^{34} +0.369965 q^{36} +(-3.98104 + 3.98104i) q^{37} +(2.10938 - 3.81451i) q^{38} -9.64208i q^{39} -2.38835i q^{41} +(-3.90317 - 3.90317i) q^{42} +(-4.14693 + 4.14693i) q^{43} -5.08815i q^{44} -7.90826i q^{46} +(-4.04146 - 4.04146i) q^{47} +(-1.29807 - 1.29807i) q^{48} +2.04146i q^{49} +3.07638i q^{51} +(-3.71401 + 3.71401i) q^{52} +(6.57175 + 6.57175i) q^{53} -4.82808i q^{54} +3.00690i q^{56} +(7.00248 + 3.87229i) q^{57} +(-0.609306 + 0.609306i) q^{58} +9.90431 q^{59} -4.21338 q^{61} +(4.98268 + 4.98268i) q^{62} +(0.786620 - 0.786620i) q^{63} +1.00000i q^{64} +9.34055 q^{66} +(-4.48345 + 4.48345i) q^{67} +(1.18498 - 1.18498i) q^{68} +14.5176 q^{69} +6.16296i q^{71} +(0.261605 - 0.261605i) q^{72} +(3.06742 - 3.06742i) q^{73} +5.63004i q^{74} +(-1.20571 - 4.18883i) q^{76} +(-10.8184 - 10.8184i) q^{77} +(-6.81798 - 6.81798i) q^{78} -14.1483 q^{79} +9.97302 q^{81} +(-1.68882 - 1.68882i) q^{82} +(-0.835746 + 0.835746i) q^{83} -5.51991 q^{84} +5.86464i q^{86} +(-1.11853 - 1.11853i) q^{87} +(-3.59786 - 3.59786i) q^{88} -4.55806 q^{89} +15.7935i q^{91} +(-5.59198 - 5.59198i) q^{92} +(-9.14693 + 9.14693i) q^{93} -5.71548 q^{94} -1.83575 q^{96} +(3.92722 - 3.92722i) q^{97} +(1.44353 + 1.44353i) q^{98} +1.88244i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} - 16 q^{16} + 32 q^{17} + 8 q^{23} - 32 q^{26} - 8 q^{28} + 32 q^{36} - 8 q^{38} + 32 q^{42} - 24 q^{43} - 32 q^{47} + 48 q^{57} - 64 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{66} + 32 q^{68} - 16 q^{73} - 16 q^{76} - 72 q^{77} + 16 q^{81} - 40 q^{82} + 16 q^{83} + 8 q^{87} - 8 q^{92} - 104 q^{93}+O(q^{100}) $ 16 * q - 8 * q^7 - 16 * q^16 + 32 * q^17 + 8 * q^23 - 32 * q^26 - 8 * q^28 + 32 * q^36 - 8 * q^38 + 32 * q^42 - 24 * q^43 - 32 * q^47 + 48 * q^57 - 64 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^66 + 32 * q^68 - 16 * q^73 - 16 * q^76 - 72 * q^77 + 16 * q^81 - 40 * q^82 + 16 * q^83 + 8 * q^87 - 8 * q^92 - 104 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.29807	+	1.29807i	0.749440	+	0.749440i	0.974374	−	0.224934i	$-0.0722166\pi$
$3$	1.29807	+	1.29807i	0.749440	+	0.749440i	−0.224934	+	0.974374i	$0.572217\pi$
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	1.83575			0.749440
$7$	−2.12620	−	2.12620i	−0.803628	−	0.803628i	0.180032	−	0.983661i	$-0.442380\pi$
$7$	−2.12620	−	2.12620i	−0.803628	−	0.803628i	−0.983661	+	0.180032i	$0.942380\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$			0.369965i			0.123322i
$10$		0			0
$11$	5.08815			1.53413			0.767067	−	0.641567i	$-0.221715\pi$
$11$	5.08815			1.53413			0.767067	+	0.641567i	$0.221715\pi$
$12$	1.29807	−	1.29807i	0.374720	−	0.374720i
$13$	−3.71401	−	3.71401i	−1.03008	−	1.03008i	−0.999533	−	0.0305473i	$-0.990275\pi$
$13$	−3.71401	−	3.71401i	−1.03008	−	1.03008i	−0.0305473	−	0.999533i	$-0.509725\pi$
$14$	−3.00690			−0.803628
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.18498	+	1.18498i	0.287400	+	0.287400i	0.836051	−	0.548651i	$-0.184858\pi$
$17$	1.18498	+	1.18498i	0.287400	+	0.287400i	−0.548651	+	0.836051i	$0.684858\pi$
$18$	0.261605	+	0.261605i	0.0616608	+	0.0616608i
$19$	4.18883	−	1.20571i	0.960983	−	0.276609i
$19$	4.18883	−	1.20571i	0.960983	−	0.276609i
$20$		0			0
$21$		−	5.51991i		−	1.20454i
$22$	3.59786	−	3.59786i	0.767067	−	0.767067i
$23$	5.59198	−	5.59198i	1.16601	−	1.16601i	0.182872	−	0.983137i	$-0.441461\pi$
$23$	5.59198	−	5.59198i	1.16601	−	1.16601i	0.983137	−	0.182872i	$-0.0585394\pi$
$24$		−	1.83575i		−	0.374720i
$25$		0			0
$26$	−5.25240			−1.03008
$27$	3.41397	−	3.41397i	0.657018	−	0.657018i
$28$	−2.12620	+	2.12620i	−0.401814	+	0.401814i
$29$	−0.861689			−0.160012			−0.0800058	−	0.996794i	$-0.525494\pi$
$29$	−0.861689			−0.160012			−0.0800058	+	0.996794i	$0.525494\pi$
$30$		0			0
$31$			7.04657i			1.26560i	0.774315	+	0.632800i	$0.218095\pi$
$31$			7.04657i			1.26560i	−0.774315	+	0.632800i	$0.781905\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	6.60477	+	6.60477i	1.14974	+	1.14974i
$34$	1.67582			0.287400
$35$		0			0
$36$	0.369965			0.0616608
$37$	−3.98104	+	3.98104i	−0.654478	+	0.654478i	−0.954068	−	0.299590i	$-0.903150\pi$
$37$	−3.98104	+	3.98104i	−0.654478	+	0.654478i	0.299590	+	0.954068i	$0.403150\pi$
$38$	2.10938	−	3.81451i	0.342187	−	0.618796i
$39$		−	9.64208i		−	1.54397i
$40$		0			0
$41$		−	2.38835i		−	0.372997i	−0.982455	−	0.186499i	$-0.940286\pi$
$41$		−	2.38835i		−	0.372997i	0.982455	−	0.186499i	$-0.0597140\pi$
$42$	−3.90317	−	3.90317i	−0.602271	−	0.602271i
$43$	−4.14693	+	4.14693i	−0.632401	+	0.632401i	−0.948670	−	0.316269i	$-0.897570\pi$
$43$	−4.14693	+	4.14693i	−0.632401	+	0.632401i	0.316269	+	0.948670i	$0.397570\pi$
$44$		−	5.08815i		−	0.767067i
$45$		0			0
$46$		−	7.90826i		−	1.16601i
$47$	−4.04146	−	4.04146i	−0.589507	−	0.589507i	0.347991	−	0.937498i	$-0.386864\pi$
$47$	−4.04146	−	4.04146i	−0.589507	−	0.589507i	−0.937498	+	0.347991i	$0.886864\pi$
$48$	−1.29807	−	1.29807i	−0.187360	−	0.187360i
$49$			2.04146i			0.291637i
$50$		0			0
$51$			3.07638i			0.430779i
$52$	−3.71401	+	3.71401i	−0.515040	+	0.515040i
$53$	6.57175	+	6.57175i	0.902699	+	0.902699i	0.995669	−	0.0929696i	$-0.0296359\pi$
$53$	6.57175	+	6.57175i	0.902699	+	0.902699i	−0.0929696	+	0.995669i	$0.529636\pi$
$54$		−	4.82808i		−	0.657018i
$55$		0			0
$56$			3.00690i			0.401814i
$57$	7.00248	+	3.87229i	0.927501	+	0.512897i
$58$	−0.609306	+	0.609306i	−0.0800058	+	0.0800058i
$59$	9.90431			1.28943			0.644716	−	0.764422i	$-0.276976\pi$
$59$	9.90431			1.28943			0.644716	+	0.764422i	$0.276976\pi$
$60$		0			0
$61$	−4.21338			−0.539468			−0.269734	−	0.962935i	$-0.586936\pi$
$61$	−4.21338			−0.539468			−0.269734	+	0.962935i	$0.586936\pi$
$62$	4.98268	+	4.98268i	0.632800	+	0.632800i
$63$	0.786620	−	0.786620i	0.0991048	−	0.0991048i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	9.34055			1.14974
$67$	−4.48345	+	4.48345i	−0.547740	+	0.547740i	−0.925787	−	0.378047i	$-0.876596\pi$
$67$	−4.48345	+	4.48345i	−0.547740	+	0.547740i	0.378047	+	0.925787i	$0.376596\pi$
$68$	1.18498	−	1.18498i	0.143700	−	0.143700i
$69$	14.5176			1.74771
$70$		0			0
$71$			6.16296i			0.731409i	0.930731	+	0.365705i	$0.119172\pi$
$71$			6.16296i			0.731409i	−0.930731	+	0.365705i	$0.880828\pi$
$72$	0.261605	−	0.261605i	0.0308304	−	0.0308304i
$73$	3.06742	−	3.06742i	0.359014	−	0.359014i	−0.504435	−	0.863449i	$-0.668299\pi$
$73$	3.06742	−	3.06742i	0.359014	−	0.359014i	0.863449	+	0.504435i	$0.168299\pi$
$74$			5.63004i			0.654478i
$75$		0			0
$76$	−1.20571	−	4.18883i	−0.138305	−	0.480491i
$77$	−10.8184	−	10.8184i	−1.23287	−	1.23287i
$78$	−6.81798	−	6.81798i	−0.771984	−	0.771984i
$79$	−14.1483			−1.59181			−0.795905	−	0.605421i	$-0.793005\pi$
$79$	−14.1483			−1.59181			−0.795905	+	0.605421i	$0.793005\pi$
$80$		0			0
$81$	9.97302			1.10811
$82$	−1.68882	−	1.68882i	−0.186499	−	0.186499i
$83$	−0.835746	+	0.835746i	−0.0917351	+	0.0917351i	−0.751485	−	0.659750i	$-0.770662\pi$
$83$	−0.835746	+	0.835746i	−0.0917351	+	0.0917351i	0.659750	+	0.751485i	$0.270662\pi$
$84$	−5.51991			−0.602271
$85$		0			0
$86$			5.86464i			0.632401i
$87$	−1.11853	−	1.11853i	−0.119919	−	0.119919i
$88$	−3.59786	−	3.59786i	−0.383534	−	0.383534i
$89$	−4.55806			−0.483153			−0.241577	−	0.970382i	$-0.577665\pi$
