LMFDB - Embedded newform 875.2.f.b.818.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(307,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,0,0,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
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} + 36x^{14} + 456x^{12} + 2616x^{10} + 7596x^{8} + 11600x^{6} + 9040x^{4} + 3200x^{2} + 400 $ x^16 + 36x^14 + 456x^12 + 2616x^10 + 7596x^8 + 11600x^6 + 9040x^4 + 3200*x^2 + 400
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			818.6
Root			$-3.13163i$ of defining polynomial
Character	$\chi$	$=$	875.818
Dual form			875.2.f.b.307.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.30038 - 1.30038i) q^{2} +(0.513743 - 0.513743i) q^{3} -1.38197i q^{4} -1.33612i q^{6} +(0.0446190 + 2.64538i) q^{7} +(0.803678 + 0.803678i) q^{8} +2.47214i q^{9} +0.381966 q^{11} +(-0.709976 - 0.709976i) q^{12} +(4.35250 - 4.35250i) q^{13} +(3.49801 + 3.38197i) q^{14} +4.85410 q^{16} +(-1.34500 - 1.34500i) q^{17} +(3.21471 + 3.21471i) q^{18} -1.33612 q^{19} +(1.38197 + 1.33612i) q^{21} +(0.496700 - 0.496700i) q^{22} +(3.90113 + 3.90113i) q^{23} +0.825768 q^{24} -11.3198i q^{26} +(2.81127 + 2.81127i) q^{27} +(3.65582 - 0.0616619i) q^{28} -4.70820i q^{29} -9.15791i q^{31} +(4.70481 - 4.70481i) q^{32} +(0.196232 - 0.196232i) q^{33} -3.49801 q^{34} +3.41641 q^{36} +(-6.31217 + 6.31217i) q^{37} +(-1.73746 + 1.73746i) q^{38} -4.47214i q^{39} +6.99602i q^{41} +(3.53454 - 0.0596164i) q^{42} +(2.10406 + 2.10406i) q^{43} -0.527864i q^{44} +10.1459 q^{46} +(3.32502 + 3.32502i) q^{47} +(2.49376 - 2.49376i) q^{48} +(-6.99602 + 0.236068i) q^{49} -1.38197 q^{51} +(-6.01501 - 6.01501i) q^{52} +(-6.00519 - 6.00519i) q^{53} +7.31143 q^{54} +(-2.09017 + 2.16189i) q^{56} +(-0.686423 + 0.686423i) q^{57} +(-6.12244 - 6.12244i) q^{58} -9.98367 q^{59} -13.4817i q^{61} +(-11.9087 - 11.9087i) q^{62} +(-6.53973 + 0.110304i) q^{63} -2.52786i q^{64} -0.510353i q^{66} +(-3.40443 + 3.40443i) q^{67} +(-1.85874 + 1.85874i) q^{68} +4.00836 q^{69} +6.23607 q^{71} +(-1.98680 + 1.98680i) q^{72} +(-10.1713 + 10.1713i) q^{73} +16.4164i q^{74} +1.84647i q^{76} +(0.0170429 + 1.01044i) q^{77} +(-5.81547 - 5.81547i) q^{78} -9.70820i q^{79} -4.52786 q^{81} +(9.09747 + 9.09747i) q^{82} +(3.83876 - 3.83876i) q^{83} +(1.84647 - 1.90983i) q^{84} +5.47214 q^{86} +(-2.41881 - 2.41881i) q^{87} +(0.306978 + 0.306978i) q^{88} +0.825768 q^{89} +(11.7082 + 11.3198i) q^{91} +(5.39123 - 5.39123i) q^{92} +(-4.70481 - 4.70481i) q^{93} +8.64755 q^{94} -4.83413i q^{96} +(4.35250 + 4.35250i) q^{97} +(-8.79049 + 9.40445i) q^{98} +0.944272i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 24 q^{11} + 24 q^{16} + 40 q^{21} - 160 q^{36} + 216 q^{46} - 40 q^{51} + 56 q^{56} + 64 q^{71} - 144 q^{81} + 16 q^{86} + 80 q^{91}+O(q^{100}) $ 16 * q + 24 * q^11 + 24 * q^16 + 40 * q^21 - 160 * q^36 + 216 * q^46 - 40 * q^51 + 56 * q^56 + 64 * q^71 - 144 * q^81 + 16 * q^86 + 80 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	1.30038	−	1.30038i	0.919506	−	0.919506i	−0.0774872	−	0.996993i	$-0.524690\pi$
$2$	1.30038	−	1.30038i	0.919506	−	0.919506i	0.996993	+	0.0774872i	$0.0246897\pi$
$3$	0.513743	−	0.513743i	0.296610	−	0.296610i	−0.543075	−	0.839684i	$-0.682740\pi$
$3$	0.513743	−	0.513743i	0.296610	−	0.296610i	0.839684	+	0.543075i	$0.182740\pi$
$4$		−	1.38197i		−	0.690983i
$5$		0			0
$5$		0			0
$6$		−	1.33612i		−	0.545469i
$7$	0.0446190	+	2.64538i	0.0168644	+	0.999858i
$7$	0.0446190	+	2.64538i	0.0168644	+	0.999858i
$8$	0.803678	+	0.803678i	0.284143	+	0.284143i
$9$			2.47214i			0.824045i
$10$		0			0
$11$	0.381966			0.115167			0.0575835	−	0.998341i	$-0.481660\pi$
$11$	0.381966			0.115167			0.0575835	+	0.998341i	$0.481660\pi$
$12$	−0.709976	−	0.709976i	−0.204952	−	0.204952i
$13$	4.35250	−	4.35250i	1.20717	−	1.20717i	0.235226	−	0.971941i	$-0.424417\pi$
$13$	4.35250	−	4.35250i	1.20717	−	1.20717i	0.971941	−	0.235226i	$-0.0755831\pi$
$14$	3.49801	+	3.38197i	0.934882	+	0.903868i
$15$		0			0
$16$	4.85410			1.21353
$17$	−1.34500	−	1.34500i	−0.326210	−	0.326210i	0.524934	−	0.851143i	$-0.324090\pi$
$17$	−1.34500	−	1.34500i	−0.326210	−	0.326210i	−0.851143	+	0.524934i	$0.824090\pi$
$18$	3.21471	+	3.21471i	0.757715	+	0.757715i
$19$	−1.33612			−0.306527			−0.153264	−	0.988185i	$-0.548978\pi$
$19$	−1.33612			−0.306527			−0.153264	+	0.988185i	$0.548978\pi$
$20$		0			0
$21$	1.38197	+	1.33612i	0.301570	+	0.291565i
$22$	0.496700	−	0.496700i	0.105897	−	0.105897i
$23$	3.90113	+	3.90113i	0.813443	+	0.813443i	0.985148	−	0.171706i	$-0.0549278\pi$
$23$	3.90113	+	3.90113i	0.813443	+	0.813443i	−0.171706	+	0.985148i	$0.554928\pi$
$24$	0.825768			0.168559
$25$		0			0
$26$		−	11.3198i		−	2.21999i
$27$	2.81127	+	2.81127i	0.541030	+	0.541030i
$28$	3.65582	−	0.0616619i	0.690885	−	0.0116530i
$29$		−	4.70820i		−	0.874292i	−0.899391	−	0.437146i	$-0.855989\pi$
$29$		−	4.70820i		−	0.874292i	0.899391	−	0.437146i	$-0.144011\pi$
$30$		0			0
$31$		−	9.15791i		−	1.64481i	−0.568903	−	0.822404i	$-0.692632\pi$
$31$		−	9.15791i		−	1.64481i	0.568903	−	0.822404i	$-0.307368\pi$
$32$	4.70481	−	4.70481i	0.831701	−	0.831701i
$33$	0.196232	−	0.196232i	0.0341597	−	0.0341597i
$34$	−3.49801			−0.599904
$35$		0			0
$36$	3.41641			0.569401
$37$	−6.31217	+	6.31217i	−1.03771	+	1.03771i	−0.0384536	+	0.999260i	$0.512243\pi$
$37$	−6.31217	+	6.31217i	−1.03771	+	1.03771i	−0.999260	+	0.0384536i	$0.987757\pi$
$38$	−1.73746	+	1.73746i	−0.281854	+	0.281854i
$39$		−	4.47214i		−	0.716115i
$40$		0			0
$41$			6.99602i			1.09259i	0.837591	+	0.546297i	$0.183963\pi$
$41$			6.99602i			1.09259i	−0.837591	+	0.546297i	$0.816037\pi$
$42$	3.53454	−	0.0596164i	0.545391	−	0.00919900i
$43$	2.10406	+	2.10406i	0.320866	+	0.320866i	0.849099	−	0.528234i	$-0.177145\pi$
$43$	2.10406	+	2.10406i	0.320866	+	0.320866i	−0.528234	+	0.849099i	$0.677145\pi$
$44$		−	0.527864i		−	0.0795785i
$45$		0			0
$46$	10.1459			1.49593
$47$	3.32502	+	3.32502i	0.485003	+	0.485003i	0.906725	−	0.421722i	$-0.138574\pi$
$47$	3.32502	+	3.32502i	0.485003	+	0.485003i	−0.421722	+	0.906725i	$0.638574\pi$
$48$	2.49376	−	2.49376i	0.359943	−	0.359943i
$49$	−6.99602	+	0.236068i	−0.999431	+	0.0337240i
$50$		0			0
$51$	−1.38197			−0.193514
$52$	−6.01501	−	6.01501i	−0.834132	−	0.834132i
$53$	−6.00519	−	6.00519i	−0.824876	−	0.824876i	0.161927	−	0.986803i	$-0.448229\pi$
$53$	−6.00519	−	6.00519i	−0.824876	−	0.824876i	−0.986803	+	0.161927i	$0.948229\pi$
$54$	7.31143			0.994960
$55$		0			0
$56$	−2.09017	+	2.16189i	−0.279311	+	0.288895i
$57$	−0.686423	+	0.686423i	−0.0909189	+	0.0909189i
$58$	−6.12244	−	6.12244i	−0.803916	−	0.803916i
$59$	−9.98367			−1.29976			−0.649882	−	0.760035i	$-0.725182\pi$
$59$	−9.98367			−1.29976			−0.649882	+	0.760035i	$0.725182\pi$
$60$		0			0
$61$		−	13.4817i		−	1.72615i	−0.505073	−	0.863076i	$-0.668535\pi$
$61$		−	13.4817i		−	1.72615i	0.505073	−	0.863076i	$-0.331465\pi$
$62$	−11.9087	−	11.9087i	−1.51241	−	1.51241i
$63$	−6.53973	+	0.110304i	−0.823928	+	0.0138970i
$64$		−	2.52786i		−	0.315983i
$65$		0			0
$66$		−	0.510353i		−	0.0628201i
$67$	−3.40443	+	3.40443i	−0.415918	+	0.415918i	−0.883794	−	0.467876i	$-0.845019\pi$
$67$	−3.40443	+	3.40443i	−0.415918	+	0.415918i	0.467876	+	0.883794i	$0.345019\pi$
$68$	−1.85874	+	1.85874i	−0.225405	+	0.225405i
$69$	4.00836			0.482550
$70$		0			0
$71$	6.23607			0.740085			0.370043	−	0.929015i	$-0.379343\pi$
$71$	6.23607			0.740085			0.370043	+	0.929015i	$0.379343\pi$
