LMFDB - Embedded newform 702.2.g.c.523.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(451,702)] 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("702.451"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 4 x^{10} - 6 x^{9} + 22 x^{8} - 45 x^{7} + 75 x^{6} - 135 x^{5} + 198 x^{4} + \cdots + 729 $ x^12 - 3x^11 + 4x^10 - 6x^9 + 22x^8 - 45x^7 + 75x^6 - 135x^5 + 198x^4 - 162x^3 + 324x^2 - 729*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			523.3
Root			$-1.26151 - 1.18685i$ of defining polynomial
Character	$\chi$	$=$	702.523
Dual form			702.2.g.c.451.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.102915 - 0.178255i) q^{5} -1.55915 q^{7} +1.00000 q^{8} +(0.102915 + 0.178255i) q^{10} +(-1.94430 + 3.36763i) q^{11} +(3.60290 - 0.138360i) q^{13} +(0.779577 - 1.35027i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.84139 - 3.18938i) q^{17} +(-3.72573 + 6.45316i) q^{19} -0.205831 q^{20} +(-1.94430 - 3.36763i) q^{22} -3.36930 q^{23} +(2.47882 + 4.29344i) q^{25} +(-1.68162 + 3.18938i) q^{26} +(0.779577 + 1.35027i) q^{28} +(-2.43817 + 4.22303i) q^{29} +(-1.50185 + 2.60128i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.84139 + 3.18938i) q^{34} +(-0.160461 + 0.277926i) q^{35} +(4.38086 + 7.58788i) q^{37} +(-3.72573 - 6.45316i) q^{38} +(0.102915 - 0.178255i) q^{40} +3.49292 q^{41} -0.686517 q^{43} +3.88861 q^{44} +(1.68465 - 2.91790i) q^{46} +(1.48380 + 2.57002i) q^{47} -4.56904 q^{49} -4.95763 q^{50} +(-1.92127 - 3.05102i) q^{52} -9.52297 q^{53} +(0.400197 + 0.693162i) q^{55} -1.55915 q^{56} +(-2.43817 - 4.22303i) q^{58} +(3.30029 + 5.71626i) q^{59} +5.35098 q^{61} +(-1.50185 - 2.60128i) q^{62} +1.00000 q^{64} +(0.346130 - 0.656472i) q^{65} -3.03379 q^{67} -3.68278 q^{68} +(-0.160461 - 0.277926i) q^{70} +(1.39708 - 2.41982i) q^{71} -15.3364 q^{73} -8.76173 q^{74} +7.45146 q^{76} +(3.03147 - 5.25066i) q^{77} +(0.829455 + 1.43666i) q^{79} +(0.102915 + 0.178255i) q^{80} +(-1.74646 + 3.02496i) q^{82} +(4.34020 + 7.51744i) q^{83} +(-0.379014 - 0.656472i) q^{85} +(0.343259 - 0.594541i) q^{86} +(-1.94430 + 3.36763i) q^{88} +(-6.25792 - 10.8390i) q^{89} +(-5.61747 + 0.215725i) q^{91} +(1.68465 + 2.91790i) q^{92} -2.96760 q^{94} +(0.766870 + 1.32826i) q^{95} +6.57834 q^{97} +(2.28452 - 3.95690i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} + 3 q^{5} - 2 q^{7} + 12 q^{8} + 3 q^{10} - 4 q^{11} + 4 q^{13} + q^{14} - 6 q^{16} + q^{17} + 9 q^{19} - 6 q^{20} - 4 q^{22} + 14 q^{23} - q^{25} - 5 q^{26} + q^{28} - q^{29}+ \cdots - 27 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 + 3 * q^5 - 2 * q^7 + 12 * q^8 + 3 * q^10 - 4 * q^11 + 4 * q^13 + q^14 - 6 * q^16 + q^17 + 9 * q^19 - 6 * q^20 - 4 * q^22 + 14 * q^23 - q^25 - 5 * q^26 + q^28 - q^29 + 8 * q^31 - 6 * q^32 + q^34 + 3 * q^35 + 15 * q^37 + 9 * q^38 + 3 * q^40 - 38 * q^41 + 4 * q^43 + 8 * q^44 - 7 * q^46 + 23 * q^47 + 54 * q^49 + 2 * q^50 + q^52 + 4 * q^53 + 24 * q^55 - 2 * q^56 - q^58 + 4 * q^59 + 16 * q^61 + 8 * q^62 + 12 * q^64 + 35 * q^65 - 28 * q^67 - 2 * q^68 + 3 * q^70 + 15 * q^71 - 90 * q^73 - 30 * q^74 - 18 * q^76 - 4 * q^77 - 12 * q^79 + 3 * q^80 + 19 * q^82 - 24 * q^83 + 7 * q^85 - 2 * q^86 - 4 * q^88 - 23 * q^89 + 8 * q^91 - 7 * q^92 - 46 * q^94 + 7 * q^95 + 8 * q^97 - 27 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.102915	−	0.178255i	0.0460251	−	0.0797179i	−0.842095	−	0.539329i	$-0.818678\pi$
$5$	0.102915	−	0.178255i	0.0460251	−	0.0797179i	0.888120	+	0.459611i	$0.152011\pi$
$6$		0			0
$7$	−1.55915			−0.589305			−0.294652	−	0.955605i	$-0.595204\pi$
$7$	−1.55915			−0.589305			−0.294652	+	0.955605i	$0.595204\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	0.102915	+	0.178255i	0.0325447	+	0.0563691i
$11$	−1.94430	+	3.36763i	−0.586230	+	1.01538i	0.408491	+	0.912762i	$0.366055\pi$
$11$	−1.94430	+	3.36763i	−0.586230	+	1.01538i	−0.994721	+	0.102618i	$0.967278\pi$
$12$		0			0
$13$	3.60290	−	0.138360i	0.999263	−	0.0383743i
$13$	3.60290	−	0.138360i	0.999263	−	0.0383743i
$14$	0.779577	−	1.35027i	0.208351	−	0.360874i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.84139	−	3.18938i	0.446602	−	0.773538i	−0.551560	−	0.834135i	$-0.685967\pi$
$17$	1.84139	−	3.18938i	0.446602	−	0.773538i	0.998162	+	0.0605972i	$0.0193005\pi$
$18$		0			0
$19$	−3.72573	+	6.45316i	−0.854741	+	1.48046i	0.0221435	+	0.999755i	$0.492951\pi$
$19$	−3.72573	+	6.45316i	−0.854741	+	1.48046i	−0.876885	+	0.480701i	$0.840382\pi$
$20$	−0.205831			−0.0460251
$21$		0			0
$22$	−1.94430	−	3.36763i	−0.414527	−	0.717982i
$23$	−3.36930			−0.702547			−0.351273	−	0.936273i	$-0.614251\pi$
$23$	−3.36930			−0.702547			−0.351273	+	0.936273i	$0.614251\pi$
$24$		0			0
$25$	2.47882	+	4.29344i	0.495763	+	0.858687i
$26$	−1.68162	+	3.18938i	−0.329794	+	0.625489i
$27$		0			0
$28$	0.779577	+	1.35027i	0.147326	+	0.255176i
$29$	−2.43817	+	4.22303i	−0.452756	+	0.784197i	−0.998556	−	0.0537185i	$-0.982893\pi$
$29$	−2.43817	+	4.22303i	−0.452756	+	0.784197i	0.545800	+	0.837916i	$0.316226\pi$
$30$		0			0
$31$	−1.50185	+	2.60128i	−0.269740	+	0.467204i	−0.968795	−	0.247865i	$-0.920271\pi$
$31$	−1.50185	+	2.60128i	−0.269740	+	0.467204i	0.699054	+	0.715068i	$0.253604\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	1.84139	+	3.18938i	0.315796	+	0.546974i