$89$	−4.55806			−0.483153			−0.241577	+	0.970382i	$0.577665\pi$
$90$		0			0
$91$			15.7935i			1.65560i
$92$	−5.59198	−	5.59198i	−0.583004	−	0.583004i
$93$	−9.14693	+	9.14693i	−0.948492	+	0.948492i
$94$	−5.71548			−0.589507
$95$		0			0
$96$	−1.83575			−0.187360
$97$	3.92722	−	3.92722i	0.398749	−	0.398749i	−0.479043	−	0.877792i	$-0.659016\pi$
$97$	3.92722	−	3.92722i	0.398749	−	0.398749i	0.877792	+	0.479043i	$0.159016\pi$
$98$	1.44353	+	1.44353i	0.145818	+	0.145818i
$99$			1.88244i			0.189192i
$100$		0			0
$101$	−5.75197			−0.572343			−0.286171	−	0.958178i	$-0.592383\pi$
$101$	−5.75197			−0.572343			−0.286171	+	0.958178i	$0.592383\pi$
$102$	2.17533	+	2.17533i	0.215390	+	0.215390i
$103$	2.55770	+	2.55770i	0.252018	+	0.252018i	0.821797	−	0.569780i	$-0.192971\pi$
$103$	2.55770	+	2.55770i	0.252018	+	0.252018i	−0.569780	+	0.821797i	$0.692971\pi$
$104$			5.25240i			0.515040i
$105$		0			0
$106$	9.29386			0.902699
$107$	−9.14167	+	9.14167i	−0.883758	+	0.883758i	−0.993914	−	0.110156i	$-0.964865\pi$
$107$	−9.14167	+	9.14167i	−0.883758	+	0.883758i	0.110156	+	0.993914i	$0.464865\pi$
$108$	−3.41397	−	3.41397i	−0.328509	−	0.328509i
$109$	3.52386			0.337524			0.168762	−	0.985657i	$-0.446023\pi$
$109$	3.52386			0.337524			0.168762	+	0.985657i	$0.446023\pi$
$110$		0			0
$111$	−10.3353			−0.980985
$112$	2.12620	+	2.12620i	0.200907	+	0.200907i
$113$	13.1281	+	13.1281i	1.23499	+	1.23499i	0.962024	+	0.272966i	$0.0880048\pi$
$113$	13.1281	+	13.1281i	1.23499	+	1.23499i	0.272966	+	0.962024i	$0.411995\pi$
$114$	7.68962	−	2.21338i	0.720199	−	0.207302i
$115$		0			0
$116$			0.861689i			0.0800058i
$117$	1.37405	−	1.37405i	0.127031	−	0.127031i
$118$	7.00340	−	7.00340i	0.644716	−	0.644716i
$119$		−	5.03902i		−	0.461926i
$120$		0			0
$121$	14.8892			1.35357
$122$	−2.97931	+	2.97931i	−0.269734	+	0.269734i
$123$	3.10024	−	3.10024i	0.279539	−	0.279539i
$124$	7.04657			0.632800
$125$		0			0
$126$		−	1.11245i		−	0.0991048i
$127$	0.600084	−	0.600084i	0.0532489	−	0.0532489i	−0.679981	−	0.733230i	$-0.738012\pi$
$127$	0.600084	−	0.600084i	0.0532489	−	0.0532489i	0.733230	+	0.679981i	$0.238012\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−10.7660			−0.947893
$130$		0			0
$131$	−2.73993			−0.239389			−0.119694	−	0.992811i	$-0.538191\pi$
$131$	−2.73993			−0.239389			−0.119694	+	0.992811i	$0.538191\pi$
$132$	6.60477	−	6.60477i	0.574871	−	0.574871i
$133$	−11.4699	−	6.34270i	−0.994564	−	0.549982i
$134$			6.34055i			0.547740i
$135$		0			0
$136$		−	1.67582i		−	0.143700i
$137$	−6.89793	−	6.89793i	−0.589330	−	0.589330i	0.348120	−	0.937450i	$-0.386820\pi$
$137$	−6.89793	−	6.89793i	−0.589330	−	0.589330i	−0.937450	+	0.348120i	$0.886820\pi$
$138$	10.2655	−	10.2655i	0.873854	−	0.873854i
$139$		−	3.37763i		−	0.286487i	−0.989687	−	0.143244i	$-0.954247\pi$
$139$		−	3.37763i		−	0.286487i	0.989687	−	0.143244i	$-0.0457532\pi$
$140$		0			0
$141$		−	10.4922i		−	0.883601i
$142$	4.35787	+	4.35787i	0.365705	+	0.365705i
$143$	−18.8974	−	18.8974i	−1.58028	−	1.58028i
$144$		−	0.369965i		−	0.0308304i
$145$		0			0
$146$		−	4.33799i		−	0.359014i
$147$	−2.64995	+	2.64995i	−0.218564	+	0.218564i
$148$	3.98104	+	3.98104i	0.327239	+	0.327239i
$149$			1.36230i			0.111604i	0.998442	+	0.0558018i	$0.0177715\pi$
$149$			1.36230i			0.111604i	−0.998442	+	0.0558018i	$0.982228\pi$
$150$		0			0
$151$		−	17.9862i		−	1.46370i	−0.681467	−	0.731849i	$-0.738658\pi$
$151$		−	17.9862i		−	1.46370i	0.681467	−	0.731849i	$-0.261342\pi$
$152$	−3.81451	−	2.10938i	−0.309398	−	0.171093i
$153$	−0.438402	+	0.438402i	−0.0354427	+	0.0354427i
$154$	−15.2996			−1.23287
$155$		0			0
$156$	−9.64208			−0.771984
$157$	11.6368	+	11.6368i	0.928721	+	0.928721i	0.997623	−	0.0689021i	$-0.0219496\pi$
$157$	11.6368	+	11.6368i	0.928721	+	0.928721i	−0.0689021	+	0.997623i	$0.521950\pi$
$158$	−10.0044	+	10.0044i	−0.795905	+	0.795905i
$159$			17.0612i			1.35304i
$160$		0			0
$161$	−23.7794			−1.87408
$162$	7.05199	−	7.05199i	0.554057	−	0.554057i
$163$	2.64736	−	2.64736i	0.207357	−	0.207357i	−0.595786	−	0.803143i	$-0.703159\pi$
$163$	2.64736	−	2.64736i	0.207357	−	0.207357i	0.803143	+	0.595786i	$0.203159\pi$
$164$	−2.38835			−0.186499
$165$		0			0
$166$			1.18192i			0.0917351i
$167$	−7.08501	+	7.08501i	−0.548254	+	0.548254i	−0.925936	−	0.377681i	$-0.876721\pi$
$167$	−7.08501	+	7.08501i	−0.548254	+	0.548254i	0.377681	+	0.925936i	$0.376721\pi$
$168$	−3.90317	+	3.90317i	−0.301136	+	0.301136i
$169$			14.5877i			1.12213i
$170$		0			0
$171$	0.446071	+	1.54972i	0.0341119	+	0.118510i
$172$	4.14693	+	4.14693i	0.316200	+	0.316200i
$173$	−2.32369	−	2.32369i	−0.176667	−	0.176667i	0.613234	−	0.789901i	$-0.289868\pi$
$173$	−2.32369	−	2.32369i	−0.176667	−	0.176667i	−0.789901	+	0.613234i	$0.789868\pi$
$174$	−1.58184			−0.119919
$175$		0			0
$176$	−5.08815			−0.383534
$177$	12.8565	+	12.8565i	0.966352	+	0.966352i
$178$	−3.22304	+	3.22304i	−0.241577	+	0.241577i
$179$	−2.05124			−0.153317			−0.0766583	−	0.997057i	$-0.524425\pi$
$179$	−2.05124			−0.153317			−0.0766583	+	0.997057i	$0.524425\pi$
$180$		0			0
$181$		−	9.43492i		−	0.701292i	−0.936508	−	0.350646i	$-0.885962\pi$
$181$		−	9.43492i		−	0.701292i	0.936508	−	0.350646i	$-0.114038\pi$
$182$	11.1677	+	11.1677i	0.827802	+	0.827802i
$183$	−5.46926	−	5.46926i	−0.404299	−	0.404299i
$184$	−7.90826			−0.583004
$185$		0			0
$186$			12.9357i			0.948492i
$187$	6.02937	+	6.02937i	0.440911	+	0.440911i
$188$	−4.04146	+	4.04146i	−0.294754	+	0.294754i
$189$	−14.5176			−1.05600
$190$		0			0
$191$	−13.5487			−0.980349			−0.490175	−	0.871624i	$-0.663067\pi$
$191$	−13.5487			−0.980349			−0.490175	+	0.871624i	$0.663067\pi$
$192$	−1.29807	+	1.29807i	−0.0936800	+	0.0936800i
$193$	3.01172	+	3.01172i	0.216788	+	0.216788i	0.807143	−	0.590355i	$-0.201012\pi$
$193$	3.01172	+	3.01172i	0.216788	+	0.216788i	−0.590355	+	0.807143i	$0.701012\pi$
$194$		−	5.55393i		−	0.398749i
$195$		0			0
$196$	2.04146			0.145818
$197$	14.2004	+	14.2004i	1.01174	+	1.01174i	0.999930	+	0.0118084i	$0.00375881\pi$
$197$	14.2004	+	14.2004i	1.01174	+	1.01174i	0.0118084	+	0.999930i	$0.496241\pi$
$198$	1.33108	+	1.33108i	0.0945960	+	0.0945960i
$199$		−	8.94564i		−	0.634140i	−0.948402	−	0.317070i	$-0.897301\pi$
$199$		−	8.94564i		−	0.634140i	0.948402	−	0.317070i	$-0.102699\pi$
$200$		0			0
$201$	−11.6396			−0.820997
$202$	−4.06726	+	4.06726i	−0.286171	+	0.286171i
$203$	1.83212	+	1.83212i	0.128590	+	0.128590i
$204$	3.07638			0.215390
$205$		0			0
$206$	3.61713			0.252018
$207$	2.06884	+	2.06884i	0.143794	+	0.143794i
$208$	3.71401	+	3.71401i	0.257520	+	0.257520i
$209$	21.3134	−	6.13484i	1.47428	−	0.424356i
$210$		0			0
$211$			24.3448i			1.67596i	0.545699	+	0.837981i	$0.316264\pi$
$211$			24.3448i			1.67596i	−0.545699	+	0.837981i	$0.683736\pi$
$212$	6.57175	−	6.57175i	0.451350	−	0.451350i
$213$	−7.99995	+	7.99995i	−0.548148	+	0.548148i
$214$			12.9283i			0.883758i
$215$		0			0
$216$	−4.82808			−0.328509
$217$	14.9824	−	14.9824i	1.01707	−	1.01707i
$218$	2.49174	−	2.49174i	0.168762	−	0.168762i
$219$	7.96344			0.538119
$220$		0			0
$221$		−	8.80207i		−	0.592091i
$222$	−7.30817	+	7.30817i	−0.490492	+	0.490492i
$223$	7.74344	+	7.74344i	0.518539	+	0.518539i	0.917129	−	0.398590i	$-0.130500\pi$
$223$	7.74344	+	7.74344i	0.518539	+	0.518539i	−0.398590	+	0.917129i	$0.630500\pi$