$72$	−1.98680	+	1.98680i	−0.234147	+	0.234147i
$73$	−10.1713	+	10.1713i	−1.19046	+	1.19046i	−0.213519	+	0.976939i	$0.568493\pi$
$73$	−10.1713	+	10.1713i	−1.19046	+	1.19046i	−0.976939	+	0.213519i	$0.931507\pi$
$74$			16.4164i			1.90837i
$75$		0			0
$76$			1.84647i			0.211805i
$77$	0.0170429	+	1.01044i	0.00194222	+	0.115151i
$78$	−5.81547	−	5.81547i	−0.658472	−	0.658472i
$79$		−	9.70820i		−	1.09226i	−0.837701	−	0.546129i	$-0.816101\pi$
$79$		−	9.70820i		−	1.09226i	0.837701	−	0.546129i	$-0.183899\pi$
$80$		0			0
$81$	−4.52786			−0.503096
$82$	9.09747	+	9.09747i	1.00465	+	1.00465i
$83$	3.83876	−	3.83876i	0.421359	−	0.421359i	−0.464313	−	0.885671i	$-0.653699\pi$
$83$	3.83876	−	3.83876i	0.421359	−	0.421359i	0.885671	+	0.464313i	$0.153699\pi$
$84$	1.84647	−	1.90983i	0.201467	−	0.208380i
$85$		0			0
$86$	5.47214			0.590076
$87$	−2.41881	−	2.41881i	−0.259323	−	0.259323i
$88$	0.306978	+	0.306978i	0.0327239	+	0.0327239i
$89$	0.825768			0.0875312			0.0437656	−	0.999042i	$-0.486065\pi$
$89$	0.825768			0.0875312			0.0437656	+	0.999042i	$0.486065\pi$
$90$		0			0
$91$	11.7082	+	11.3198i	1.22735	+	1.18664i
$92$	5.39123	−	5.39123i	0.562075	−	0.562075i
$93$	−4.70481	−	4.70481i	−0.487866	−	0.487866i
$94$	8.64755			0.891927
$95$		0			0
$96$		−	4.83413i		−	0.493381i
$97$	4.35250	+	4.35250i	0.441930	+	0.441930i	0.892660	−	0.450730i	$-0.148836\pi$
$97$	4.35250	+	4.35250i	0.441930	+	0.441930i	−0.450730	+	0.892660i	$0.648836\pi$
$98$	−8.79049	+	9.40445i	−0.887974	+	0.949993i
$99$			0.944272i			0.0949029i
$100$		0			0
$101$			1.33612i			0.132949i	0.997788	+	0.0664745i	$0.0211751\pi$
$101$			1.33612i			0.132949i	−0.997788	+	0.0664745i	$0.978825\pi$
$102$	−1.79708	+	1.79708i	−0.177937	+	0.177937i
$103$	−1.54123	+	1.54123i	−0.151862	+	0.151862i	−0.778949	−	0.627087i	$-0.784247\pi$
$103$	−1.54123	+	1.54123i	−0.151862	+	0.151862i	0.627087	+	0.778949i	$0.284247\pi$
$104$	6.99602			0.686016
$105$		0			0
$106$	−15.6180			−1.51696
$107$	8.60595	−	8.60595i	0.831968	−	0.831968i	−0.155818	−	0.987786i	$-0.549801\pi$
$107$	8.60595	−	8.60595i	0.831968	−	0.831968i	0.987786	+	0.155818i	$0.0498012\pi$
$108$	3.88508	−	3.88508i	0.373842	−	0.373842i
$109$			7.00000i			0.670478i	0.942133	+	0.335239i	$0.108817\pi$
$109$			7.00000i			0.670478i	−0.942133	+	0.335239i	$0.891183\pi$
$110$		0			0
$111$			6.48567i			0.615592i
$112$	0.216585	+	12.8409i	0.0204654	+	1.21335i
$113$	−4.39783	−	4.39783i	−0.413713	−	0.413713i	0.469317	−	0.883030i	$-0.344500\pi$
$113$	−4.39783	−	4.39783i	−0.413713	−	0.413713i	−0.883030	+	0.469317i	$0.844500\pi$
$114$			1.78522i			0.167201i
$115$		0			0
$116$	−6.50658			−0.604121
$117$	10.7600	+	10.7600i	0.994760	+	0.994760i
$118$	−12.9826	+	12.9826i	−1.19514	+	1.19514i
$119$	3.49801	−	3.61803i	0.320662	−	0.331665i
$120$		0			0
$121$	−10.8541			−0.986737
$122$	−17.5313	−	17.5313i	−1.58721	−	1.58721i
$123$	3.59416	+	3.59416i	0.324074	+	0.324074i
$124$	−12.6559			−1.13653
$125$		0			0
$126$	−8.36068	+	8.64755i	−0.744829	+	0.770385i
$127$	−6.31217	+	6.31217i	−0.560114	+	0.560114i	−0.929340	−	0.369226i	$-0.879623\pi$
$127$	−6.31217	+	6.31217i	−0.560114	+	0.560114i	0.369226	+	0.929340i	$0.379623\pi$
$128$	6.12244	+	6.12244i	0.541153	+	0.541153i
$129$	2.16189			0.190344
$130$		0			0
$131$		−	17.4900i		−	1.52811i	−0.645150	−	0.764056i	$-0.723205\pi$
$131$		−	17.4900i		−	1.52811i	0.645150	−	0.764056i	$-0.276795\pi$
$132$	−0.271187	−	0.271187i	−0.0236038	−	0.0236038i
$133$	−0.0596164	−	3.53454i	−0.00516939	−	0.306483i
$134$			8.85410i			0.764878i
$135$		0			0
$136$		−	2.16189i		−	0.185380i
$137$	5.01179	−	5.01179i	0.428186	−	0.428186i	−0.459824	−	0.888010i	$-0.652088\pi$
$137$	5.01179	−	5.01179i	0.428186	−	0.428186i	0.888010	+	0.459824i	$0.152088\pi$
$138$	5.21239	−	5.21239i	0.443708	−	0.443708i
$139$	−3.49801			−0.296697			−0.148349	−	0.988935i	$-0.547396\pi$
$139$	−3.49801			−0.296697			−0.148349	+	0.988935i	$0.547396\pi$
$140$		0			0
$141$	3.41641			0.287713
$142$	8.10925	−	8.10925i	0.680513	−	0.680513i
$143$	1.66251	−	1.66251i	0.139026	−	0.139026i
$144$			12.0000i			1.00000i
$145$		0			0
$146$			26.4530i			2.18927i
$147$	−3.47288	+	3.71543i	−0.286438	+	0.306444i
$148$	8.72320	+	8.72320i	0.717043	+	0.717043i
$149$		−	8.32624i		−	0.682112i	−0.940043	−	0.341056i	$-0.889215\pi$
$149$		−	8.32624i		−	0.682112i	0.940043	−	0.341056i	$-0.110785\pi$
$150$		0			0
$151$	−1.85410			−0.150885			−0.0754423	−	0.997150i	$-0.524037\pi$
$151$	−1.85410			−0.150885			−0.0754423	+	0.997150i	$0.524037\pi$
$152$	−1.07381	−	1.07381i	−0.0870975	−	0.0870975i
$153$	3.32502	−	3.32502i	0.268812	−	0.268812i
$154$	1.33612	+	1.29180i	0.107668	+	0.104096i
$155$		0			0
$156$	−6.18034			−0.494823
$157$	−4.23122	−	4.23122i	−0.337688	−	0.337688i	0.517808	−	0.855497i	$-0.326748\pi$
$157$	−4.23122	−	4.23122i	−0.337688	−	0.337688i	−0.855497	+	0.517808i	$0.826748\pi$
$158$	−12.6243	−	12.6243i	−1.00434	−	1.00434i
$159$	−6.17025			−0.489333
$160$		0			0
$161$	−10.1459	+	10.4940i	−0.799609	+	0.827045i
$162$	−5.88793	+	5.88793i	−0.462600	+	0.462600i
$163$	−1.30038	−	1.30038i	−0.101853	−	0.101853i	0.654344	−	0.756197i	$-0.272945\pi$
$163$	−1.30038	−	1.30038i	−0.101853	−	0.101853i	−0.756197	+	0.654344i	$0.772945\pi$
$164$	9.66826			0.754964
$165$		0			0
$166$		−	9.98367i		−	0.774883i
$167$	−1.54123	−	1.54123i	−0.119264	−	0.119264i	0.644956	−	0.764220i	$-0.276876\pi$
$167$	−1.54123	−	1.54123i	−0.119264	−	0.119264i	−0.764220	+	0.644956i	$0.776876\pi$
$168$	0.0368449	+	2.18447i	0.00284265	+	0.168535i
$169$		−	24.8885i		−	1.91450i
$170$		0			0
$171$		−	3.30307i		−	0.252592i
$172$	2.90773	−	2.90773i	0.221713	−	0.221713i
$173$	1.54123	−	1.54123i	0.117178	−	0.117178i	−0.646087	−	0.763264i	$-0.723596\pi$
$173$	1.54123	−	1.54123i	0.117178	−	0.117178i	0.763264	+	0.646087i	$0.223596\pi$
$174$	−6.29073			−0.476899
$175$		0			0
$176$	1.85410			0.139758
$177$	−5.12904	+	5.12904i	−0.385523	+	0.385523i
$178$	1.07381	−	1.07381i	0.0804855	−	0.0804855i
$179$		−	16.0344i		−	1.19847i	−0.800573	−	0.599235i	$-0.795471\pi$
$179$		−	16.0344i		−	1.19847i	0.800573	−	0.599235i	$-0.204529\pi$
$180$		0			0
$181$			21.3035i			1.58347i	0.610862	+	0.791737i	$0.290823\pi$
$181$			21.3035i			1.58347i	−0.610862	+	0.791737i	$0.709177\pi$
$182$	29.9451	−	0.505078i	2.21968	−	0.0374389i
$183$	−6.92612	−	6.92612i	−0.511994	−	0.511994i
$184$			6.27051i			0.462268i
$185$		0			0
$186$	−12.2361			−0.897192
$187$	−0.513743	−	0.513743i	−0.0375686	−	0.0375686i
$188$	4.59506	−	4.59506i	0.335129	−	0.335129i
$189$	−7.31143	+	7.56231i	−0.531829	+	0.550077i
$190$		0			0
$191$	−1.29180			−0.0934711			−0.0467355	−	0.998907i	$-0.514882\pi$
$191$	−1.29180			−0.0934711			−0.0467355	+	0.998907i	$0.514882\pi$
$192$	−1.29867	−	1.29867i	−0.0937236	−	0.0937236i
$193$	14.4214	+	14.4214i	1.03808	+	1.03808i	0.999246	+	0.0388302i	$0.0123632\pi$
$193$	14.4214	+	14.4214i	1.03808	+	1.03808i	0.0388302	+	0.999246i	$0.487637\pi$
$194$	11.3198			0.812714
$195$		0			0
$196$	0.326238	+	9.66826i	0.0233027	+	0.690590i
$197$	6.00519	−	6.00519i	0.427852	−	0.427852i	−0.460044	−	0.887896i	$-0.652166\pi$
$197$	6.00519	−	6.00519i	0.427852	−	0.427852i	0.887896	+	0.460044i	$0.152166\pi$
$198$	1.22791	+	1.22791i	0.0872638	+	0.0872638i
$199$	−15.3282			−1.08658			−0.543292	−	0.839544i	$-0.682822\pi$
$199$	−15.3282			−1.08658			−0.543292	+	0.839544i	$0.682822\pi$
$200$		0			0
$201$			3.49801i			0.246731i
$202$	1.73746	+	1.73746i	0.122247	+	0.122247i
$203$	12.4550	−	0.210075i	0.874167	−	0.0147444i
$204$			1.90983i			0.133715i
$205$		0			0
$206$			4.00836i			0.279276i
$207$	−9.64413	+	9.64413i	−0.670314	+	0.670314i
$208$	21.1275	−	21.1275i	1.46493	−	1.46493i
$209$	−0.510353			−0.0353018
$210$		0			0
$211$	−12.4721			−0.858617			−0.429309	−	0.903158i	$-0.641243\pi$
$211$	−12.4721			−0.858617			−0.429309	+	0.903158i	$0.641243\pi$
$212$	−8.29897	+	8.29897i	−0.569975	+	0.569975i
$213$	3.20374	−	3.20374i	0.219516	−	0.219516i
$214$		−	22.3820i		−	1.53000i
$215$		0			0
$216$			4.51871i			0.307460i
$217$	24.2261	−	0.408617i	1.64457	−	0.0277387i
$218$	9.10265	+	9.10265i	0.616509	+	0.616509i
$219$			10.4508i			0.706203i
$220$		0			0
$221$	−11.7082			−0.787579
$222$	8.43382	+	8.43382i	0.566041	+	0.566041i
$223$	−6.52875	+	6.52875i	−0.437198	+	0.437198i	−0.891068	−	0.453870i	$-0.850043\pi$
$223$	−6.52875	+	6.52875i	−0.437198	+	0.437198i	0.453870	+	0.891068i	$0.350043\pi$
$224$	12.6559	+	12.2361i	0.845609	+	0.817557i
$225$		0			0
$226$	−11.4377			−0.760824
$227$	−21.1275	−	21.1275i	−1.40228	−	1.40228i	−0.792804	−	0.609476i	$-0.791380\pi$
$227$	−21.1275	−	21.1275i	−1.40228	−	1.40228i	−0.609476	−	0.792804i	$-0.708620\pi$
$228$	0.948613	+	0.948613i	0.0628234	+	0.0628234i
$229$	−10.8094			−0.714308			−0.357154	−	0.934045i	$-0.616253\pi$
$229$	−10.8094			−0.714308			−0.357154	+	0.934045i	$0.616253\pi$
$230$		0			0
$231$	0.527864	+	0.510353i	0.0347309	+	0.0335787i
$232$	3.78388	−	3.78388i	0.248424	−	0.248424i
$233$	10.8273	+	10.8273i	0.709317	+	0.709317i	0.966392	−	0.257074i	$-0.0827586\pi$
$233$	10.8273	+	10.8273i	0.709317	+	0.709317i	−0.257074	+	0.966392i	$0.582759\pi$
$234$	27.9841			1.82938
$235$		0			0
$236$			13.7971i			0.898115i
$237$	−4.98752	−	4.98752i	−0.323974	−	0.323974i
$238$	−0.156078	−	9.25355i	−0.0101170	−	0.599818i
$239$			19.9443i			1.29009i	0.764146	+	0.645044i	$0.223161\pi$
$239$			19.9443i			1.29009i	−0.764146	+	0.645044i	$0.776839\pi$
$240$		0			0
$241$			18.3158i			1.17983i	0.807467	+	0.589913i	$0.200838\pi$
$241$			18.3158i			1.17983i	−0.807467	+	0.589913i	$0.799162\pi$
$242$	−14.1144	+	14.1144i	−0.907310	+	0.907310i
$243$	−10.7600	+	10.7600i	−0.690253	+	0.690253i
$244$	−18.6312			−1.19274
$245$		0			0
$246$	9.34752			0.595976
$247$	−5.81547	+	5.81547i	−0.370029	+	0.370029i
$248$	7.36001	−	7.36001i	0.467361	−	0.467361i
$249$		−	3.94427i		−	0.249958i
$250$		0			0
$251$		−	6.48567i		−	0.409372i	−0.978828	−	0.204686i	$-0.934383\pi$
$251$		−	6.48567i		−	0.409372i	0.978828	−	0.204686i	$-0.0656173\pi$
$252$	0.152437	+	9.03768i	0.00960261	+	0.569320i
$253$	1.49010	+	1.49010i	0.0936818	+	0.0936818i
$254$			16.4164i			1.03006i
$255$		0			0
$256$	20.9787			1.31117
$257$	4.10995	+	4.10995i	0.256371	+	0.256371i	0.823577	−	0.567205i	$-0.191975\pi$
$257$	4.10995	+	4.10995i	0.256371	+	0.256371i	−0.567205	+	0.823577i	$0.691975\pi$
$258$	2.81127	−	2.81127i	0.175022	−	0.175022i
$259$	−16.9797	−	16.4164i	−1.05507	−	1.02007i
$260$		0			0
$261$	11.6393			0.720456
$262$	−22.7437	−	22.7437i	−1.40511	−	1.40511i
$263$	16.2185	+	16.2185i	1.00008	+	1.00008i	1.00000		7.50320e-5i	$2.38834e-5\pi$
$263$	16.2185	+	16.2185i	1.00008	+	1.00008i	7.50320e−5		1.00000i	$0.499976\pi$
$264$	0.315415			0.0194125
$265$		0			0
$266$	−4.67376	−	4.51871i	−0.286567	−	0.277060i
$267$	0.424233	−	0.424233i	0.0259626	−	0.0259626i
$268$	4.70481	+	4.70481i	0.287392	+	0.287392i
$269$	−19.1416			−1.16708			−0.583541	−	0.812083i	$-0.698333\pi$
$269$	−19.1416			−1.16708			−0.583541	+	0.812083i	$0.698333\pi$
$270$		0			0
$271$		−	12.1456i		−	0.737790i	−0.929471	−	0.368895i	$-0.879736\pi$
$271$		−	12.1456i		−	0.737790i	0.929471	−	0.368895i	$-0.120264\pi$
$272$	−6.52875	−	6.52875i	−0.395864	−	0.395864i
$273$	11.8305	−	0.199542i	0.716013	−	0.0120768i
$274$		−	13.0344i		−	0.787439i
$275$		0			0
$276$		−	5.53942i		−	0.333434i
$277$	−4.39783	+	4.39783i	−0.264240	+	0.264240i	−0.826774	−	0.562534i	$-0.809827\pi$
$277$	−4.39783	+	4.39783i	−0.264240	+	0.264240i	0.562534	+	0.826774i	$0.309827\pi$
$278$	−4.54873	+	4.54873i	−0.272815	+	0.272815i
$279$	22.6396			1.35540
$280$		0			0
$281$	−21.1246			−1.26019			−0.630094	−	0.776519i	$-0.716984\pi$
$281$	−21.1246			−1.26019			−0.630094	+	0.776519i	$0.716984\pi$
$282$	4.44262	−	4.44262i	0.264554	−	0.264554i
$283$	16.0650	−	16.0650i	0.954966	−	0.954966i	−0.0440630	−	0.999029i	$-0.514030\pi$
$283$	16.0650	−	16.0650i	0.954966	−	0.954966i	0.999029	+	0.0440630i	$0.0140302\pi$
$284$		−	8.61803i		−	0.511386i
$285$		0			0
$286$		−	4.32378i		−	0.255670i
$287$	−18.5071	+	0.312155i	−1.09244	+	0.0184259i
$288$	11.6309	+	11.6309i	0.685359	+	0.685359i
$289$		−	13.3820i		−	0.787174i
$290$		0			0
$291$	4.47214			0.262161
$292$	14.0564	+	14.0564i	0.822586	+	0.822586i
$293$	2.29753	−	2.29753i	0.134223	−	0.134223i	−0.636803	−	0.771026i	$-0.719744\pi$
$293$	2.29753	−	2.29753i	0.134223	−	0.134223i	0.771026	+	0.636803i	$0.219744\pi$
$294$	0.315415	+	9.34752i	0.0183954	+	0.545159i
$295$		0			0
$296$	−10.1459			−0.589718
$297$	1.07381	+	1.07381i	0.0623088	+	0.0623088i
$298$	−10.8273	−	10.8273i	−0.627206	−	0.627206i
$299$	33.9594			1.96392
$300$		0			0
$301$	−5.47214	+	5.65990i	−0.315409	+	0.326231i
$302$	−2.41103	+	2.41103i	−0.138739	+	0.138739i
$303$	0.686423	+	0.686423i	0.0394340	+	0.0394340i
$304$	−6.48567			−0.371978
$305$		0			0
$306$		−	8.64755i		−	0.494348i
$307$	0.588697	+	0.588697i	0.0335987	+	0.0335987i	0.723707	−	0.690108i	$-0.242437\pi$
$307$	0.588697	+	0.588697i	0.0335987	+	0.0335987i	−0.690108	+	0.723707i	$0.742437\pi$
$308$	1.39640	−	0.0235528i	0.0795672	−	0.00134204i
$309$			1.58359i			0.0900874i
$310$		0			0
$311$		−	6.99602i		−	0.396708i	−0.980130	−	0.198354i	$-0.936440\pi$
$311$		−	6.99602i		−	0.396708i	0.980130	−	0.198354i	$-0.0635595\pi$
$312$	3.59416	−	3.59416i	0.203479	−	0.203479i
$313$	−16.6537	+	16.6537i	−0.941323	+	0.941323i	−0.998371	−	0.0570482i	$-0.981831\pi$
$313$	−16.6537	+	16.6537i	−0.941323	+	0.941323i	0.0570482	+	0.998371i	$0.481831\pi$
$314$	−11.0044			−0.621013
$315$		0			0
$316$	−13.4164			−0.754732
$317$	23.7138	−	23.7138i	1.33190	−	1.33190i	0.428228	−	0.903671i	$-0.359138\pi$
$317$	23.7138	−	23.7138i	1.33190	−	1.33190i	0.903671	−	0.428228i	$-0.140862\pi$
$318$	−8.02366	+	8.02366i	−0.449944	+	0.449944i
$319$		−	1.79837i		−	0.100690i
$320$		0			0
$321$		−	8.84249i		−	0.493540i
$322$	0.452700	+	26.8397i	0.0252280	+	1.49572i
$323$	1.79708	+	1.79708i	0.0999921	+	0.0999921i
$324$			6.25735i			0.347631i
$325$		0			0
$326$	−3.38197			−0.187310
$327$	3.59620	+	3.59620i	0.198870	+	0.198870i
$328$	−5.62254	+	5.62254i	−0.310453	+	0.310453i
$329$	−8.64755	+	8.94427i	−0.476755	+	0.493114i
$330$		0			0
$331$	28.0689			1.54281			0.771403	−	0.636347i	$-0.219555\pi$
$331$	28.0689			1.54281			0.771403	+	0.636347i	$0.219555\pi$
$332$	−5.30503	−	5.30503i	−0.291152	−	0.291152i
$333$	−15.6045	−	15.6045i	−0.855123	−	0.855123i
$334$	−4.00836			−0.219328
$335$		0			0
$336$	6.70820	+	6.48567i	0.365963	+	0.353822i
$337$	−0.117255	+	0.117255i	−0.00638729	+	0.00638729i	−0.710293	−	0.703906i	$-0.751438\pi$
$337$	−0.117255	+	0.117255i	−0.00638729	+	0.00638729i	0.703906	+	0.710293i	$0.251438\pi$
$338$	−32.3645	−	32.3645i	−1.76040	−	1.76040i
$339$	−4.51871			−0.245423
$340$		0			0
$341$		−	3.49801i		−	0.189428i
$342$	−4.29524	−	4.29524i	−0.232260	−	0.232260i