$224$	3.00690			0.200907
$225$		0			0
$226$	18.5660			1.23499
$227$	−1.35188	+	1.35188i	−0.0897277	+	0.0897277i	−0.750546	−	0.660818i	$-0.770209\pi$
$227$	−1.35188	+	1.35188i	−0.0897277	+	0.0897277i	0.660818	+	0.750546i	$0.270209\pi$
$228$	3.87229	−	7.00248i	0.256448	−	0.463751i
$229$			29.2012i			1.92967i	0.262852	+	0.964836i	$0.415337\pi$
$229$			29.2012i			1.92967i	−0.262852	+	0.964836i	$0.584663\pi$
$230$		0			0
$231$		−	28.0861i		−	1.84793i
$232$	0.609306	+	0.609306i	0.0400029	+	0.0400029i
$233$	−17.3007	+	17.3007i	−1.13340	+	1.13340i	−0.143797	+	0.989607i	$0.545931\pi$
$233$	−17.3007	+	17.3007i	−1.13340	+	1.13340i	−0.989607	+	0.143797i	$0.954069\pi$
$234$		−	1.94320i		−	0.127031i
$235$		0			0
$236$		−	9.90431i		−	0.644716i
$237$	−18.3655	−	18.3655i	−1.19297	−	1.19297i
$238$	−3.56313	−	3.56313i	−0.230963	−	0.230963i
$239$			0.129605i			0.00838347i	0.999991	+	0.00419174i	$0.00133428\pi$
$239$			0.129605i			0.00838347i	−0.999991	+	0.00419174i	$0.998666\pi$
$240$		0			0
$241$			15.3241i			0.987109i	0.869715	+	0.493555i	$0.164303\pi$
$241$			15.3241i			0.987109i	−0.869715	+	0.493555i	$0.835697\pi$
$242$	10.5283	−	10.5283i	0.676784	−	0.676784i
$243$	2.70377	+	2.70377i	0.173447	+	0.173447i
$244$			4.21338i			0.269734i
$245$		0			0
$246$		−	4.38440i		−	0.279539i
$247$	−20.0354	−	11.0793i	−1.27482	−	0.704960i
$248$	4.98268	−	4.98268i	0.316400	−	0.316400i
$249$	−2.16971			−0.137500
$250$		0			0
$251$	16.8877			1.06594			0.532970	−	0.846134i	$-0.321076\pi$
$251$	16.8877			1.06594			0.532970	+	0.846134i	$0.321076\pi$
$252$	−0.786620	−	0.786620i	−0.0495524	−	0.0495524i
$253$	28.4528	−	28.4528i	1.78881	−	1.78881i
$254$		−	0.848647i		−	0.0532489i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−3.34251	+	3.34251i	−0.208500	+	0.208500i	−0.803630	−	0.595130i	$-0.797101\pi$
$257$	−3.34251	+	3.34251i	−0.208500	+	0.208500i	0.595130	+	0.803630i	$0.297101\pi$
$258$	−7.61271	+	7.61271i	−0.473947	+	0.473947i
$259$	16.9290			1.05191
$260$		0			0
$261$		−	0.318795i		−	0.0197329i
$262$	−1.93742	+	1.93742i	−0.119694	+	0.119694i
$263$	−12.0052	+	12.0052i	−0.740274	+	0.740274i	−0.972631	−	0.232356i	$-0.925356\pi$
$263$	−12.0052	+	12.0052i	−0.740274	+	0.740274i	0.232356	+	0.972631i	$0.425356\pi$
$264$		−	9.34055i		−	0.574871i
$265$		0			0
$266$	−12.5954	+	3.62546i	−0.772273	+	0.222291i
$267$	−5.91668	−	5.91668i	−0.362095	−	0.362095i
$268$	4.48345	+	4.48345i	0.273870	+	0.273870i
$269$	14.4405			0.880450			0.440225	−	0.897887i	$-0.354899\pi$
$269$	14.4405			0.880450			0.440225	+	0.897887i	$0.354899\pi$
$270$		0			0
$271$	7.96012			0.483543			0.241771	−	0.970333i	$-0.422272\pi$
$271$	7.96012			0.483543			0.241771	+	0.970333i	$0.422272\pi$
$272$	−1.18498	−	1.18498i	−0.0718501	−	0.0718501i
$273$	−20.5010	+	20.5010i	−1.24078	+	1.24078i
$274$	−9.75515			−0.589330
$275$		0			0
$276$		−	14.5176i		−	0.873854i
$277$	18.9230	+	18.9230i	1.13697	+	1.13697i	0.988990	+	0.147985i	$0.0472789\pi$
$277$	18.9230	+	18.9230i	1.13697	+	1.13697i	0.147985	+	0.988990i	$0.452721\pi$
$278$	−2.38835	−	2.38835i	−0.143244	−	0.143244i
$279$	−2.60698			−0.156076
$280$		0			0
$281$		−	4.26593i		−	0.254484i	−0.991872	−	0.127242i	$-0.959388\pi$
$281$		−	4.26593i		−	0.254484i	0.991872	−	0.127242i	$-0.0406124\pi$
$282$	−7.41909	−	7.41909i	−0.441800	−	0.441800i
$283$	7.11427	−	7.11427i	0.422899	−	0.422899i	−0.463301	−	0.886201i	$-0.653335\pi$
$283$	7.11427	−	7.11427i	0.422899	−	0.422899i	0.886201	+	0.463301i	$0.153335\pi$
$284$	6.16296			0.365705
$285$		0			0
$286$	−26.7250			−1.58028
$287$	−5.07811	+	5.07811i	−0.299751	+	0.299751i
$288$	−0.261605	−	0.261605i	−0.0154152	−	0.0154152i
$289$		−	14.1916i		−	0.834802i
$290$		0			0
$291$	10.1956			0.597677
$292$	−3.06742	−	3.06742i	−0.179507	−	0.179507i
$293$	13.8921	+	13.8921i	0.811587	+	0.811587i	0.984872	−	0.173284i	$-0.0554380\pi$
$293$	13.8921	+	13.8921i	0.811587	+	0.811587i	−0.173284	+	0.984872i	$0.555438\pi$
$294$			3.74760i			0.218564i
$295$		0			0
$296$	5.63004			0.327239
$297$	17.3708	−	17.3708i	1.00795	−	1.00795i
$298$	0.963289	+	0.963289i	0.0558018	+	0.0558018i
$299$	−41.5373			−2.40217
$300$		0			0
$301$	17.6344			1.01643
$302$	−12.7182	−	12.7182i	−0.731849	−	0.731849i
$303$	−7.46645	−	7.46645i	−0.428937	−	0.428937i
$304$	−4.18883	+	1.20571i	−0.240246	+	0.0691523i
$305$		0			0
$306$			0.619994i			0.0354427i
$307$	14.3328	−	14.3328i	0.818017	−	0.818017i	−0.167803	−	0.985821i	$-0.553667\pi$
$307$	14.3328	−	14.3328i	0.818017	−	0.818017i	0.985821	+	0.167803i	$0.0536673\pi$
$308$	−10.8184	+	10.8184i	−0.616437	+	0.616437i
$309$			6.64014i			0.377744i
$310$		0			0
$311$	17.3743			0.985208			0.492604	−	0.870253i	$-0.336045\pi$
$311$	17.3743			0.985208			0.492604	+	0.870253i	$0.336045\pi$
$312$	−6.81798	+	6.81798i	−0.385992	+	0.385992i
$313$	17.5452	−	17.5452i	0.991716	−	0.991716i	−0.00825027	−	0.999966i	$-0.502626\pi$
$313$	17.5452	−	17.5452i	0.991716	−	0.991716i	0.999966	+	0.00825027i	$0.00262617\pi$
$314$	16.4570			0.928721
$315$		0			0
$316$			14.1483i			0.795905i
$317$	−3.10285	+	3.10285i	−0.174274	+	0.174274i	−0.788854	−	0.614580i	$-0.789325\pi$
$317$	−3.10285	+	3.10285i	−0.174274	+	0.174274i	0.614580	+	0.788854i	$0.289325\pi$
$318$	12.0641	+	12.0641i	0.676519	+	0.676519i
$319$	−4.38440			−0.245479
$320$		0			0
$321$	−23.7330			−1.32465
$322$	−16.8145	+	16.8145i	−0.937038	+	0.937038i
$323$	6.39243	+	3.53494i	0.355684	+	0.196689i
$324$		−	9.97302i		−	0.554057i
$325$		0			0
$326$		−	3.74393i		−	0.207357i
$327$	4.57421	+	4.57421i	0.252954	+	0.252954i
$328$	−1.68882	+	1.68882i	−0.0932493	+	0.0932493i
$329$			17.1859i			0.947489i
$330$		0			0
$331$			9.73065i			0.534845i	0.963579	+	0.267422i	$0.0861719\pi$
$331$			9.73065i			0.534845i	−0.963579	+	0.267422i	$0.913828\pi$
$332$	0.835746	+	0.835746i	0.0458675	+	0.0458675i
$333$	−1.47284	−	1.47284i	−0.0807113	−	0.0807113i
$334$			10.0197i			0.548254i
$335$		0			0
$336$			5.51991i			0.301136i
$337$	−8.08845	+	8.08845i	−0.440606	+	0.440606i	−0.892216	−	0.451610i	$-0.850850\pi$
$337$	−8.08845	+	8.08845i	−0.440606	+	0.440606i	0.451610	+	0.892216i	$0.350850\pi$
$338$	10.3151	+	10.3151i	0.561066	+	0.561066i
$339$			34.0824i			1.85110i
$340$		0			0
$341$			35.8540i			1.94160i
$342$	1.41124	+	0.780397i	0.0763109	+	0.0421990i
$343$	−10.5429	+	10.5429i	−0.569261	+	0.569261i
$344$	5.86464			0.316200
$345$		0			0
$346$	−3.28619			−0.176667
$347$	0.343845	+	0.343845i	0.0184586	+	0.0184586i	0.716276	−	0.697817i	$-0.245845\pi$
$347$	0.343845	+	0.343845i	0.0184586	+	0.0184586i	−0.697817	+	0.716276i	$0.745845\pi$
$348$	−1.11853	+	1.11853i	−0.0599596	+	0.0599596i
$349$		−	5.83245i		−	0.312204i	−0.987741	−	0.156102i	$-0.950107\pi$
$349$		−	5.83245i		−	0.312204i	0.987741	−	0.156102i	$-0.0498928\pi$
$350$		0			0
$351$	−25.3590			−1.35356
$352$	−3.59786	+	3.59786i	−0.191767	+	0.191767i
$353$	13.0183	−	13.0183i	0.692894	−	0.692894i	−0.269974	−	0.962868i	$-0.587015\pi$
$353$	13.0183	−	13.0183i	0.692894	−	0.692894i	0.962868	+	0.269974i	$0.0870151\pi$
$354$	18.1818			0.966352
$355$		0			0
$356$			4.55806i			0.241577i
$357$	6.54100	−	6.54100i	0.346186	−	0.346186i
$358$	−1.45044	+	1.45044i	−0.0766583	+	0.0766583i
$359$		−	0.962915i		−	0.0508207i	−0.999677	−	0.0254104i	$-0.991911\pi$
$359$		−	0.962915i		−	0.0508207i	0.999677	−	0.0254104i	$-0.00808924\pi$
$360$		0			0
$361$	16.0925	−	10.1010i	0.846975	−	0.531633i
$362$	−6.67149	−	6.67149i	−0.350646	−	0.350646i
$363$	19.3273	+	19.3273i	1.01442	+	1.01442i
$364$	15.7935			0.827802
$365$		0			0
$366$	−7.73470			−0.404299
$367$	13.3776	+	13.3776i	0.698307	+	0.698307i	0.964045	−	0.265738i	$-0.0856157\pi$
$367$	13.3776	+	13.3776i	0.698307	+	0.698307i	−0.265738	+	0.964045i	$0.585616\pi$
$368$	−5.59198	+	5.59198i	−0.291502	+	0.291502i
$369$	0.883605			0.0459986
$370$		0			0
$371$		−	27.9457i		−	1.45087i
$372$	9.14693	+	9.14693i	0.474246	+	0.474246i
$373$	−18.0468	−	18.0468i	−0.934430	−	0.934430i	0.0635491	−	0.997979i	$-0.479758\pi$
$373$	−18.0468	−	18.0468i	−0.934430	−	0.934430i	−0.997979	+	0.0635491i	$0.979758\pi$
$374$	8.52681			0.440911
$375$		0			0
$376$			5.71548i			0.294754i
$377$	3.20032	+	3.20032i	0.164825	+	0.164825i
$378$	−10.2655	+	10.2655i	−0.527998	+	0.527998i
$379$	−12.7401			−0.654417			−0.327208	−	0.944952i	$-0.606108\pi$
$379$	−12.7401			−0.654417			−0.327208	+	0.944952i	$0.606108\pi$
$380$		0			0
$381$	1.55790			0.0798137
$382$	−9.58038	+	9.58038i	−0.490175	+	0.490175i
$383$	−18.5820	−	18.5820i	−0.949496	−	0.949496i	0.0492886	−	0.998785i	$-0.484305\pi$
$383$	−18.5820	−	18.5820i	−0.949496	−	0.949496i	−0.998785	+	0.0492886i	$0.984305\pi$
$384$			1.83575i			0.0936800i
$385$		0			0
$386$	4.25921			0.216788
$387$	−1.53422	−	1.53422i	−0.0779887	−	0.0779887i
$388$	−3.92722	−	3.92722i	−0.199374	−	0.199374i
$389$		−	20.2721i		−	1.02784i	−0.857839	−	0.513918i	$-0.828193\pi$
$389$		−	20.2721i		−	1.02784i	0.857839	−	0.513918i	$-0.171807\pi$
$390$		0			0
$391$	13.2528			0.670223
$392$	1.44353	−	1.44353i	0.0729092	−	0.0729092i
$393$	−3.55662	−	3.55662i	−0.179408	−	0.179408i
$394$	20.0824			1.01174
$395$		0			0
$396$	1.88244			0.0945960
$397$	−2.26530	−	2.26530i	−0.113692	−	0.113692i	0.647972	−	0.761664i	$-0.275617\pi$
$397$	−2.26530	−	2.26530i	−0.113692	−	0.113692i	−0.761664	+	0.647972i	$0.775617\pi$
$398$	−6.32552	−	6.32552i	−0.317070	−	0.317070i
$399$	−6.65542	−	23.1219i	−0.333188	−	1.15754i
$400$		0			0
$401$			32.2428i			1.61013i	0.593187	+	0.805065i	$0.297869\pi$
$401$			32.2428i			1.61013i	−0.593187	+	0.805065i	$0.702131\pi$
$402$	−8.23047	+	8.23047i	−0.410498	+	0.410498i
$403$	26.1710	−	26.1710i	1.30367	−	1.30367i
$404$			5.75197i			0.286171i
$405$		0			0
$406$	2.59101			0.128590
$407$	−20.2561	+	20.2561i	−1.00406	+	1.00406i
$408$	2.17533	−	2.17533i	0.107695	−	0.107695i
$409$	−24.8591			−1.22921			−0.614603	−	0.788837i	$-0.710684\pi$
$409$	−24.8591			−1.22921			−0.614603	+	0.788837i	$0.710684\pi$
$410$		0			0
$411$		−	17.9080i		−	0.883336i
$412$	2.55770	−	2.55770i	0.126009	−	0.126009i
$413$	−21.0585	−	21.0585i	−1.03622	−	1.03622i
$414$	2.92578			0.143794
$415$		0			0
$416$	5.25240			0.257520
$417$	4.38440	−	4.38440i	0.214705	−	0.214705i
$418$	10.7328	−	19.4088i	0.524960	−	0.949316i
$419$		−	22.4745i		−	1.09795i	−0.835838	−	0.548976i	$-0.815018\pi$
$419$		−	22.4745i		−	1.09795i	0.835838	−	0.548976i	$-0.184982\pi$
$420$		0			0
$421$		−	35.7769i		−	1.74366i	−0.489810	−	0.871829i	$-0.662934\pi$
$421$		−	35.7769i		−	1.74366i	0.489810	−	0.871829i	$-0.337066\pi$
$422$	17.2143	+	17.2143i	0.837981	+	0.837981i
$423$	1.49520	−	1.49520i	0.0726990	−	0.0726990i
$424$		−	9.29386i		−	0.451350i
$425$		0			0
$426$			11.3136i			0.548148i
$427$	8.95849	+	8.95849i	0.433532	+	0.433532i
$428$	9.14167	+	9.14167i	0.441879	+	0.441879i
$429$		−	49.0603i		−	2.36865i
$430$		0			0
$431$			12.8172i			0.617385i	0.951162	+	0.308692i	$0.0998913\pi$
$431$			12.8172i			0.617385i	−0.951162	+	0.308692i	$0.900109\pi$
$432$	−3.41397	+	3.41397i	−0.164255	+	0.164255i
$433$	2.48060	+	2.48060i	0.119210	+	0.119210i	0.764195	−	0.644985i	$-0.223136\pi$
$433$	2.48060	+	2.48060i	0.119210	+	0.119210i	−0.644985	+	0.764195i	$0.723136\pi$
$434$		−	21.1883i		−	1.01707i
$435$		0			0
$436$		−	3.52386i		−	0.168762i
$437$	16.6815	−	30.1662i	0.797985	−	1.44304i
$438$	5.63100	−	5.63100i	0.269060	−	0.269060i
$439$	−17.9413			−0.856289			−0.428145	−	0.903710i	$-0.640833\pi$
$439$	−17.9413			−0.856289			−0.428145	+	0.903710i	$0.640833\pi$
$440$		0			0
$441$	−0.755268			−0.0359651
$442$	−6.22400	−	6.22400i	−0.296046	−	0.296046i
$443$	5.60748	−	5.60748i	0.266419	−	0.266419i	−0.561236	−	0.827656i	$-0.689674\pi$
$443$	5.60748	−	5.60748i	0.266419	−	0.266419i	0.827656	+	0.561236i	$0.189674\pi$
$444$			10.3353i			0.490492i
$445$		0			0
$446$	10.9509			0.518539
$447$	−1.76835	+	1.76835i	−0.0836403	+	0.0836403i
$448$	2.12620	−	2.12620i	0.100454	−	0.100454i
$449$	−16.8105			−0.793336			−0.396668	−	0.917962i	$-0.629834\pi$
$449$	−16.8105			−0.793336			−0.396668	+	0.917962i	$0.629834\pi$
$450$		0			0
$451$		−	12.1523i		−	0.572228i
$452$	13.1281	−	13.1281i	0.617495	−	0.617495i
$453$	23.3474	−	23.3474i	1.09695	−	1.09695i
$454$			1.91185i			0.0897277i
$455$		0			0
$456$	−2.21338	−	7.68962i	−0.103651	−	0.360100i
$457$	−20.4027	−	20.4027i	−0.954400	−	0.954400i	0.0446050	−	0.999005i	$-0.485797\pi$
$457$	−20.4027	−	20.4027i	−0.954400	−	0.954400i	−0.999005	+	0.0446050i	$0.985797\pi$
$458$	20.6484	+	20.6484i	0.964836	+	0.964836i
$459$	8.09098			0.377655
$460$		0			0
$461$	27.3301			1.27289			0.636444	−	0.771323i	$-0.280404\pi$
$461$	27.3301			1.27289			0.636444	+	0.771323i	$0.280404\pi$
$462$	−19.8599	−	19.8599i	−0.923965	−	0.923965i
$463$	−11.7495	+	11.7495i	−0.546047	+	0.546047i	−0.925295	−	0.379248i	$-0.876183\pi$
$463$	−11.7495	+	11.7495i	−0.546047	+	0.546047i	0.379248	+	0.925295i	$0.376183\pi$
$464$	0.861689			0.0400029
$465$		0			0
$466$			24.4668i			1.13340i
$467$	−9.93355	−	9.93355i	−0.459670	−	0.459670i	0.438877	−	0.898547i	$-0.355376\pi$
$467$	−9.93355	−	9.93355i	−0.459670	−	0.459670i	−0.898547	+	0.438877i	$0.855376\pi$
$468$	−1.37405	−	1.37405i	−0.0635156	−	0.0635156i
$469$	19.0654			0.880359
$470$		0			0
$471$			30.2108i			1.39204i
$472$	−7.00340	−	7.00340i	−0.322358	−	0.322358i
$473$	−21.1002	+	21.1002i	−0.970188	+	0.970188i
$474$	−25.9727			−1.19297
$475$		0			0
$476$	−5.03902			−0.230963
$477$	−2.43132	+	2.43132i	−0.111322	+	0.111322i
$478$	0.0916448	+	0.0916448i	0.00419174	+	0.00419174i
$479$		−	32.9298i		−	1.50460i	−0.658819	−	0.752301i	$-0.728944\pi$
$479$		−	32.9298i		−	1.50460i	0.658819	−	0.752301i	$-0.271056\pi$
$480$		0			0
$481$	29.5712			1.34833
$482$	10.8357	+	10.8357i	0.493555	+	0.493555i
$483$	−30.8672	−	30.8672i	−1.40451	−	1.40451i
$484$		−	14.8892i		−	0.676784i
$485$		0			0
$486$	3.82370			0.173447
$487$	11.4970	−	11.4970i	0.520979	−	0.520979i	−0.396888	−	0.917867i	$-0.629910\pi$
$487$	11.4970	−	11.4970i	0.520979	−	0.520979i	0.917867	+	0.396888i	$0.129910\pi$
$488$	2.97931	+	2.97931i	0.134867	+	0.134867i
$489$	6.87291			0.310804
$490$		0			0
$491$	−44.0285			−1.98698			−0.993488	−	0.113935i	$-0.963654\pi$
$491$	−44.0285			−1.98698			−0.993488	+	0.113935i	$0.963654\pi$
$492$	−3.10024	−	3.10024i	−0.139770	−	0.139770i
$493$	−1.02109	−	1.02109i	−0.0459874	−	0.0459874i
$494$	−22.0014	+	6.33288i	−0.989889	+	0.284930i
$495$		0			0
$496$		−	7.04657i		−	0.316400i
$497$	13.1037	−	13.1037i	0.587781	−	0.587781i
$498$	−1.53422	+	1.53422i	−0.0687500	+	0.0687500i