$343$	−0.936644	−	18.4966i	−0.0505740	−	0.998720i
$344$			3.38197i			0.182343i
$345$		0			0
$346$		−	4.00836i		−	0.215491i
$347$	19.4332	−	19.4332i	1.04323	−	1.04323i	0.0442066	−	0.999022i	$-0.485924\pi$
$347$	19.4332	−	19.4332i	1.04323	−	1.04323i	0.999022	−	0.0442066i	$-0.0140760\pi$
$348$	−3.34271	+	3.34271i	−0.179188	+	0.179188i
$349$	33.6440			1.80092			0.900460	−	0.434938i	$-0.143230\pi$
$349$	33.6440			1.80092			0.900460	+	0.434938i	$0.143230\pi$
$350$		0			0
$351$	24.4721			1.30623
$352$	1.79708	−	1.79708i	0.0957846	−	0.0957846i
$353$	−4.23122	+	4.23122i	−0.225205	+	0.225205i	−0.810686	−	0.585481i	$-0.800906\pi$
$353$	−4.23122	+	4.23122i	−0.225205	+	0.225205i	0.585481	+	0.810686i	$0.300906\pi$
$354$			13.3394i			0.708981i
$355$		0			0
$356$		−	1.14118i		−	0.0604826i
$357$	−0.0616619	−	3.65582i	−0.00326350	−	0.193486i
$358$	−20.8508	−	20.8508i	−1.10200	−	1.10200i
$359$			8.70820i			0.459601i	0.973238	+	0.229801i	$0.0738074\pi$
$359$			8.70820i			0.459601i	−0.973238	+	0.229801i	$0.926193\pi$
$360$		0			0
$361$	−17.2148			−0.906041
$362$	27.7026	+	27.7026i	1.45601	+	1.45601i
$363$	−5.57622	+	5.57622i	−0.292676	+	0.292676i
$364$	15.6436	−	16.1803i	0.819946	−	0.848080i
$365$		0			0
$366$	−18.0132			−0.941563
$367$	−8.11631	−	8.11631i	−0.423668	−	0.423668i	0.462797	−	0.886464i	$-0.346846\pi$
$367$	−8.11631	−	8.11631i	−0.423668	−	0.423668i	−0.886464	+	0.462797i	$0.846846\pi$
$368$	18.9365	+	18.9365i	0.987133	+	0.987133i
$369$	−17.2951			−0.900347
$370$		0			0
$371$	15.6180	−	16.1539i	0.810848	−	0.838670i
$372$	−6.50189	+	6.50189i	−0.337107	+	0.337107i
$373$	11.9379	+	11.9379i	0.618122	+	0.618122i	0.945049	−	0.326928i	$-0.106013\pi$
$373$	11.9379	+	11.9379i	0.618122	+	0.618122i	−0.326928	+	0.945049i	$0.606013\pi$
$374$	−1.33612			−0.0690892
$375$		0			0
$376$			5.34448i			0.275621i
$377$	−20.4925	−	20.4925i	−1.05542	−	1.05542i
$378$	0.326229	+	19.3415i	0.0167794	+	0.994819i
$379$			23.7082i			1.21781i	0.793244	+	0.608904i	$0.208391\pi$
$379$			23.7082i			1.21781i	−0.793244	+	0.608904i	$0.791609\pi$
$380$		0			0
$381$			6.48567i			0.332271i
$382$	−1.67982	+	1.67982i	−0.0859472	+	0.0859472i
$383$	−17.6062	+	17.6062i	−0.899637	+	0.899637i	−0.995404	−	0.0957670i	$-0.969470\pi$
$383$	−17.6062	+	17.6062i	−0.899637	+	0.899637i	0.0957670	+	0.995404i	$0.469470\pi$
$384$	6.29073			0.321022
$385$		0			0
$386$	37.5066			1.90903
$387$	−5.20151	+	5.20151i	−0.264408	+	0.264408i
$388$	6.01501	−	6.01501i	0.305366	−	0.305366i
$389$			22.8541i			1.15875i	0.815061	+	0.579374i	$0.196703\pi$
$389$			22.8541i			1.15875i	−0.815061	+	0.579374i	$0.803297\pi$
$390$		0			0
$391$		−	10.4940i		−	0.530706i
$392$	−5.81227	−	5.43282i	−0.293564	−	0.274399i
$393$	−8.98539	−	8.98539i	−0.453253	−	0.453253i
$394$		−	15.6180i		−	0.786825i
$395$		0			0
$396$	1.30495			0.0655763
$397$	−10.6101	−	10.6101i	−0.532504	−	0.532504i	0.388813	−	0.921317i	$-0.372885\pi$
$397$	−10.6101	−	10.6101i	−0.532504	−	0.532504i	−0.921317	+	0.388813i	$0.872885\pi$
$398$	−19.9324	+	19.9324i	−0.999121	+	0.999121i
$399$	−1.84647	−	1.78522i	−0.0924393	−	0.0893727i
$400$		0			0
$401$	21.0344			1.05041			0.525205	−	0.850976i	$-0.323989\pi$
$401$	21.0344			1.05041			0.525205	+	0.850976i	$0.323989\pi$
$402$	4.54873	+	4.54873i	0.226870	+	0.226870i
$403$	−39.8598	−	39.8598i	−1.98556	−	1.98556i
$404$	1.84647			0.0918655
$405$		0			0
$406$	15.9230	−	16.4693i	0.790245	−	0.817360i
$407$	−2.41103	+	2.41103i	−0.119510	+	0.119510i
$408$	−1.11066	−	1.11066i	−0.0549856	−	0.0549856i
$409$	−12.1456			−0.600559			−0.300280	−	0.953851i	$-0.597080\pi$
$409$	−12.1456			−0.600559			−0.300280	+	0.953851i	$0.597080\pi$
$410$		0			0
$411$		−	5.14955i		−	0.254008i
$412$	2.12993	+	2.12993i	0.104934	+	0.104934i
$413$	−0.445462	−	26.4106i	−0.0219197	−	1.29958i
$414$			25.0820i			1.23271i
$415$		0			0
$416$		−	40.9554i		−	2.00800i
$417$	−1.79708	+	1.79708i	−0.0880033	+	0.0880033i
$418$	−0.663651	+	0.663651i	−0.0324602	+	0.0324602i
$419$	7.82179			0.382119			0.191060	−	0.981578i	$-0.438808\pi$
$419$	7.82179			0.382119			0.191060	+	0.981578i	$0.438808\pi$
$420$		0			0
$421$	−22.7082			−1.10673			−0.553365	−	0.832939i	$-0.686657\pi$
$421$	−22.7082			−1.10673			−0.553365	+	0.832939i	$0.686657\pi$
$422$	−16.2185	+	16.2185i	−0.789504	+	0.789504i
$423$	−8.21989	+	8.21989i	−0.399665	+	0.399665i
$424$		−	9.65248i		−	0.468766i
$425$		0			0
$426$		−	8.33214i		−	0.403693i
$427$	35.6641	−	0.601539i	1.72591	−	0.0291105i
$428$	−11.8931	−	11.8931i	−0.574876	−	0.574876i
$429$		−	1.70820i		−	0.0824729i
$430$		0			0
$431$	38.8328			1.87051			0.935255	−	0.353973i	$-0.115170\pi$
$431$	38.8328			1.87051			0.935255	+	0.353973i	$0.115170\pi$
$432$	13.6462	+	13.6462i	0.656553	+	0.656553i
$433$	−14.5238	+	14.5238i	−0.697968	+	0.697968i	−0.963972	−	0.266004i	$-0.914297\pi$
$433$	−14.5238	+	14.5238i	−0.697968	+	0.697968i	0.266004	+	0.963972i	$0.414297\pi$
$434$	30.9717	−	32.0344i	1.48669	−	1.53770i
$435$		0			0
$436$	9.67376			0.463289
$437$	−5.21239	−	5.21239i	−0.249342	−	0.249342i
$438$	13.5901	+	13.5901i	0.649358	+	0.649358i
$439$	−15.1332			−0.722269			−0.361135	−	0.932514i	$-0.617611\pi$
$439$	−15.1332			−0.722269			−0.361135	+	0.932514i	$0.617611\pi$
$440$		0			0
$441$	−0.583592	−	17.2951i	−0.0277901	−	0.823577i
$442$	−15.2251	+	15.2251i	−0.724184	+	0.724184i
$443$	−15.4148	−	15.4148i	−0.732380	−	0.732380i	0.238711	−	0.971091i	$-0.423275\pi$
$443$	−15.4148	−	15.4148i	−0.732380	−	0.732380i	−0.971091	+	0.238711i	$0.923275\pi$
$444$	8.96297			0.425364
$445$		0			0
$446$			16.9797i			0.804012i
$447$	−4.27755	−	4.27755i	−0.202321	−	0.202321i
$448$	6.68715	−	0.112791i	0.315938	−	0.00532886i
$449$		−	30.2361i		−	1.42693i	−0.700692	−	0.713464i	$-0.747125\pi$
$449$		−	30.2361i		−	1.42693i	0.700692	−	0.713464i	$-0.252875\pi$
$450$		0			0
$451$			2.67224i			0.125831i
$452$	−6.07766	+	6.07766i	−0.285869	+	0.285869i
$453$	−0.952532	+	0.952532i	−0.0447539	+	0.0447539i
$454$	−54.9474			−2.57881
$455$		0			0
$456$	−1.10333			−0.0516680
$457$	1.72461	−	1.72461i	0.0806739	−	0.0806739i	−0.665618	−	0.746292i	$-0.731832\pi$
$457$	1.72461	−	1.72461i	0.0806739	−	0.0806739i	0.746292	+	0.665618i	$0.231832\pi$
$458$	−14.0564	+	14.0564i	−0.656811	+	0.656811i
$459$		−	7.56231i		−	0.352978i
$460$		0			0
$461$		−	8.84249i		−	0.411836i	−0.978569	−	0.205918i	$-0.933982\pi$
$461$		−	8.84249i		−	0.411836i	0.978569	−	0.205918i	$-0.0660180\pi$
$462$	1.35007	−	0.0227714i	0.0628111	−	0.00105942i
$463$	5.62574	+	5.62574i	0.261451	+	0.261451i	0.825643	−	0.564193i	$-0.190812\pi$
$463$	5.62574	+	5.62574i	0.261451	+	0.261451i	−0.564193	+	0.825643i	$0.690812\pi$
$464$		−	22.8541i		−	1.06098i
$465$		0			0
$466$	28.1591			1.30444
$467$	10.2926	+	10.2926i	0.476283	+	0.476283i	0.903941	−	0.427658i	$-0.140661\pi$
$467$	10.2926	+	10.2926i	0.476283	+	0.476283i	−0.427658	+	0.903941i	$0.640661\pi$
$468$	14.8699	−	14.8699i	0.687362	−	0.687362i
$469$	−9.15791	−	8.85410i	−0.422873	−	0.408844i
$470$		0			0
$471$	−4.34752			−0.200323
$472$	−8.02366	−	8.02366i	−0.369319	−	0.369319i
$473$	0.803678	+	0.803678i	0.0369531	+	0.0369531i
$474$	−12.9713			−0.595793
$475$		0			0
$476$	−5.00000	−	4.83413i	−0.229175	−	0.221572i
$477$	14.8456	−	14.8456i	0.679735	−	0.679735i
$478$	25.9351	+	25.9351i	1.18624	+	1.18624i
$479$	−16.6643			−0.761410			−0.380705	−	0.924696i	$-0.624319\pi$
$479$	−16.6643			−0.761410			−0.380705	+	0.924696i	$0.624319\pi$
$480$		0			0
$481$			54.9474i			2.50539i
$482$	23.8175	+	23.8175i	1.08486	+	1.08486i
$483$	0.178849	+	10.6036i	0.00813792	+	0.482481i
$484$			15.0000i			0.681818i
$485$		0			0
$486$			27.9841i			1.26938i
$487$	21.2303	−	21.2303i	0.962036	−	0.962036i	−0.0372694	−	0.999305i	$-0.511866\pi$
$487$	21.2303	−	21.2303i	0.962036	−	0.962036i	0.999305	+	0.0372694i	$0.0118660\pi$
$488$	10.8349	−	10.8349i	0.490474	−	0.490474i
$489$	−1.33612			−0.0604215
$490$		0			0
$491$	11.7639			0.530899			0.265449	−	0.964125i	$-0.414480\pi$
$491$	11.7639			0.530899			0.265449	+	0.964125i	$0.414480\pi$
$492$	4.96700	−	4.96700i	0.223930	−	0.223930i
$493$	−6.33252	+	6.33252i	−0.285202	+	0.285202i
$494$			15.1246i			0.680488i
$495$		0			0
$496$		−	44.4534i		−	1.99602i
$497$	0.278247	+	16.4967i	0.0124811	+	0.739980i
$498$	−5.12904	−	5.12904i	−0.229838	−	0.229838i
$499$		−	19.9787i		−	0.894370i	−0.894441	−	0.447185i	$-0.852427\pi$
$499$		−	19.9787i		−	0.894370i	0.894441	−	0.447185i	$-0.147573\pi$
$500$		0			0
$501$	−1.58359			−0.0707497
$502$	−8.43382	−	8.43382i	−0.376420	−	0.376420i
$503$	26.4612	−	26.4612i	1.17984	−	1.17984i	0.200061	−	0.979783i	$-0.435886\pi$
$503$	26.4612	−	26.4612i	1.17984	−	1.17984i	0.979783	−	0.200061i	$-0.0641140\pi$
$504$	−5.34448	−	5.16718i	−0.238062	−	0.230165i
$505$		0			0
$506$	3.87539			0.172282
$507$	−12.7863	−	12.7863i	−0.567860	−	0.567860i
$508$	8.72320	+	8.72320i	0.387029	+	0.387029i
$509$	37.7728			1.67425			0.837125	−	0.547011i	$-0.184235\pi$
$509$	37.7728			1.67425			0.837125	+	0.547011i	$0.184235\pi$
$510$		0			0
$511$	−27.3607	−	26.4530i	−1.21037	−	1.17021i
$512$	15.0354	−	15.0354i	0.664476	−	0.664476i
$513$	−3.75620	−	3.75620i	−0.165840	−	0.165840i
$514$	10.6890			0.471470
$515$		0			0
$516$		−	2.98766i		−	0.131524i
$517$	1.27004	+	1.27004i	0.0558564	+	0.0558564i
$518$	−43.4276	+	0.732484i	−1.90810	+	0.0321835i
$519$		−	1.58359i		−	0.0695120i
$520$		0			0
$521$		−	8.13720i		−	0.356497i	−0.983985	−	0.178249i	$-0.942957\pi$
$521$		−	8.13720i		−	0.356497i	0.983985	−	0.178249i	$-0.0570431\pi$
$522$	15.1355	−	15.1355i	0.662464	−	0.662464i
$523$	−15.6262	+	15.6262i	−0.683287	+	0.683287i	−0.960739	−	0.277452i	$-0.910510\pi$
$523$	−15.6262	+	15.6262i	−0.683287	+	0.683287i	0.277452	+	0.960739i	$0.410510\pi$
$524$	−24.1706			−1.05590
$525$		0			0
$526$	42.1803			1.83915
$527$	−12.3174	+	12.3174i	−0.536553	+	0.536553i
$528$	0.952532	−	0.952532i	0.0414536	−	0.0414536i
$529$			7.43769i			0.323378i
$530$		0			0
$531$		−	24.6810i		−	1.07106i
$532$	−4.88461	+	0.0823878i	−0.211775	+	0.00357196i
$533$	30.4502	+	30.4502i	1.31894	+	1.31894i
$534$		−	1.10333i		−	0.0477456i
$535$		0			0
$536$	−5.47214			−0.236360
$537$	−8.23758	−	8.23758i	−0.355478	−	0.355478i
$538$	−24.8913	+	24.8913i	−1.07314	+	1.07314i
$539$	−2.67224	+	0.0901699i	−0.115102	+	0.00388389i
$540$		0			0
$541$	−20.2705			−0.871497			−0.435749	−	0.900068i	$-0.643516\pi$
$541$	−20.2705			−0.871497			−0.435749	+	0.900068i	$0.643516\pi$
$542$	−15.7938	−	15.7938i	−0.678403	−	0.678403i
$543$	10.9445	+	10.9445i	0.469674	+	0.469674i
$544$	−12.6559			−0.542618
$545$		0			0
$546$	15.1246	−	15.6436i	0.647274	−	0.669483i
$547$	20.5439	−	20.5439i	0.878392	−	0.878392i	−0.114976	−	0.993368i	$-0.536679\pi$
$547$	20.5439	−	20.5439i	0.878392	−	0.878392i	0.993368	+	0.114976i	$0.0366792\pi$
$548$	−6.92612	−	6.92612i	−0.295869	−	0.295869i
$549$	33.3286			1.42243
$550$		0			0
$551$			6.29073i			0.267994i
$552$	3.22143	+	3.22143i	0.137113	+	0.137113i
$553$	25.6818	−	0.433170i	1.09210	−	0.0184203i
$554$			11.4377i			0.485941i
$555$		0			0
$556$			4.83413i			0.205013i
$557$	−10.3306	+	10.3306i	−0.437720	+	0.437720i	−0.891244	−	0.453524i	$-0.850167\pi$
$557$	−10.3306	+	10.3306i	−0.437720	+	0.437720i	0.453524	+	0.891244i	$0.350167\pi$
$558$	29.4400	−	29.4400i	1.24630	−	1.24630i
$559$	18.3158			0.774676
$560$		0			0
$561$	−0.527864			−0.0222864
$562$	−27.4700	+	27.4700i	−1.15875	+	1.15875i
$563$	3.52125	−	3.52125i	0.148403	−	0.148403i	−0.629001	−	0.777404i	$-0.716536\pi$
$563$	3.52125	−	3.52125i	0.148403	−	0.148403i	0.777404	+	0.629001i	$0.216536\pi$
$564$		−	4.72136i		−	0.198805i
$565$		0			0
$566$		−	41.7812i		−	1.75619i
$567$	−0.202029	−	11.9779i	−0.00848441	−	0.503024i
$568$	5.01179	+	5.01179i	0.210290	+	0.210290i
$569$			41.5967i			1.74383i	0.489660	+	0.871913i	$0.337121\pi$
$569$			41.5967i			1.74383i	−0.489660	+	0.871913i	$0.662879\pi$
$570$		0			0
$571$	−26.5279			−1.11016			−0.555078	−	0.831798i	$-0.687312\pi$
$571$	−26.5279			−1.11016			−0.555078	+	0.831798i	$0.687312\pi$
$572$	−2.29753	−	2.29753i	−0.0960645	−	0.0960645i
$573$	−0.663651	+	0.663651i	−0.0277244	+	0.0277244i
$574$	−23.6603	+	24.4721i	−0.987562	+	1.02145i
$575$		0			0
$576$	6.24922			0.260384
$577$	5.25871	+	5.25871i	0.218923	+	0.218923i	0.808044	−	0.589122i	$-0.200526\pi$
$577$	5.25871	+	5.25871i	0.218923	+	0.218923i	−0.589122	+	0.808044i	$0.700526\pi$
$578$	−17.4016	−	17.4016i	−0.723812	−	0.723812i
$579$	14.8178			0.615807
$580$		0			0
$581$	10.3262	+	9.98367i	0.428405	+	0.414193i
$582$	5.81547	−	5.81547i	0.241059	−	0.241059i
$583$	−2.29378	−	2.29378i	−0.0949986	−	0.0949986i
$584$	−16.3489			−0.676521
$585$		0			0
$586$		−	5.97531i		−	0.246838i
$587$	12.4688	+	12.4688i	0.514643	+	0.514643i	0.915945	−	0.401303i	$-0.131442\pi$
$587$	12.4688	+	12.4688i	0.514643	+	0.514643i	−0.401303	+	0.915945i	$0.631442\pi$
$588$	5.13460	+	4.79940i	0.211748	+	0.197924i
$589$			12.2361i			0.504178i
$590$		0			0
$591$		−	6.17025i		−	0.253810i
$592$	−30.6399	+	30.6399i	−1.25929	+	1.25929i
$593$	21.2774	−	21.2774i	0.873758	−	0.873758i	−0.119122	−	0.992880i	$-0.538008\pi$
$593$	21.2774	−	21.2774i	0.873758	−	0.873758i	0.992880	+	0.119122i	$0.0380079\pi$
$594$	2.79272			0.114587
$595$		0			0
$596$	−11.5066			−0.471328
$597$	−7.87474	+	7.87474i	−0.322291	+	0.322291i
$598$	44.1600	−	44.1600i	1.80584	−	1.80584i
$599$			1.79837i			0.0734796i	0.999325	+	0.0367398i	$0.0116973\pi$
$599$			1.79837i			0.0734796i	−0.999325	+	0.0367398i	$0.988303\pi$
$600$		0			0
$601$			6.99602i			0.285374i	0.989768	+	0.142687i	$0.0455742\pi$
$601$			6.99602i			0.285374i	−0.989768	+	0.142687i	$0.954426\pi$
$602$	0.244161	+	14.4759i	0.00995127	+	0.589992i
$603$	−8.41622	−	8.41622i	−0.342735	−	0.342735i
$604$			2.56231i			0.104259i
$605$		0			0
$606$	1.78522			0.0725195
$607$	−21.8375	−	21.8375i	−0.886355	−	0.886355i	0.107816	−	0.994171i	$-0.465614\pi$
$607$	−21.8375	−	21.8375i	−0.886355	−	0.886355i	−0.994171	+	0.107816i	$0.965614\pi$
$608$	−6.28620	+	6.28620i	−0.254939	+	0.254939i
$609$	6.29073	−	6.50658i	0.254913	−	0.263660i
$610$		0			0
$611$	28.9443			1.17096
$612$	−4.59506	−	4.59506i	−0.185744	−	0.185744i
$613$	16.2185	+	16.2185i	0.655059	+	0.655059i	0.954207	−	0.299148i	$-0.0967024\pi$
$613$	16.2185	+	16.2185i	0.655059	+	0.655059i	−0.299148	+	0.954207i	$0.596702\pi$
$614$	1.53106			0.0617885
$615$		0			0
$616$	−0.798374	+	0.825768i	−0.0321674	+	0.0332711i
$617$	−15.0354	+	15.0354i	−0.605301	+	0.605301i	−0.941714	−	0.336413i	$-0.890786\pi$
$617$	−15.0354	+	15.0354i	−0.605301	+	0.605301i	0.336413	+	0.941714i	$0.390786\pi$
$618$	2.05927	+	2.05927i	0.0828359	+	0.0828359i
$619$	24.4861			0.984178			0.492089	−	0.870545i	$-0.336233\pi$
$619$	24.4861			0.984178			0.492089	+	0.870545i	$0.336233\pi$
$620$		0			0
$621$			21.9343i			0.880193i
$622$	−9.09747	−	9.09747i	−0.364775	−	0.364775i