$499$			28.2982i			1.26680i	0.773823	+	0.633401i	$0.218342\pi$
$499$			28.2982i			1.26680i	−0.773823	+	0.633401i	$0.781658\pi$
$500$		0			0
$501$	−18.3936			−0.821768
$502$	11.9414	−	11.9414i	0.532970	−	0.532970i
$503$	−16.2003	+	16.2003i	−0.722334	+	0.722334i	−0.969080	−	0.246746i	$-0.920639\pi$
$503$	−16.2003	+	16.2003i	−0.722334	+	0.722334i	0.246746	+	0.969080i	$0.420639\pi$
$504$	−1.11245			−0.0495524
$505$		0			0
$506$		−	40.2384i		−	1.78881i
$507$	−18.9359	+	18.9359i	−0.840971	+	0.840971i
$508$	−0.600084	−	0.600084i	−0.0266244	−	0.0266244i
$509$	−2.34337			−0.103868			−0.0519341	−	0.998651i	$-0.516539\pi$
$509$	−2.34337			−0.103868			−0.0519341	+	0.998651i	$0.516539\pi$
$510$		0			0
$511$	−13.0439			−0.577028
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	10.1843	−	18.4168i	0.449646	−	0.813120i
$514$			4.72703i			0.208500i
$515$		0			0
$516$			10.7660i			0.473947i
$517$	−20.5635	−	20.5635i	−0.904383	−	0.904383i
$518$	11.9706	−	11.9706i	0.525957	−	0.525957i
$519$		−	6.03261i		−	0.264802i
$520$		0			0
$521$		−	28.9799i		−	1.26963i	−0.772663	−	0.634817i	$-0.781076\pi$
$521$		−	28.9799i		−	1.26963i	0.772663	−	0.634817i	$-0.218924\pi$
$522$	−0.225422	−	0.225422i	−0.00986645	−	0.00986645i
$523$	−3.06442	−	3.06442i	−0.133998	−	0.133998i	0.636927	−	0.770924i	$-0.280205\pi$
$523$	−3.06442	−	3.06442i	−0.133998	−	0.133998i	−0.770924	+	0.636927i	$0.780205\pi$
$524$			2.73993i			0.119694i
$525$		0			0
$526$			16.9780i			0.740274i
$527$	−8.35006	+	8.35006i	−0.363734	+	0.363734i
$528$	−6.60477	−	6.60477i	−0.287436	−	0.287436i
$529$		−	39.5405i		−	1.71915i
$530$		0			0
$531$			3.66425i			0.159015i
$532$	−6.34270	+	11.4699i	−0.274991	+	0.497282i
$533$	−8.87034	+	8.87034i	−0.384217	+	0.384217i
$534$	−8.36744			−0.362095
$535$		0			0
$536$	6.34055			0.273870
$537$	−2.66265	−	2.66265i	−0.114902	−	0.114902i
$538$	10.2109	−	10.2109i	0.440225	−	0.440225i
$539$			10.3872i			0.447410i
$540$		0			0
$541$	33.9129			1.45803			0.729015	−	0.684497i	$-0.239978\pi$
$541$	33.9129			1.45803			0.729015	+	0.684497i	$0.239978\pi$
$542$	5.62865	−	5.62865i	0.241771	−	0.241771i
$543$	12.2472	−	12.2472i	0.525576	−	0.525576i
$544$	−1.67582			−0.0718501
$545$		0			0
$546$			28.9928i			1.24078i
$547$	−17.4092	+	17.4092i	−0.744364	+	0.744364i	−0.973414	−	0.229051i	$-0.926438\pi$
$547$	−17.4092	+	17.4092i	−0.744364	+	0.744364i	0.229051	+	0.973414i	$0.426438\pi$
$548$	−6.89793	+	6.89793i	−0.294665	+	0.294665i
$549$		−	1.55880i		−	0.0665281i
$550$		0			0
$551$	−3.60947	+	1.03895i	−0.153768	+	0.0442607i
$552$	−10.2655	−	10.2655i	−0.436927	−	0.436927i
$553$	30.0822	+	30.0822i	1.27922	+	1.27922i
$554$	26.7612			1.13697
$555$		0			0
$556$	−3.37763			−0.143244
$557$	1.84342	+	1.84342i	0.0781080	+	0.0781080i	0.745081	−	0.666973i	$-0.232411\pi$
$557$	1.84342	+	1.84342i	0.0781080	+	0.0781080i	−0.666973	+	0.745081i	$0.732411\pi$
$558$	−1.84342	+	1.84342i	−0.0780380	+	0.0780380i
$559$	30.8035			1.30285
$560$		0			0
$561$			15.6531i			0.660873i
$562$	−3.01646	−	3.01646i	−0.127242	−	0.127242i
$563$	−16.3506	−	16.3506i	−0.689094	−	0.689094i	0.272937	−	0.962032i	$-0.412005\pi$
$563$	−16.3506	−	16.3506i	−0.689094	−	0.689094i	−0.962032	+	0.272937i	$0.912005\pi$
$564$	−10.4922			−0.441800
$565$		0			0
$566$		−	10.0611i		−	0.422899i
$567$	−21.2046	−	21.2046i	−0.890511	−	0.890511i
$568$	4.35787	−	4.35787i	0.182852	−	0.182852i
$569$	30.4112			1.27490			0.637451	−	0.770491i	$-0.279989\pi$
$569$	30.4112			1.27490			0.637451	+	0.770491i	$0.279989\pi$
$570$		0			0
$571$	30.4118			1.27270			0.636348	−	0.771402i	$-0.280444\pi$
$571$	30.4118			1.27270			0.636348	+	0.771402i	$0.280444\pi$
$572$	−18.8974	+	18.8974i	−0.790141	+	0.790141i
$573$	−17.5871	−	17.5871i	−0.734713	−	0.734713i
$574$			7.18153i			0.299751i
$575$		0			0
$576$	−0.369965			−0.0154152
$577$	−7.89112	−	7.89112i	−0.328512	−	0.328512i	0.523509	−	0.852020i	$-0.324623\pi$
$577$	−7.89112	−	7.89112i	−0.328512	−	0.328512i	−0.852020	+	0.523509i	$0.824623\pi$
$578$	−10.0350	−	10.0350i	−0.417401	−	0.417401i
$579$			7.81883i			0.324940i
$580$		0			0
$581$	3.55393			0.147442
$582$	7.20938	−	7.20938i	0.298838	−	0.298838i
$583$	33.4380	+	33.4380i	1.38486	+	1.38486i
$584$	−4.33799			−0.179507
$585$		0			0
$586$	19.6464			0.811587
$587$	−16.8305	−	16.8305i	−0.694668	−	0.694668i	0.268588	−	0.963255i	$-0.413443\pi$
$587$	−16.8305	−	16.8305i	−0.694668	−	0.694668i	−0.963255	+	0.268588i	$0.913443\pi$
$588$	2.64995	+	2.64995i	0.109282	+	0.109282i
$589$	8.49613	+	29.5168i	0.350077	+	1.21622i
$590$		0			0
$591$			36.8663i			1.51648i
$592$	3.98104	−	3.98104i	0.163620	−	0.163620i
$593$	18.8140	−	18.8140i	0.772598	−	0.772598i	−0.205962	−	0.978560i	$-0.566032\pi$
$593$	18.8140	−	18.8140i	0.772598	−	0.772598i	0.978560	+	0.205962i	$0.0660322\pi$
$594$		−	24.5660i		−	1.00795i
$595$		0			0
$596$	1.36230			0.0558018
$597$	11.6121	−	11.6121i	0.475250	−	0.475250i
$598$	−29.3713	+	29.3713i	−1.20108	+	1.20108i
$599$	9.11726			0.372521			0.186261	−	0.982500i	$-0.440363\pi$
$599$	9.11726			0.372521			0.186261	+	0.982500i	$0.440363\pi$
$600$		0			0
$601$		−	38.3056i		−	1.56252i	−0.624207	−	0.781259i	$-0.714578\pi$
$601$		−	38.3056i		−	1.56252i	0.624207	−	0.781259i	$-0.285422\pi$
$602$	12.4694	−	12.4694i	0.508215	−	0.508215i
$603$	−1.65872	−	1.65872i	−0.0675482	−	0.0675482i
$604$	−17.9862			−0.731849
$605$		0			0
$606$	−10.5592			−0.428937
$607$	28.8183	−	28.8183i	1.16970	−	1.16970i	0.187416	−	0.982281i	$-0.439989\pi$
$607$	28.8183	−	28.8183i	1.16970	−	1.16970i	0.982281	−	0.187416i	$-0.0600113\pi$
$608$	−2.10938	+	3.81451i	−0.0855467	+	0.154699i
$609$			4.75645i			0.192741i
$610$		0			0
$611$			30.0200i			1.21448i
$612$	0.438402	+	0.438402i	0.0177213	+	0.0177213i
$613$	−14.2307	+	14.2307i	−0.574773	+	0.574773i	−0.933458	−	0.358686i	$-0.883225\pi$
$613$	−14.2307	+	14.2307i	−0.574773	+	0.574773i	0.358686	+	0.933458i	$0.383225\pi$
$614$		−	20.2697i		−	0.818017i
$615$		0			0
$616$			15.2996i			0.616437i
$617$	1.34578	+	1.34578i	0.0541791	+	0.0541791i	0.733677	−	0.679498i	$-0.237802\pi$
$617$	1.34578	+	1.34578i	0.0541791	+	0.0541791i	−0.679498	+	0.733677i	$0.737802\pi$
$618$	4.69529	+	4.69529i	0.188872	+	0.188872i
$619$			4.97546i			0.199981i	0.994988	+	0.0999903i	$0.0318812\pi$
$619$			4.97546i			0.199981i	−0.994988	+	0.0999903i	$0.968119\pi$
$620$		0			0
$621$		−	38.1817i		−	1.53218i
$622$	12.2855	−	12.2855i	0.492604	−	0.492604i
$623$	9.69135	+	9.69135i	0.388276	+	0.388276i
$624$			9.64208i			0.385992i
$625$		0			0
$626$		−	24.8127i		−	0.991716i
$627$	35.6297	+	19.7028i	1.42291	+	0.786853i
$628$	11.6368	−	11.6368i	0.464361	−	0.464361i
$629$	−9.43492			−0.376195
$630$		0			0
$631$	−45.2032			−1.79951			−0.899755	−	0.436395i	$-0.856255\pi$
$631$	−45.2032			−1.79951			−0.899755	+	0.436395i	$0.856255\pi$
$632$	10.0044	+	10.0044i	0.397953	+	0.397953i
$633$	−31.6012	+	31.6012i	−1.25603	+	1.25603i
$634$			4.38810i			0.174274i
$635$		0			0
$636$	17.0612			0.676519
$637$	7.58199	−	7.58199i	0.300409	−	0.300409i
$638$	−3.10024	+	3.10024i	−0.122740	+	0.122740i
$639$	−2.28008			−0.0901986
$640$		0			0
$641$			15.9890i			0.631529i	0.948838	+	0.315764i	$0.102261\pi$
$641$			15.9890i			0.631529i	−0.948838	+	0.315764i	$0.897739\pi$
$642$	−16.7818	+	16.7818i	−0.662324	+	0.662324i