$623$	0.0368449	+	2.18447i	0.00147616	+	0.0875188i
$624$		−	21.7082i		−	0.869024i
$625$		0			0
$626$			43.3122i			1.73110i
$627$	−0.262190	+	0.262190i	−0.0104709	+	0.0104709i
$628$	−5.84741	+	5.84741i	−0.233337	+	0.233337i
$629$	16.9797			0.677025
$630$		0			0
$631$	1.23607			0.0492071			0.0246035	−	0.999697i	$-0.492168\pi$
$631$	1.23607			0.0492071			0.0246035	+	0.999697i	$0.492168\pi$
$632$	7.80227	−	7.80227i	0.310358	−	0.310358i
$633$	−6.40747	+	6.40747i	−0.254674	+	0.254674i
$634$		−	61.6738i		−	2.44938i
$635$		0			0
$636$			8.52708i			0.338121i
$637$	−29.4227	+	31.4777i	−1.16577	+	1.24719i
$638$	−2.33857	−	2.33857i	−0.0925847	−	0.0925847i
$639$			15.4164i			0.609864i
$640$		0			0
$641$	−12.5066			−0.493980			−0.246990	−	0.969018i	$-0.579442\pi$
$641$	−12.5066			−0.493980			−0.246990	+	0.969018i	$0.579442\pi$
$642$	−11.4986	−	11.4986i	−0.453813	−	0.453813i
$643$	29.5899	−	29.5899i	1.16691	−	1.16691i	0.183984	−	0.982929i	$-0.441101\pi$
$643$	29.5899	−	29.5899i	1.16691	−	1.16691i	0.982929	−	0.183984i	$-0.0588994\pi$
$644$	14.5024	+	14.0213i	0.571474	+	0.552516i
$645$		0			0
$646$	4.67376			0.183887
$647$	27.4600	+	27.4600i	1.07956	+	1.07956i	0.996548	+	0.0830161i	$0.0264553\pi$
$647$	27.4600	+	27.4600i	1.07956	+	1.07956i	0.0830161	+	0.996548i	$0.473545\pi$
$648$	−3.63894	−	3.63894i	−0.142951	−	0.142951i
$649$	−3.81342			−0.149690
$650$		0			0
$651$	12.2361	−	12.6559i	0.479569	−	0.496024i
$652$	−1.79708	+	1.79708i	−0.0703790	+	0.0703790i
$653$	10.3306	+	10.3306i	0.404266	+	0.404266i	0.879733	−	0.475467i	$-0.157721\pi$
$653$	10.3306	+	10.3306i	0.404266	+	0.404266i	−0.475467	+	0.879733i	$0.657721\pi$
$654$	9.35284			0.365725
$655$		0			0
$656$			33.9594i			1.32589i
$657$	−25.1448	−	25.1448i	−0.980991	−	0.980991i
$658$	0.385845	+	22.8760i	0.0150418	+	0.891800i
$659$			35.4721i			1.38180i	0.722951	+	0.690899i	$0.242785\pi$
$659$			35.4721i			1.38180i	−0.722951	+	0.690899i	$0.757215\pi$
$660$		0			0
$661$		−	6.17025i		−	0.239995i	−0.992774	−	0.119997i	$-0.961711\pi$
$661$		−	6.17025i		−	0.239995i	0.992774	−	0.119997i	$-0.0382886\pi$
$662$	36.5002	−	36.5002i	1.41862	−	1.41862i
$663$	−6.01501	+	6.01501i	−0.233604	+	0.233604i
$664$	6.17025			0.239452
$665$		0			0
$666$	−40.5836			−1.57258
$667$	18.3673	−	18.3673i	0.711186	−	0.711186i
$668$	−2.12993	+	2.12993i	−0.0824093	+	0.0824093i
$669$			6.70820i			0.259354i
$670$		0			0
$671$		−	5.14955i		−	0.198796i
$672$	12.7881	−	0.215694i	0.493311	−	0.00832058i
$673$	−8.22650	−	8.22650i	−0.317108	−	0.317108i	0.530547	−	0.847655i	$-0.321987\pi$
$673$	−8.22650	−	8.22650i	−0.317108	−	0.317108i	−0.847655	+	0.530547i	$0.821987\pi$
$674$			0.304952i			0.0117463i
$675$		0			0
$676$	−34.3951			−1.32289
$677$	12.5438	+	12.5438i	0.482096	+	0.482096i	0.905800	−	0.423705i	$-0.139271\pi$
$677$	12.5438	+	12.5438i	0.482096	+	0.482096i	−0.423705	+	0.905800i	$0.639271\pi$
$678$	−5.87604	+	5.87604i	−0.225668	+	0.225668i
$679$	−11.3198	+	11.7082i	−0.434414	+	0.449320i
$680$		0			0
$681$	−21.7082			−0.831860
$682$	−4.54873	−	4.54873i	−0.174180	−	0.174180i
$683$	9.71660	+	9.71660i	0.371795	+	0.371795i	0.868131	−	0.496335i	$-0.165321\pi$
$683$	9.71660	+	9.71660i	0.371795	+	0.371795i	−0.496335	+	0.868131i	$0.665321\pi$
$684$	−4.56473			−0.174537
$685$		0			0
$686$	−25.2705	−	22.8345i	−0.964833	−	0.871826i
$687$	−5.55328	+	5.55328i	−0.211871	+	0.211871i
$688$	10.2133	+	10.2133i	0.389378	+	0.389378i
$689$	−52.2752			−1.99153
$690$		0			0
$691$			39.1089i			1.48777i	0.668305	+	0.743887i	$0.267020\pi$
$691$			39.1089i			1.48777i	−0.668305	+	0.743887i	$0.732980\pi$
$692$	−2.12993	−	2.12993i	−0.0809677	−	0.0809677i
$693$	−2.49795	+	0.0421325i	−0.0948894	+	0.00160048i
$694$		−	50.5410i		−	1.91851i
$695$		0			0
$696$		−	3.88788i		−	0.147370i
$697$	9.40962	−	9.40962i	0.356415	−	0.356415i
$698$	43.7499	−	43.7499i	1.65596	−	1.65596i
$699$	11.1249			0.420781
$700$		0			0
$701$	−20.7639			−0.784243			−0.392121	−	0.919913i	$-0.628259\pi$
$701$	−20.7639			−0.784243			−0.392121	+	0.919913i	$0.628259\pi$
$702$	31.8230	−	31.8230i	1.20108	−	1.20108i
$703$	8.43382	−	8.43382i	0.318087	−	0.318087i
$704$		−	0.965558i		−	0.0363908i
$705$		0			0
$706$			11.0044i			0.414155i
$707$	−3.53454	+	0.0596164i	−0.132930	+	0.00224210i
$708$	7.08817	+	7.08817i	0.266390	+	0.266390i
$709$			28.6869i			1.07736i	0.842511	+	0.538680i	$0.181077\pi$
$709$			28.6869i			1.07736i	−0.842511	+	0.538680i	$0.818923\pi$
$710$		0			0
$711$	24.0000			0.900070
$712$	0.663651	+	0.663651i	0.0248714	+	0.0248714i
$713$	35.7262	−	35.7262i	1.33796	−	1.33796i
$714$	−4.83413	−	4.67376i	−0.180913	−	0.174911i
$715$		0			0
$716$	−22.1591			−0.828123
$717$	10.2462	+	10.2462i	0.382653	+	0.382653i
$718$	11.3240	+	11.3240i	0.422606	+	0.422606i
$719$	18.6312			0.694828			0.347414	−	0.937712i	$-0.387060\pi$
$719$	18.6312			0.694828			0.347414	+	0.937712i	$0.387060\pi$
$720$		0			0
$721$	−4.14590	−	4.00836i	−0.154401	−	0.149279i
$722$	−22.3857	+	22.3857i	−0.833110	+	0.833110i
$723$	9.40962	+	9.40962i	0.349948	+	0.349948i
$724$	29.4407			1.09415
$725$		0			0
$726$			14.5024i			0.538234i
$727$	22.2763	+	22.2763i	0.826180	+	0.826180i	0.986986	−	0.160806i	$-0.0514092\pi$
$727$	22.2763	+	22.2763i	0.826180	+	0.826180i	−0.160806	+	0.986986i	$0.551409\pi$
$728$	0.312155	+	18.5071i	0.0115692	+	0.685918i
$729$		−	2.52786i		−	0.0936246i
$730$		0			0
$731$		−	5.65990i		−	0.209339i
$732$	−9.57167	+	9.57167i	−0.353779	+	0.353779i
$733$	−15.0662	+	15.0662i	−0.556481	+	0.556481i	−0.928304	−	0.371823i	$-0.878733\pi$
$733$	−15.0662	+	15.0662i	−0.556481	+	0.556481i	0.371823	+	0.928304i	$0.378733\pi$
$734$	−21.1085			−0.779130
$735$		0			0
$736$	36.7082			1.35308
$737$	−1.30038	+	1.30038i	−0.0479000	+	0.0479000i
$738$	−22.4902	+	22.4902i	−0.827875	+	0.827875i
$739$		−	9.58359i		−	0.352538i	−0.984342	−	0.176269i	$-0.943597\pi$
$739$		−	9.58359i		−	0.352538i	0.984342	−	0.176269i	$-0.0564029\pi$
$740$		0			0
$741$			5.97531i			0.219509i
$742$	−0.696861	−	41.3156i	−0.0255826	−	1.51674i
$743$	17.5189	+	17.5189i	0.642705	+	0.642705i	0.951220	−	0.308515i	$-0.0998319\pi$
$743$	17.5189	+	17.5189i	0.642705	+	0.642705i	−0.308515	+	0.951220i	$0.599832\pi$
$744$		−	7.56231i		−	0.277248i
$745$		0			0
$746$	31.0476			1.13673
$747$	9.48993	+	9.48993i	0.347219	+	0.347219i
$748$	−0.709976	+	0.709976i	−0.0259593	+	0.0259593i
$749$	23.1499	+	22.3820i	0.845881	+	0.817819i
$750$		0			0
$751$	9.96556			0.363648			0.181824	−	0.983331i	$-0.441800\pi$
$751$	9.96556			0.363648			0.181824	+	0.983331i	$0.441800\pi$
$752$	16.1400	+	16.1400i	0.588564	+	0.588564i
$753$	−3.33197	−	3.33197i	−0.121424	−	0.121424i
$754$	−53.2959			−1.94092
$755$		0			0
$756$	10.4508	+	10.1042i	0.380094	+	0.367484i
$757$	−28.4634	+	28.4634i	−1.03452	+	1.03452i	−0.0351367	+	0.999383i	$0.511187\pi$
$757$	−28.4634	+	28.4634i	−1.03452	+	1.03452i	−0.999383	+	0.0351367i	$0.988813\pi$
$758$	30.8296	+	30.8296i	1.11978	+	1.11978i
$759$	1.53106			0.0555739
$760$		0			0
$761$			48.4618i			1.75674i	0.477983	+	0.878369i	$0.341368\pi$
$761$			48.4618i			1.75674i	−0.477983	+	0.878369i	$0.658632\pi$
$762$	8.43382	+	8.43382i	0.305525	+	0.305525i
$763$	−18.5176	+	0.312333i	−0.670383	+	0.0113072i
$764$			1.78522i			0.0645869i
$765$		0			0
$766$			45.7895i			1.65444i
$767$	−43.4540	+	43.4540i	−1.56903	+	1.56903i
$768$	10.7777	−	10.7777i	0.388906	−	0.388906i