$643$	−2.95575	+	2.95575i	−0.116563	+	0.116563i	−0.762982	−	0.646419i	$-0.776266\pi$
$643$	−2.95575	+	2.95575i	−0.116563	+	0.116563i	0.646419	+	0.762982i	$0.276266\pi$
$644$			23.7794i			0.937038i
$645$		0			0
$646$	7.01971	−	2.02055i	0.276187	−	0.0794976i
$647$	6.22116	+	6.22116i	0.244579	+	0.244579i	0.818741	−	0.574162i	$-0.194672\pi$
$647$	6.22116	+	6.22116i	0.244579	+	0.244579i	−0.574162	+	0.818741i	$0.694672\pi$
$648$	−7.05199	−	7.05199i	−0.277028	−	0.277028i
$649$	50.3946			1.97816
$650$		0			0
$651$	38.8964			1.52447
$652$	−2.64736	−	2.64736i	−0.103679	−	0.103679i
$653$	24.5703	−	24.5703i	0.961512	−	0.961512i	−0.0377745	−	0.999286i	$-0.512027\pi$
$653$	24.5703	−	24.5703i	0.961512	−	0.961512i	0.999286	+	0.0377745i	$0.0120268\pi$
$654$	6.46891			0.252954
$655$		0			0
$656$			2.38835i			0.0932493i
$657$	1.13484	+	1.13484i	0.0442742	+	0.0442742i
$658$	12.1523	+	12.1523i	0.473745	+	0.473745i
$659$	−34.2721			−1.33505			−0.667526	−	0.744586i	$-0.732647\pi$
$659$	−34.2721			−1.33505			−0.667526	+	0.744586i	$0.732647\pi$
$660$		0			0
$661$		−	3.17654i		−	0.123553i	−0.998090	−	0.0617765i	$-0.980323\pi$
$661$		−	3.17654i		−	0.123553i	0.998090	−	0.0617765i	$-0.0196766\pi$
$662$	6.88061	+	6.88061i	0.267422	+	0.267422i
$663$	11.4257	−	11.4257i	0.443737	−	0.443737i
$664$	1.18192			0.0458675
$665$		0			0
$666$	−2.08292			−0.0807113
$667$	−4.81855	+	4.81855i	−0.186575	+	0.186575i
$668$	7.08501	+	7.08501i	0.274127	+	0.274127i
$669$			20.1030i			0.777228i
$670$		0			0
$671$	−21.4383			−0.827616
$672$	3.90317	+	3.90317i	0.150568	+	0.150568i
$673$	1.20017	+	1.20017i	0.0462631	+	0.0462631i	0.729860	−	0.683597i	$-0.239585\pi$
$673$	1.20017	+	1.20017i	0.0462631	+	0.0462631i	−0.683597	+	0.729860i	$0.739585\pi$
$674$			11.4388i			0.440606i
$675$		0			0
$676$	14.5877			0.561066
$677$	3.35361	−	3.35361i	0.128890	−	0.128890i	−0.639719	−	0.768609i	$-0.720949\pi$
$677$	3.35361	−	3.35361i	0.128890	−	0.128890i	0.768609	+	0.639719i	$0.220949\pi$
$678$	24.0999	+	24.0999i	0.925551	+	0.925551i
$679$	−16.7001			−0.640892
$680$		0			0
$681$	−3.50968			−0.134491
$682$	25.3526	+	25.3526i	0.970801	+	0.970801i
$683$	−23.9988	−	23.9988i	−0.918289	−	0.918289i	0.0786159	−	0.996905i	$-0.474950\pi$
$683$	−23.9988	−	23.9988i	−0.918289	−	0.918289i	−0.996905	+	0.0786159i	$0.974950\pi$
$684$	1.54972	−	0.446071i	0.0592550	−	0.0170559i
$685$		0			0
$686$			14.9098i			0.569261i
$687$	−37.9052	+	37.9052i	−1.44617	+	1.44617i
$688$	4.14693	−	4.14693i	0.158100	−	0.158100i
$689$		−	48.8151i		−	1.85971i
$690$		0			0
$691$	−14.1434			−0.538039			−0.269019	−	0.963135i	$-0.586700\pi$
$691$	−14.1434			−0.538039			−0.269019	+	0.963135i	$0.586700\pi$
$692$	−2.32369	+	2.32369i	−0.0883333	+	0.0883333i
$693$	4.00244	−	4.00244i	0.152040	−	0.152040i
$694$	0.486270			0.0184586
$695$		0			0
$696$			1.58184i			0.0599596i
$697$	2.83015	−	2.83015i	0.107200	−	0.107200i
$698$	−4.12417	−	4.12417i	−0.156102	−	0.156102i
$699$	−44.9149			−1.69884
$700$		0			0
$701$	5.47101			0.206637			0.103319	−	0.994648i	$-0.467054\pi$
$701$	5.47101			0.206637			0.103319	+	0.994648i	$0.467054\pi$
$702$	−17.9315	+	17.9315i	−0.676782	+	0.676782i
$703$	−11.8759	+	21.4758i	−0.447907	+	0.809977i
$704$			5.08815i			0.191767i
$705$		0			0
$706$		−	18.4106i		−	0.692894i
$707$	12.2298	+	12.2298i	0.459951	+	0.459951i
$708$	12.8565	−	12.8565i	0.483176	−	0.483176i
$709$			0.200479i			0.00752916i	0.999993	+	0.00376458i	$0.00119831\pi$
$709$			0.200479i			0.00752916i	−0.999993	+	0.00376458i	$0.998802\pi$
$710$		0			0
$711$		−	5.23438i		−	0.196305i
$712$	3.22304	+	3.22304i	0.120788	+	0.120788i
$713$	39.4043	+	39.4043i	1.47570	+	1.47570i
$714$		−	9.25036i		−	0.346186i
$715$		0			0
$716$			2.05124i			0.0766583i
$717$	−0.168237	+	0.168237i	−0.00628291	+	0.00628291i
$718$	−0.680884	−	0.680884i	−0.0254104	−	0.0254104i
$719$			30.9955i			1.15594i	0.816059	+	0.577969i	$0.196155\pi$
$719$			30.9955i			1.15594i	−0.816059	+	0.577969i	$0.803845\pi$
$720$		0			0
$721$		−	10.8764i		−	0.405057i
$722$	4.23662	−	18.5216i	0.157671	−	0.689304i
$723$	−19.8917	+	19.8917i	−0.739780	+	0.739780i
$724$	−9.43492			−0.350646
$725$		0			0
$726$	27.3329			1.01442
$727$	31.2393	+	31.2393i	1.15860	+	1.15860i	0.984777	+	0.173825i	$0.0556126\pi$
$727$	31.2393	+	31.2393i	1.15860	+	1.15860i	0.173825	+	0.984777i	$0.444387\pi$
$728$	11.1677	−	11.1677i	0.413901	−	0.413901i
$729$		−	22.8997i		−	0.848137i
$730$		0			0
$731$	−9.82808			−0.363505
$732$	−5.46926	+	5.46926i	−0.202150	+	0.202150i
$733$	−18.8184	+	18.8184i	−0.695072	+	0.695072i	−0.963343	−	0.268271i	$-0.913548\pi$
$733$	−18.8184	+	18.8184i	−0.695072	+	0.695072i	0.268271	+	0.963343i	$0.413548\pi$
$734$	18.9188			0.698307
$735$		0			0
$736$			7.90826i			0.291502i
$737$	−22.8124	+	22.8124i	−0.840307	+	0.840307i
$738$	0.624803	−	0.624803i	0.0229993	−	0.0229993i
$739$			14.0680i			0.517499i	0.965944	+	0.258749i	$0.0833104\pi$
$739$			14.0680i			0.517499i	−0.965944	+	0.258749i	$0.916690\pi$
$740$		0			0
$741$	−11.6256	−	40.3890i	−0.427076	−	1.48373i
$742$	−19.7606	−	19.7606i	−0.725435	−	0.725435i
$743$	−4.38124	−	4.38124i	−0.160732	−	0.160732i	0.622159	−	0.782891i	$-0.286256\pi$
$743$	−4.38124	−	4.38124i	−0.160732	−	0.160732i	−0.782891	+	0.622159i	$0.786256\pi$
$744$	12.9357			0.474246
$745$		0			0
$746$	−25.5221			−0.934430
$747$	−0.309197	−	0.309197i	−0.0113129	−	0.0113129i
$748$	6.02937	−	6.02937i	0.220455	−	0.220455i
$749$	38.8740			1.42043
$750$		0			0
$751$			13.3649i			0.487691i	0.969814	+	0.243846i	$0.0784090\pi$
$751$			13.3649i			0.487691i	−0.969814	+	0.243846i	$0.921591\pi$
$752$	4.04146	+	4.04146i	0.147377	+	0.147377i
$753$	21.9214	+	21.9214i	0.798859	+	0.798859i
$754$	4.52594			0.164825
$755$		0			0
$756$			14.5176i			0.527998i
$757$	20.6682	+	20.6682i	0.751198	+	0.751198i	0.974703	−	0.223505i	$-0.0717497\pi$
$757$	20.6682	+	20.6682i	0.751198	+	0.751198i	−0.223505	+	0.974703i	$0.571750\pi$
$758$	−9.00864	+	9.00864i	−0.327208	+	0.327208i
$759$	73.8675			2.68122
$760$		0			0
$761$	−1.48072			−0.0536760			−0.0268380	−	0.999640i	$-0.508544\pi$
$761$	−1.48072			−0.0536760			−0.0268380	+	0.999640i	$0.508544\pi$
$762$	1.10160	−	1.10160i	0.0399069	−	0.0399069i
$763$	−7.49242	−	7.49242i	−0.271244	−	0.271244i
$764$			13.5487i			0.490175i
$765$		0			0
$766$	−26.2789			−0.949496
$767$	−36.7847	−	36.7847i	−1.32822	−	1.32822i
$768$	1.29807	+	1.29807i	0.0468400	+	0.0468400i
$769$			37.5080i			1.35257i	0.736639	+	0.676286i	$0.236412\pi$
$769$			37.5080i			1.35257i	−0.736639	+	0.676286i	$0.763588\pi$
$770$		0			0
$771$	−8.67763			−0.312517
$772$	3.01172	−	3.01172i	0.108394	−	0.108394i
$773$	10.2801	+	10.2801i	0.369750	+	0.369750i	0.867386	−	0.497636i	$-0.165798\pi$
$773$	10.2801	+	10.2801i	0.369750	+	0.369750i	−0.497636	+	0.867386i	$0.665798\pi$
$774$	−2.16971			−0.0779887
$775$		0			0
$776$	−5.55393			−0.199374
$777$	21.9750	+	21.9750i	0.788347	+	0.788347i
$778$	−14.3345	−	14.3345i	−0.513918	−	0.513918i
$779$	−2.87966	−	10.0044i	−0.103174	−	0.358444i
$780$		0			0
$781$			31.3581i			1.12208i
$782$	9.37115	−	9.37115i	0.335111	−	0.335111i
$783$	−2.94178	+	2.94178i	−0.105131	+	0.105131i
$784$		−	2.04146i		−	0.0729092i
$785$		0			0
$786$	−5.02982			−0.179408
$787$	23.0345	−	23.0345i	0.821091	−	0.821091i	−0.165174	−	0.986264i	$-0.552819\pi$
$787$	23.0345	−	23.0345i	0.821091	−	0.821091i	0.986264	+	0.165174i	$0.0528185\pi$
$788$	14.2004	−	14.2004i	0.505869	−	0.505869i
$789$	−31.1672			−1.10958
$790$		0			0
$791$		−	55.8260i		−	1.98495i
$792$	1.33108	−	1.33108i	0.0472980	−	0.0472980i
$793$	15.6485	+	15.6485i	0.555696	+	0.555696i
$794$	−3.20362			−0.113692
$795$		0			0
$796$	−8.94564			−0.317070
$797$	11.4253	−	11.4253i	0.404706	−	0.404706i	−0.475182	−	0.879888i	$-0.657618\pi$
$797$	11.4253	−	11.4253i	0.404706	−	0.404706i	0.879888	+	0.475182i	$0.157618\pi$
$798$	−21.0558	−	11.6436i	−0.745366	−	0.412179i
$799$		−	9.57811i		−	0.338849i
$800$		0			0
$801$		−	1.68632i		−	0.0595833i
$802$	22.7991	+	22.7991i	0.805065	+	0.805065i
$803$	15.6075	−	15.6075i	0.550776	−	0.550776i
$804$			11.6396i			0.410498i
$805$		0			0
$806$		−	37.0114i		−	1.30367i
$807$	18.7447	+	18.7447i	0.659845	+	0.659845i
$808$	4.06726	+	4.06726i	0.143086	+	0.143086i
$809$			20.2274i			0.711156i	0.934647	+	0.355578i	$0.115716\pi$
$809$			20.2274i			0.711156i	−0.934647	+	0.355578i	$0.884284\pi$
$810$		0			0
$811$		−	4.69034i		−	0.164700i	−0.996603	−	0.0823501i	$-0.973757\pi$
$811$		−	4.69034i		−	0.164700i	0.996603	−	0.0823501i	$-0.0262426\pi$
$812$	1.83212	−	1.83212i	0.0642949	−	0.0642949i
$813$	10.3328	+	10.3328i	0.362387	+	0.362387i
$814$			28.6464i			1.00406i
$815$		0			0
$816$		−	3.07638i		−	0.107695i
$817$	−12.3708	+	22.3708i	−0.432798	+	0.782654i
$818$	−17.5781	+	17.5781i	−0.614603	+	0.614603i
$819$	−5.84302			−0.204172
$820$		0			0
$821$	−20.4026			−0.712055			−0.356027	−	0.934476i	$-0.615869\pi$
$821$	−20.4026			−0.712055			−0.356027	+	0.934476i	$0.615869\pi$
$822$	−12.6629	−	12.6629i	−0.441668	−	0.441668i
$823$	4.18493	−	4.18493i	0.145878	−	0.145878i	−0.630396	−	0.776274i	$-0.717108\pi$
$823$	4.18493	−	4.18493i	0.145878	−	0.145878i	0.776274	+	0.630396i	$0.217108\pi$
$824$		−	3.61713i		−	0.126009i
$825$		0			0
$826$	−29.7813			−1.03622
$827$	0.0540683	−	0.0540683i	0.00188014	−	0.00188014i	−0.706166	−	0.708046i	$-0.749577\pi$
$827$	0.0540683	−	0.0540683i	0.00188014	−	0.00188014i	0.708046	+	0.706166i	$0.249577\pi$
$828$	2.06884	−	2.06884i	0.0718971	−	0.0718971i
$829$	−41.6466			−1.44644			−0.723222	−	0.690615i	$-0.757340\pi$
$829$	−41.6466			−1.44644			−0.723222	+	0.690615i	$0.757340\pi$
$830$		0			0
$831$			49.1268i			1.70419i
$832$	3.71401	−	3.71401i	0.128760	−	0.128760i
$833$	−2.41909	+	2.41909i	−0.0838166	+	0.0838166i
$834$		−	6.20048i		−	0.214705i
$835$		0			0
$836$	−6.13484	−	21.3134i	−0.212178	−	0.737138i
$837$	24.0567	+	24.0567i	0.831523	+	0.831523i
$838$	−15.8919	−	15.8919i	−0.548976	−	0.548976i
$839$	−3.89309			−0.134404			−0.0672022	−	0.997739i	$-0.521407\pi$
$839$	−3.89309			−0.134404			−0.0672022	+	0.997739i	$0.521407\pi$
$840$		0			0
$841$	−28.2575			−0.974396
$842$	−25.2981	−	25.2981i	−0.871829	−	0.871829i
$843$	5.53746	−	5.53746i	0.190720	−	0.190720i
$844$	24.3448			0.837981
$845$		0			0
$846$		−	2.11453i		−	0.0726990i
$847$	−31.6575	−	31.6575i	−1.08777	−	1.08777i
$848$	−6.57175	−	6.57175i	−0.225675	−	0.225675i
$849$	18.4696			0.633876
$850$		0			0
$851$			44.5238i			1.52625i
$852$	7.99995	+	7.99995i	0.274074	+	0.274074i
$853$	10.0390	−	10.0390i	0.343730	−	0.343730i	−0.514038	−	0.857767i	$-0.671851\pi$
$853$	10.0390	−	10.0390i	0.343730	−	0.343730i	0.857767	+	0.514038i	$0.171851\pi$
$854$	12.6692			0.433532
$855$		0			0
$856$	12.9283			0.441879
$857$	3.48995	−	3.48995i	0.119214	−	0.119214i	−0.644983	−	0.764197i	$-0.723135\pi$
$857$	3.48995	−	3.48995i	0.119214	−	0.119214i	0.764197	+	0.644983i	$0.223135\pi$
$858$	−34.6909	−	34.6909i	−1.18433	−	1.18433i
$859$		−	21.6236i		−	0.737789i	−0.929471	−	0.368894i	$-0.879736\pi$
$859$		−	21.6236i		−	0.737789i	0.929471	−	0.368894i	$-0.120264\pi$
$860$		0			0
$861$	−13.1835			−0.449291
$862$	9.06315	+	9.06315i	0.308692	+	0.308692i
$863$	−25.9867	−	25.9867i	−0.884599	−	0.884599i	0.109399	−	0.993998i	$-0.465107\pi$
$863$	−25.9867	−	25.9867i	−0.884599	−	0.884599i	−0.993998	+	0.109399i	$0.965107\pi$
$864$			4.82808i			0.164255i
$865$		0			0
$866$	3.50810			0.119210
$867$	18.4217	−	18.4217i	0.625634	−	0.625634i
$868$	−14.9824	−	14.9824i	−0.508536	−	0.508536i
$869$	−71.9887			−2.44205
$870$		0			0
$871$	33.3031			1.12843
$872$	−2.49174	−	2.49174i	−0.0843810	−	0.0843810i
$873$	1.45293	+	1.45293i	0.0491744	+	0.0491744i
$874$	−9.53508	−	33.1263i	−0.322529	−	1.12051i
$875$		0			0
$876$		−	7.96344i		−	0.269060i
$877$	−20.4804	+	20.4804i	−0.691573	+	0.691573i	−0.962578	−	0.271005i	$-0.912644\pi$
$877$	−20.4804	+	20.4804i	−0.691573	+	0.691573i	0.271005	+	0.962578i	$0.412644\pi$
$878$	−12.6864	+	12.6864i	−0.428145	+	0.428145i
$879$			36.0659i			1.21647i
$880$		0			0
$881$	−26.3529			−0.887852			−0.443926	−	0.896063i	$-0.646415\pi$
$881$	−26.3529			−0.887852			−0.443926	+	0.896063i	$0.646415\pi$
$882$	−0.534055	+	0.534055i	−0.0179826	+	0.0179826i
$883$	−15.8220	+	15.8220i	−0.532452	+	0.532452i	−0.921301	−	0.388849i	$-0.872873\pi$
$883$	−15.8220	+	15.8220i	−0.532452	+	0.532452i	0.388849	+	0.921301i	$0.372873\pi$
$884$	−8.80207			−0.296046
$885$		0			0
$886$		−	7.93017i		−	0.266419i
$887$	32.2731	−	32.2731i	1.08363	−	1.08363i	0.0874579	−	0.996168i	$-0.472126\pi$
$887$	32.2731	−	32.2731i	1.08363	−	1.08363i	0.996168	−	0.0874579i	$-0.0278743\pi$
$888$	7.30817	+	7.30817i	0.245246	+	0.245246i
$889$	−2.55180			−0.0855846
$890$		0			0
$891$	50.7442			1.69999
$892$	7.74344	−	7.74344i	0.259269	−	0.259269i
$893$	−21.8018	−	12.0561i	−0.729569	−	0.403443i
$894$			2.50083i			0.0836403i
$895$		0			0
$896$		−	3.00690i		−	0.100454i
$897$	−53.9183	−	53.9183i	−1.80028	−	1.80028i
$898$	−11.8868	+	11.8868i	−0.396668	+	0.396668i
$899$		−	6.07195i		−	0.202511i
$900$		0			0
$901$			15.5748i			0.518872i
$902$	−8.59295	−	8.59295i	−0.286114	−	0.286114i
$903$	22.8907	+	22.8907i	0.761754	+	0.761754i
$904$		−	18.5660i		−	0.617495i
$905$		0			0
$906$		−	33.0182i		−	1.09695i
$907$	−17.8874	+	17.8874i	−0.593942	+	0.593942i	−0.938694	−	0.344752i	$-0.887963\pi$
$907$	−17.8874	+	17.8874i	−0.593942	+	0.593942i	0.344752	+	0.938694i	$0.387963\pi$
$908$	1.35188	+	1.35188i	0.0448638	+	0.0448638i
$909$		−	2.12803i		−	0.0705822i
$910$		0			0
$911$			8.78015i			0.290899i	0.989366	+	0.145450i	$0.0464629\pi$
$911$			8.78015i			0.290899i	−0.989366	+	0.145450i	$0.953537\pi$
$912$	−7.00248	−	3.87229i	−0.231875	−	0.128224i
$913$	−4.25240	+	4.25240i	−0.140734	+	0.140734i
$914$	−28.8538			−0.954400
$915$		0			0
$916$	29.2012			0.964836
$917$	5.82564	+	5.82564i	0.192380	+	0.192380i
$918$	5.72119	−	5.72119i	0.188827	−	0.188827i
$919$			21.7772i			0.718365i	0.933267	+	0.359182i	$0.116944\pi$
$919$			21.7772i			0.718365i	−0.933267	+	0.359182i	$0.883056\pi$
$920$		0			0
$921$	37.2100			1.22611
$922$	19.3253	−	19.3253i	0.636444	−	0.636444i
$923$	22.8893	−	22.8893i	0.753410	−	0.753410i
$924$	−28.0861			−0.923965
$925$		0			0
$926$			16.6164i			0.546047i
$927$	−0.946259	+	0.946259i	−0.0310792	+	0.0310792i
$928$	0.609306	−	0.609306i	0.0200015	−	0.0200015i
$929$			29.3526i			0.963027i	0.876439	+	0.481514i	$0.159913\pi$
$929$			29.3526i			0.963027i	−0.876439	+	0.481514i	$0.840087\pi$
$930$		0			0
$931$	2.46141	+	8.55131i	0.0806694	+	0.280258i