$769$	27.9841			1.00913			0.504566	−	0.863373i	$-0.331653\pi$
$769$	27.9841			1.00913			0.504566	+	0.863373i	$0.331653\pi$
$770$		0			0
$771$	4.22291			0.152084
$772$	19.9299	−	19.9299i	0.717293	−	0.717293i
$773$	−18.8763	+	18.8763i	−0.678933	+	0.678933i	−0.959759	−	0.280826i	$-0.909392\pi$
$773$	−18.8763	+	18.8763i	−0.678933	+	0.678933i	0.280826	+	0.959759i	$0.409392\pi$
$774$			13.5279i			0.486249i
$775$		0			0
$776$			6.99602i			0.251142i
$777$	−17.1570	+	0.289384i	−0.615505	+	0.0103816i
$778$	29.7190	+	29.7190i	1.06548	+	1.06548i
$779$		−	9.34752i		−	0.334910i
$780$		0			0
$781$	2.38197			0.0852334
$782$	−13.6462	−	13.6462i	−0.487987	−	0.487987i
$783$	13.2360	−	13.2360i	0.473018	−	0.473018i
$784$	−33.9594	+	1.14590i	−1.21284	+	0.0409249i
$785$		0			0
$786$	−23.3688			−0.833538
$787$	4.67001	+	4.67001i	0.166468	+	0.166468i	0.785425	−	0.618957i	$-0.212444\pi$
$787$	4.67001	+	4.67001i	0.166468	+	0.166468i	−0.618957	+	0.785425i	$0.712444\pi$
$788$	−8.29897	−	8.29897i	−0.295639	−	0.295639i
$789$	16.6643			0.593264
$790$		0			0
$791$	11.4377	−	11.8301i	0.406678	−	0.420632i
$792$	−0.758890	+	0.758890i	−0.0269660	+	0.0269660i
$793$	−58.6791	−	58.6791i	−2.08375	−	2.08375i
$794$	−27.5942			−0.979281
$795$		0			0
$796$			21.1830i			0.750811i
$797$	−5.77245	−	5.77245i	−0.204471	−	0.204471i	0.597442	−	0.801912i	$-0.296184\pi$
$797$	−5.77245	−	5.77245i	−0.204471	−	0.204471i	−0.801912	+	0.597442i	$0.796184\pi$
$798$	−4.72257	+	0.0796547i	−0.167177	+	0.00281974i
$799$		−	8.94427i		−	0.316426i
$800$		0			0
$801$			2.04141i			0.0721297i
$802$	27.3527	−	27.3527i	0.965858	−	0.965858i
$803$	−3.88508	+	3.88508i	−0.137102	+	0.137102i
$804$	4.83413			0.170487
$805$		0			0
$806$	−103.666			−3.65147
$807$	−9.83386	+	9.83386i	−0.346168	+	0.346168i
$808$	−1.07381	+	1.07381i	−0.0377765	+	0.0377765i
$809$		−	34.3050i		−	1.20610i	−0.797704	−	0.603049i	$-0.793952\pi$
$809$		−	34.3050i		−	1.20610i	0.797704	−	0.603049i	$-0.206048\pi$
$810$		0			0
$811$		−	40.1296i		−	1.40914i	−0.709633	−	0.704571i	$-0.751139\pi$
$811$		−	40.1296i		−	1.40914i	0.709633	−	0.704571i	$-0.248861\pi$
$812$	−0.290317	−	17.2123i	−0.0101881	−	0.604035i
$813$	−6.23970	−	6.23970i	−0.218836	−	0.218836i
$814$			6.27051i			0.219781i
$815$		0			0
$816$	−6.70820			−0.234834
$817$	−2.81127	−	2.81127i	−0.0983540	−	0.0983540i
$818$	−15.7938	+	15.7938i	−0.552218	+	0.552218i
$819$	−27.9841	+	28.9443i	−0.977843	+	1.01139i
$820$		0			0
$821$	−12.9230			−0.451015			−0.225508	−	0.974241i	$-0.572404\pi$
$821$	−12.9230			−0.451015			−0.225508	+	0.974241i	$0.572404\pi$
$822$	−6.69636	−	6.69636i	−0.233562	−	0.233562i
$823$	−1.22791	−	1.22791i	−0.0428023	−	0.0428023i	0.685382	−	0.728184i	$-0.259635\pi$
$823$	−1.22791	−	1.22791i	−0.0428023	−	0.0428023i	−0.728184	+	0.685382i	$0.759635\pi$
$824$	−2.47730			−0.0863010
$825$		0			0
$826$	−34.9230	−	33.7644i	−1.21513	−	1.17482i
$827$	−8.10925	+	8.10925i	−0.281986	+	0.281986i	−0.833901	−	0.551915i	$-0.813897\pi$
$827$	−8.10925	+	8.10925i	−0.281986	+	0.281986i	0.551915	+	0.833901i	$0.313897\pi$
$828$	13.3279	+	13.3279i	0.463175	+	0.463175i
$829$	7.31143			0.253937			0.126968	−	0.991907i	$-0.459475\pi$
$829$	7.31143			0.253937			0.126968	+	0.991907i	$0.459475\pi$
$830$		0			0
$831$			4.51871i			0.156752i
$832$	−11.0025	−	11.0025i	−0.381444	−	0.381444i
$833$	9.72713	+	9.09211i	0.337025	+	0.315023i
$834$			4.67376i			0.161839i
$835$		0			0
$836$			0.705290i			0.0243930i
$837$	25.7454	−	25.7454i	0.889890	−	0.889890i
$838$	10.1713	−	10.1713i	0.351361	−	0.351361i
$839$	36.6316			1.26466			0.632332	−	0.774697i	$-0.282098\pi$
$839$	36.6316			1.26466			0.632332	+	0.774697i	$0.282098\pi$
$840$		0			0
$841$	6.83282			0.235614
$842$	−29.5292	+	29.5292i	−1.01765	+	1.01765i
$843$	−10.8526	+	10.8526i	−0.373784	+	0.373784i
$844$			17.2361i			0.593290i
$845$		0			0
$846$			21.3779i			0.734988i
$847$	−0.484299	−	28.7132i	−0.0166407	−	0.986596i
$848$	−29.1498	−	29.1498i	−1.00101	−	1.00101i
$849$		−	16.5066i		−	0.566504i
$850$		0			0
$851$	−49.2492			−1.68824
$852$	−4.42746	−	4.42746i	−0.151682	−	0.151682i
$853$	−6.18261	+	6.18261i	−0.211689	+	0.211689i	−0.804984	−	0.593296i	$-0.797826\pi$
$853$	−6.18261	+	6.18261i	−0.211689	+	0.211689i	0.593296	+	0.804984i	$0.297826\pi$
$854$	45.5946	−	47.1591i	1.56021	−	1.61375i
$855$		0			0
$856$	13.8328			0.472796
$857$	19.4650	+	19.4650i	0.664911	+	0.664911i	0.956534	−	0.291622i	$-0.0941951\pi$
$857$	19.4650	+	19.4650i	0.664911	+	0.664911i	−0.291622	+	0.956534i	$0.594195\pi$
$858$	−2.22131	−	2.22131i	−0.0758343	−	0.0758343i
$859$	−31.7975			−1.08492			−0.542458	−	0.840083i	$-0.682506\pi$
$859$	−31.7975			−1.08492			−0.542458	+	0.840083i	$0.682506\pi$
$860$		0			0
$861$	−9.34752	+	9.66826i	−0.318563	+	0.329493i
$862$	50.4973	−	50.4973i	1.71995	−	1.71995i
$863$	6.80887	+	6.80887i	0.231777	+	0.231777i	0.813434	−	0.581657i	$-0.197596\pi$
$863$	6.80887	+	6.80887i	0.231777	+	0.231777i	−0.581657	+	0.813434i	$0.697596\pi$
$864$	26.4530			0.899950
$865$		0			0
$866$			37.7728i			1.28357i
$867$	−6.87489	−	6.87489i	−0.233484	−	0.233484i
$868$	−0.564694	−	33.4796i	−0.0191670	−	1.13637i
$869$		−	3.70820i		−	0.125792i
$870$		0			0
$871$			29.6356i			1.00416i
$872$	−5.62574	+	5.62574i	−0.190512	+	0.190512i
$873$	−10.7600	+	10.7600i	−0.364170	+	0.364170i
$874$	−13.5561			−0.458543
$875$		0			0
$876$	14.4427			0.487974
$877$	−0.803678	+	0.803678i	−0.0271383	+	0.0271383i	−0.720546	−	0.693407i	$-0.756109\pi$
$877$	−0.803678	+	0.803678i	−0.0271383	+	0.0271383i	0.693407	+	0.720546i	$0.256109\pi$
$878$	−19.6789	+	19.6789i	−0.664131	+	0.664131i
$879$		−	2.36068i		−	0.0796238i
$880$		0			0
$881$		−	32.1129i		−	1.08191i	−0.841051	−	0.540956i	$-0.818063\pi$
$881$		−	32.1129i		−	1.08191i	0.841051	−	0.540956i	$-0.181937\pi$
$882$	−23.2491	−	21.7313i	−0.782837	−	0.731731i
$883$	−20.9958	−	20.9958i	−0.706564	−	0.706564i	0.259247	−	0.965811i	$-0.416526\pi$
$883$	−20.9958	−	20.9958i	−0.706564	−	0.706564i	−0.965811	+	0.259247i	$0.916526\pi$
$884$			16.1803i			0.544204i
$885$		0			0
$886$	−40.0902			−1.34686
$887$	41.1062	+	41.1062i	1.38021	+	1.38021i	0.844229	+	0.535982i	$0.180059\pi$
$887$	41.1062	+	41.1062i	1.38021	+	1.38021i	0.535982	+	0.844229i	$0.319941\pi$
$888$	−5.21239	+	5.21239i	−0.174916	+	0.174916i
$889$	−16.9797	−	16.4164i	−0.569481	−	0.550589i
$890$		0			0
$891$	−1.72949			−0.0579401
$892$	9.02251	+	9.02251i	0.302096	+	0.302096i
$893$	−4.44262	−	4.44262i	−0.148667	−	0.148667i
$894$	−11.1249			−0.372071
$895$		0			0
$896$	−15.9230	+	16.4693i	−0.531950	+	0.550202i
$897$	17.4464	−	17.4464i	0.582518	−	0.582518i
$898$	−39.3183	−	39.3183i	−1.31207	−	1.31207i
$899$	−43.1173			−1.43804
$900$		0			0
$901$			16.1539i			0.538165i
$902$	3.47492	+	3.47492i	0.115702	+	0.115702i
$903$	0.0964613	+	5.71901i	0.00321003	+	0.190317i
$904$		−	7.06888i		−	0.235108i
$905$		0			0
$906$			2.47730i			0.0823029i
$907$	−34.4238	+	34.4238i	−1.14302	+	1.14302i	−0.155129	+	0.987894i	$0.549579\pi$
$907$	−34.4238	+	34.4238i	−1.14302	+	1.14302i	−0.987894	+	0.155129i	$0.950421\pi$
$908$	−29.1975	+	29.1975i	−0.968952	+	0.968952i
$909$	−3.30307			−0.109556
$910$		0			0
$911$	25.8328			0.855879			0.427940	−	0.903807i	$-0.359240\pi$
$911$	25.8328			0.855879			0.427940	+	0.903807i	$0.359240\pi$
$912$	−3.33197	+	3.33197i	−0.110332	+	0.110332i
$913$	1.46628	−	1.46628i	0.0485266	−	0.0485266i
$914$		−	4.48529i		−	0.148360i
$915$		0			0
$916$			14.9383i			0.493575i
$917$	46.2677	−	0.780388i	1.52790	−	0.0257707i
$918$	−9.83386	−	9.83386i	−0.324566	−	0.324566i
$919$		−	37.2705i		−	1.22944i	−0.788745	−	0.614720i	$-0.789269\pi$
$919$		−	37.2705i		−	1.22944i	0.788745	−	0.614720i	$-0.210731\pi$
$920$		0			0
$921$	0.604878			0.0199314
$922$	−11.4986	−	11.4986i	−0.378686	−	0.378686i
$923$	27.1425	−	27.1425i	0.893406	−	0.893406i
$924$	0.705290	−	0.729490i	0.0232023	−	0.0239985i
$925$		0			0
$926$	14.6312			0.480811
$927$	−3.81013	−	3.81013i	−0.125141	−	0.125141i
$928$	−22.1512	−	22.1512i	−0.727149	−	0.727149i
$929$	35.4904			1.16440			0.582202	−	0.813044i	$-0.302191\pi$
$929$	35.4904			1.16440			0.582202	+	0.813044i	$0.302191\pi$
$930$		0			0
$931$	9.34752	−	0.315415i	0.306353	−	0.0103373i
$932$	14.9629	−	14.9629i	0.490126	−	0.490126i
$933$	−3.59416	−	3.59416i	−0.117667	−	0.117667i
$934$	26.7684			0.875890
$935$		0			0
$936$			17.2951i			0.565308i
$937$	3.79243	+	3.79243i	0.123893	+	0.123893i	0.766335	−	0.642441i	$-0.222078\pi$
$937$	3.79243	+	3.79243i	0.123893	+	0.123893i	−0.642441	+	0.766335i	$0.722078\pi$
$938$	−23.4224	+	0.395061i	−0.764769	+	0.0128992i
$939$			17.1115i			0.558411i
$940$		0			0
$941$			29.8305i			0.972448i	0.873834	+	0.486224i	$0.161626\pi$
$941$			29.8305i			0.972448i	−0.873834	+	0.486224i	$0.838374\pi$
$942$	−5.65342	+	5.65342i	−0.184199	+	0.184199i
$943$	−27.2924	+	27.2924i	−0.888763	+	0.888763i
$944$	−48.4618			−1.57730
$945$		0			0
$946$	2.09017			0.0679573
$947$	−31.5161	+	31.5161i	−1.02413	+	1.02413i	−0.0244325	+	0.999701i	$0.507778\pi$
$947$	−31.5161	+	31.5161i	−1.02413	+	1.02413i	−0.999701	+	0.0244325i	$0.992222\pi$
$948$	−6.89259	+	6.89259i	−0.223861	+	0.223861i
$949$			88.5410i			2.87416i
$950$		0			0
$951$		−	24.3656i		−	0.790108i
$952$	5.71901	−	0.0964613i	0.185354	−	0.00312633i
$953$	−24.3277	−	24.3277i	−0.788053	−	0.788053i	0.193122	−	0.981175i	$-0.438139\pi$
$953$	−24.3277	−	24.3277i	−0.788053	−	0.788053i	−0.981175	+	0.193122i	$0.938139\pi$
$954$		−	38.6099i		−	1.25004i
$955$		0			0
$956$	27.5623			0.891429
$957$	−0.923902	−	0.923902i	−0.0298655	−	0.0298655i
$958$	−21.6699	+	21.6699i	−0.700121	+	0.700121i
$959$	13.4817	+	13.0344i	0.435346	+	0.420904i
$960$		0			0
$961$	−52.8673			−1.70540
$962$	71.4524	+	71.4524i	2.30372	+	2.30372i
$963$	21.2751	+	21.2751i	0.685579	+	0.685579i
$964$	25.3118			0.815239
$965$		0			0
$966$	14.0213	+	13.5561i	0.451127	+	0.436162i
$967$	13.9972	−	13.9972i	0.450119	−	0.450119i	−0.445275	−	0.895394i	$-0.646894\pi$
$967$	13.9972	−	13.9972i	0.450119	−	0.450119i	0.895394	+	0.445275i	$0.146894\pi$
$968$	−8.72320	−	8.72320i	−0.280374	−	0.280374i
$969$	1.84647			0.0593173
$970$		0			0
$971$		−	31.7975i		−	1.02043i	−0.860047	−	0.510215i	$-0.829566\pi$
$971$		−	31.7975i		−	1.02043i	0.860047	−	0.510215i	$-0.170434\pi$
$972$	14.8699	+	14.8699i	0.476953	+	0.476953i
$973$	−0.156078	−	9.25355i	−0.00500362	−	0.296655i
$974$		−	55.2148i		−	1.76920i
$975$		0			0
$976$		−	65.4415i		−	2.09473i
$977$	−24.8692	+	24.8692i	−0.795637	+	0.795637i	−0.982404	−	0.186767i	$-0.940199\pi$
$977$	−24.8692	+	24.8692i	−0.795637	+	0.795637i	0.186767	+	0.982404i	$0.440199\pi$
$978$	−1.73746	+	1.73746i	−0.0555579	+	0.0555579i
$979$	0.315415			0.0100807
$980$		0			0
$981$	−17.3050			−0.552505
$982$	15.2976	−	15.2976i	0.488165	−	0.488165i
$983$	−32.3263	+	32.3263i	−1.03105	+	1.03105i	−0.0315450	+	0.999502i	$0.510043\pi$
$983$	−32.3263	+	32.3263i	−1.03105	+	1.03105i	−0.999502	+	0.0315450i	$0.989957\pi$
$984$			5.77709i			0.184167i
$985$		0			0
$986$			16.4693i			0.524491i
$987$	0.152437	+	9.03768i	0.00485211	+	0.287673i
$988$	8.03678	+	8.03678i	0.255684	+	0.255684i
$989$			16.4164i			0.522011i
$990$		0			0
$991$	36.1591			1.14863			0.574315	−	0.818634i	$-0.305268\pi$
$991$	36.1591			1.14863			0.574315	+	0.818634i	$0.305268\pi$
$992$	−43.0862	−	43.0862i	−1.36799	−	1.36799i
$993$	14.4202	−	14.4202i	0.457611	−	0.457611i
$994$	21.8138	+	21.0902i	0.691892	+	0.668940i
$995$		0			0
$996$	−5.45085			−0.172717
$997$	15.0662	+	15.0662i	0.477150	+	0.477150i	0.904219	−	0.427069i	$-0.140454\pi$
$997$	15.0662	+	15.0662i	0.477150	+	0.477150i	−0.427069	+	0.904219i	$0.640454\pi$
$998$	−25.9799	−	25.9799i	−0.822379	−	0.822379i
$999$	−35.4904			−1.12287

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.f.b.818.6	yes	16
5.2	odd	4	inner	875.2.f.b.307.5	yes	16
5.3	odd	4	inner	875.2.f.b.307.4	yes	16
5.4	even	2	inner	875.2.f.b.818.3	yes	16
7.6	odd	2	inner	875.2.f.b.818.5	yes	16
35.13	even	4	inner	875.2.f.b.307.3	✓	16
35.27	even	4	inner	875.2.f.b.307.6	yes	16
35.34	odd	2	inner	875.2.f.b.818.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
875.2.f.b.307.3	✓	16	35.13	even	4	inner
875.2.f.b.307.4	yes	16	5.3	odd	4	inner
875.2.f.b.307.5	yes	16	5.2	odd	4	inner
875.2.f.b.307.6	yes	16	35.27	even	4	inner
875.2.f.b.818.3	yes	16	5.4	even	2	inner
875.2.f.b.818.4	yes	16	35.34	odd	2	inner
875.2.f.b.818.5	yes	16	7.6	odd	2	inner
875.2.f.b.818.6	yes	16	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30038 - 1.30038i) q^{2} +(0.513743 - 0.513743i) q^{3} -1.38197i q^{4} -1.33612i q^{6} +(0.0446190 + 2.64538i) q^{7} +(0.803678 + 0.803678i) q^{8} +2.47214i q^{9} +0.381966 q^{11} +(-0.709976 - 0.709976i) q^{12} +(4.35250 - 4.35250i) q^{13} +(3.49801 + 3.38197i) q^{14} +4.85410 q^{16} +(-1.34500 - 1.34500i) q^{17} +(3.21471 + 3.21471i) q^{18} -1.33612 q^{19} +(1.38197 + 1.33612i) q^{21} +(0.496700 - 0.496700i) q^{22} +(3.90113 + 3.90113i) q^{23} +0.825768 q^{24} -11.3198i q^{26} +(2.81127 + 2.81127i) q^{27} +(3.65582 - 0.0616619i) q^{28} -4.70820i q^{29} -9.15791i q^{31} +(4.70481 - 4.70481i) q^{32} +(0.196232 - 0.196232i) q^{33} -3.49801 q^{34} +3.41641 q^{36} +(-6.31217 + 6.31217i) q^{37} +(-1.73746 + 1.73746i) q^{38} -4.47214i q^{39} +6.99602i q^{41} +(3.53454 - 0.0596164i) q^{42} +(2.10406 + 2.10406i) q^{43} -0.527864i q^{44} +10.1459 q^{46} +(3.32502 + 3.32502i) q^{47} +(2.49376 - 2.49376i) q^{48} +(-6.99602 + 0.236068i) q^{49} -1.38197 q^{51} +(-6.01501 - 6.01501i) q^{52} +(-6.00519 - 6.00519i) q^{53} +7.31143 q^{54} +(-2.09017 + 2.16189i) q^{56} +(-0.686423 + 0.686423i) q^{57} +(-6.12244 - 6.12244i) q^{58} -9.98367 q^{59} -13.4817i q^{61} +(-11.9087 - 11.9087i) q^{62} +(-6.53973 + 0.110304i) q^{63} -2.52786i q^{64} -0.510353i q^{66} +(-3.40443 + 3.40443i) q^{67} +(-1.85874 + 1.85874i) q^{68} +4.00836 q^{69} +6.23607 q^{71} +(-1.98680 + 1.98680i) q^{72} +(-10.1713 + 10.1713i) q^{73} +16.4164i q^{74} +1.84647i q^{76} +(0.0170429 + 1.01044i) q^{77} +(-5.81547 - 5.81547i) q^{78} -9.70820i q^{79} -4.52786 q^{81} +(9.09747 + 9.09747i) q^{82} +(3.83876 - 3.83876i) q^{83} +(1.84647 - 1.90983i) q^{84} +5.47214 q^{86} +(-2.41881 - 2.41881i) q^{87} +(0.306978 + 0.306978i) q^{88} +0.825768 q^{89} +(11.7082 + 11.3198i) q^{91} +(5.39123 - 5.39123i) q^{92} +(-4.70481 - 4.70481i) q^{93} +8.64755 q^{94} -4.83413i q^{96} +(4.35250 + 4.35250i) q^{97} +(-8.79049 + 9.40445i) q^{98} +0.944272i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 24 q^{11} + 24 q^{16} + 40 q^{21} - 160 q^{36} + 216 q^{46} - 40 q^{51} + 56 q^{56} + 64 q^{71} - 144 q^{81} + 16 q^{86} + 80 q^{91}+O(q^{100}) \) 16 * q + 24 * q^11 + 24 * q^16 + 40 * q^21 - 160 * q^36 + 216 * q^46 - 40 * q^51 + 56 * q^56 + 64 * q^71 - 144 * q^81 + 16 * q^86 + 80 * q^91

Introduction

L-functions

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