$932$	17.3007	+	17.3007i	0.566702	+	0.566702i
$933$	22.5531	+	22.5531i	0.738355	+	0.738355i
$934$	−14.0482			−0.459670
$935$		0			0
$936$	−1.94320			−0.0635156
$937$	39.6877	+	39.6877i	1.29654	+	1.29654i	0.930662	+	0.365880i	$0.119232\pi$
$937$	39.6877	+	39.6877i	1.29654	+	1.29654i	0.365880	+	0.930662i	$0.380768\pi$
$938$	13.4813	−	13.4813i	0.440179	−	0.440179i
$939$	45.5499			1.48646
$940$		0			0
$941$		−	24.8913i		−	0.811432i	−0.913999	−	0.405716i	$-0.867022\pi$
$941$		−	24.8913i		−	0.811432i	0.913999	−	0.405716i	$-0.132978\pi$
$942$	21.3623	+	21.3623i	0.696021	+	0.696021i
$943$	−13.3556	−	13.3556i	−0.434918	−	0.434918i
$944$	−9.90431			−0.322358
$945$		0			0
$946$			29.8402i			0.970188i
$947$	17.8063	+	17.8063i	0.578628	+	0.578628i	0.934525	−	0.355897i	$-0.115825\pi$
$947$	17.8063	+	17.8063i	0.578628	+	0.578628i	−0.355897	+	0.934525i	$0.615825\pi$
$948$	−18.3655	+	18.3655i	−0.596483	+	0.596483i
$949$	−22.7848			−0.739627
$950$		0			0
$951$	−8.05544			−0.261215
$952$	−3.56313	+	3.56313i	−0.115482	+	0.115482i
$953$	−40.1672	−	40.1672i	−1.30114	−	1.30114i	−0.927622	−	0.373521i	$-0.878150\pi$
$953$	−40.1672	−	40.1672i	−1.30114	−	1.30114i	−0.373521	−	0.927622i	$-0.621850\pi$
$954$			3.43840i			0.111322i
$955$		0			0
$956$	0.129605			0.00419174
$957$	−5.69125	−	5.69125i	−0.183972	−	0.183972i
$958$	−23.2849	−	23.2849i	−0.752301	−	0.752301i
$959$			29.3328i			0.947205i
$960$		0			0
$961$	−18.6541			−0.601746
$962$	20.9100	−	20.9100i	0.674165	−	0.674165i
$963$	−3.38210	−	3.38210i	−0.108987	−	0.108987i
$964$	15.3241			0.493555
$965$		0			0
$966$	−43.6529			−1.40451
$967$	−37.7044	−	37.7044i	−1.21249	−	1.21249i	−0.970204	−	0.242288i	$-0.922102\pi$
$967$	−37.7044	−	37.7044i	−1.21249	−	1.21249i	−0.242288	−	0.970204i	$-0.577898\pi$
$968$	−10.5283	−	10.5283i	−0.338392	−	0.338392i
$969$	3.70922	+	12.8864i	0.119157	+	0.413971i
$970$		0			0
$971$		−	59.9297i		−	1.92323i	−0.274394	−	0.961617i	$-0.588477\pi$
$971$		−	59.9297i		−	1.92323i	0.274394	−	0.961617i	$-0.411523\pi$
$972$	2.70377	−	2.70377i	0.0867234	−	0.0867234i
$973$	−7.18153	+	7.18153i	−0.230229	+	0.230229i
$974$		−	16.2592i		−	0.520979i
$975$		0			0
$976$	4.21338			0.134867
$977$	−42.1006	+	42.1006i	−1.34692	+	1.34692i	−0.457927	+	0.888990i	$0.651408\pi$
$977$	−42.1006	+	42.1006i	−1.34692	+	1.34692i	−0.888990	+	0.457927i	$0.848592\pi$
$978$	4.85988	−	4.85988i	0.155402	−	0.155402i
$979$	−23.1921			−0.741222
$980$		0			0
$981$			1.30370i			0.0416240i
$982$	−31.1328	+	31.1328i	−0.993488	+	0.993488i
$983$	17.8001	+	17.8001i	0.567736	+	0.567736i	0.931494	−	0.363758i	$-0.118506\pi$
$983$	17.8001	+	17.8001i	0.567736	+	0.567736i	−0.363758	+	0.931494i	$0.618506\pi$
$984$	−4.38440			−0.139770
$985$		0			0
$986$	−1.44403			−0.0459874
$987$	−22.3085	+	22.3085i	−0.710087	+	0.710087i
$988$	−11.0793	+	20.0354i	−0.352480	+	0.637410i
$989$			46.3791i			1.47477i
$990$		0			0
$991$		−	52.1903i		−	1.65788i	−0.559337	−	0.828940i	$-0.688944\pi$
$991$		−	52.1903i		−	1.65788i	0.559337	−	0.828940i	$-0.311056\pi$
$992$	−4.98268	−	4.98268i	−0.158200	−	0.158200i
$993$	−12.6311	+	12.6311i	−0.400834	+	0.400834i
$994$		−	18.5314i		−	0.587781i
$995$		0			0
$996$			2.16971i			0.0687500i
$997$	−15.2861	−	15.2861i	−0.484117	−	0.484117i	0.422327	−	0.906444i	$-0.361213\pi$
$997$	−15.2861	−	15.2861i	−0.484117	−	0.484117i	−0.906444	+	0.422327i	$0.861213\pi$
$998$	20.0099	+	20.0099i	0.633401	+	0.633401i
$999$			27.1822i			0.860008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.f.c.607.7		16
5.2	odd	4		190.2.f.b.113.7	yes	16
5.3	odd	4	inner	950.2.f.c.493.2		16
5.4	even	2		190.2.f.b.37.2	✓	16
15.2	even	4		1710.2.p.b.1063.3		16
15.14	odd	2		1710.2.p.b.37.7		16
19.18	odd	2	inner	950.2.f.c.607.2		16
95.18	even	4	inner	950.2.f.c.493.7		16
95.37	even	4		190.2.f.b.113.2	yes	16
95.94	odd	2		190.2.f.b.37.7	yes	16
285.227	odd	4		1710.2.p.b.1063.7		16
285.284	even	2		1710.2.p.b.37.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.f.b.37.2	✓	16	5.4	even	2
190.2.f.b.37.7	yes	16	95.94	odd	2
190.2.f.b.113.2	yes	16	95.37	even	4
190.2.f.b.113.7	yes	16	5.2	odd	4
950.2.f.c.493.2		16	5.3	odd	4	inner
950.2.f.c.493.7		16	95.18	even	4	inner
950.2.f.c.607.2		16	19.18	odd	2	inner
950.2.f.c.607.7		16	1.1	even	1	trivial
1710.2.p.b.37.3		16	285.284	even	2
1710.2.p.b.37.7		16	15.14	odd	2
1710.2.p.b.1063.3		16	15.2	even	4
1710.2.p.b.1063.7		16	285.227	odd	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.29807 + 1.29807i) q^{3} -1.00000i q^{4} +1.83575 q^{6} +(-2.12620 - 2.12620i) q^{7} +(-0.707107 - 0.707107i) q^{8} +0.369965i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.29807 + 1.29807i) q^{3} -1.00000i q^{4} +1.83575 q^{6} +(-2.12620 - 2.12620i) q^{7} +(-0.707107 - 0.707107i) q^{8} +0.369965i q^{9} +5.08815 q^{11} +(1.29807 - 1.29807i) q^{12} +(-3.71401 - 3.71401i) q^{13} -3.00690 q^{14} -1.00000 q^{16} +(1.18498 + 1.18498i) q^{17} +(0.261605 + 0.261605i) q^{18} +(4.18883 - 1.20571i) q^{19} -5.51991i q^{21} +(3.59786 - 3.59786i) q^{22} +(5.59198 - 5.59198i) q^{23} -1.83575i q^{24} -5.25240 q^{26} +(3.41397 - 3.41397i) q^{27} +(-2.12620 + 2.12620i) q^{28} -0.861689 q^{29} +7.04657i q^{31} +(-0.707107 + 0.707107i) q^{32} +(6.60477 + 6.60477i) q^{33} +1.67582 q^{34} +0.369965 q^{36} +(-3.98104 + 3.98104i) q^{37} +(2.10938 - 3.81451i) q^{38} -9.64208i q^{39} -2.38835i q^{41} +(-3.90317 - 3.90317i) q^{42} +(-4.14693 + 4.14693i) q^{43} -5.08815i q^{44} -7.90826i q^{46} +(-4.04146 - 4.04146i) q^{47} +(-1.29807 - 1.29807i) q^{48} +2.04146i q^{49} +3.07638i q^{51} +(-3.71401 + 3.71401i) q^{52} +(6.57175 + 6.57175i) q^{53} -4.82808i q^{54} +3.00690i q^{56} +(7.00248 + 3.87229i) q^{57} +(-0.609306 + 0.609306i) q^{58} +9.90431 q^{59} -4.21338 q^{61} +(4.98268 + 4.98268i) q^{62} +(0.786620 - 0.786620i) q^{63} +1.00000i q^{64} +9.34055 q^{66} +(-4.48345 + 4.48345i) q^{67} +(1.18498 - 1.18498i) q^{68} +14.5176 q^{69} +6.16296i q^{71} +(0.261605 - 0.261605i) q^{72} +(3.06742 - 3.06742i) q^{73} +5.63004i q^{74} +(-1.20571 - 4.18883i) q^{76} +(-10.8184 - 10.8184i) q^{77} +(-6.81798 - 6.81798i) q^{78} -14.1483 q^{79} +9.97302 q^{81} +(-1.68882 - 1.68882i) q^{82} +(-0.835746 + 0.835746i) q^{83} -5.51991 q^{84} +5.86464i q^{86} +(-1.11853 - 1.11853i) q^{87} +(-3.59786 - 3.59786i) q^{88} -4.55806 q^{89} +15.7935i q^{91} +(-5.59198 - 5.59198i) q^{92} +(-9.14693 + 9.14693i) q^{93} -5.71548 q^{94} -1.83575 q^{96} +(3.92722 - 3.92722i) q^{97} +(1.44353 + 1.44353i) q^{98} +1.88244i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} - 16 q^{16} + 32 q^{17} + 8 q^{23} - 32 q^{26} - 8 q^{28} + 32 q^{36} - 8 q^{38} + 32 q^{42} - 24 q^{43} - 32 q^{47} + 48 q^{57} - 64 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{66} + 32 q^{68} - 16 q^{73} - 16 q^{76} - 72 q^{77} + 16 q^{81} - 40 q^{82} + 16 q^{83} + 8 q^{87} - 8 q^{92} - 104 q^{93}+O(q^{100}) \) 16 * q - 8 * q^7 - 16 * q^16 + 32 * q^17 + 8 * q^23 - 32 * q^26 - 8 * q^28 + 32 * q^36 - 8 * q^38 + 32 * q^42 - 24 * q^43 - 32 * q^47 + 48 * q^57 - 64 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^66 + 32 * q^68 - 16 * q^73 - 16 * q^76 - 72 * q^77 + 16 * q^81 - 40 * q^82 + 16 * q^83 + 8 * q^87 - 8 * q^92 - 104 * q^93

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