$35$	−0.160461	+	0.277926i	−0.0271228	+	0.0469781i
$36$		0			0
$37$	4.38086	+	7.58788i	0.720210	+	1.24744i	0.960916	+	0.276842i	$0.0892877\pi$
$37$	4.38086	+	7.58788i	0.720210	+	1.24744i	−0.240706	+	0.970598i	$0.577379\pi$
$38$	−3.72573	−	6.45316i	−0.604393	−	1.04684i
$39$		0			0
$40$	0.102915	−	0.178255i	0.0162723	−	0.0281845i
$41$	3.49292			0.545502			0.272751	−	0.962085i	$-0.412066\pi$
$41$	3.49292			0.545502			0.272751	+	0.962085i	$0.412066\pi$
$42$		0			0
$43$	−0.686517			−0.104693			−0.0523464	−	0.998629i	$-0.516670\pi$
$43$	−0.686517			−0.104693			−0.0523464	+	0.998629i	$0.516670\pi$
$44$	3.88861			0.586230
$45$		0			0
$46$	1.68465	−	2.91790i	0.248388	−	0.430220i
$47$	1.48380	+	2.57002i	0.216434	+	0.374875i	0.953715	−	0.300711i	$-0.0972239\pi$
$47$	1.48380	+	2.57002i	0.216434	+	0.374875i	−0.737281	+	0.675586i	$0.763891\pi$
$48$		0			0
$49$	−4.56904			−0.652720
$50$	−4.95763			−0.701115
$51$		0			0
$52$	−1.92127	−	3.05102i	−0.266432	−	0.423100i
$53$	−9.52297			−1.30808			−0.654041	−	0.756460i	$-0.726927\pi$
$53$	−9.52297			−1.30808			−0.654041	+	0.756460i	$0.726927\pi$
$54$		0			0
$55$	0.400197	+	0.693162i	0.0539626	+	0.0934660i
$56$	−1.55915			−0.208351
$57$		0			0
$58$	−2.43817	−	4.22303i	−0.320147	−	0.554511i
$59$	3.30029	+	5.71626i	0.429661	+	0.744194i	0.996843	−	0.0793982i	$-0.0252999\pi$
$59$	3.30029	+	5.71626i	0.429661	+	0.744194i	−0.567182	+	0.823592i	$0.691967\pi$
$60$		0			0
$61$	5.35098			0.685122			0.342561	−	0.939496i	$-0.388706\pi$
$61$	5.35098			0.685122			0.342561	+	0.939496i	$0.388706\pi$
$62$	−1.50185	−	2.60128i	−0.190735	−	0.330363i
$63$		0			0
$64$	1.00000			0.125000
$65$	0.346130	−	0.656472i	0.0429321	−	0.0814253i
$66$		0			0
$67$	−3.03379			−0.370637			−0.185318	−	0.982679i	$-0.559332\pi$
$67$	−3.03379			−0.370637			−0.185318	+	0.982679i	$0.559332\pi$
$68$	−3.68278			−0.446602
$69$		0			0
$70$	−0.160461	−	0.277926i	−0.0191787	−	0.0332186i
$71$	1.39708	−	2.41982i	0.165803	−	0.287180i	−0.771137	−	0.636669i	$-0.780312\pi$
$71$	1.39708	−	2.41982i	0.165803	−	0.287180i	0.936940	+	0.349489i	$0.113645\pi$
$72$		0			0
$73$	−15.3364			−1.79499			−0.897493	−	0.441028i	$-0.854614\pi$
$73$	−15.3364			−1.79499			−0.897493	+	0.441028i	$0.854614\pi$
$74$	−8.76173			−1.01853
$75$		0			0
$76$	7.45146			0.854741
$77$	3.03147	−	5.25066i	0.345468	−	0.598368i
$78$		0			0
$79$	0.829455	+	1.43666i	0.0933210	+	0.161637i	0.908907	−	0.417000i	$-0.136918\pi$
$79$	0.829455	+	1.43666i	0.0933210	+	0.161637i	−0.815586	+	0.578636i	$0.803585\pi$
$80$	0.102915	+	0.178255i	0.0115063	+	0.0199295i
$81$		0			0
$82$	−1.74646	+	3.02496i	−0.192864	+	0.334051i
$83$	4.34020	+	7.51744i	0.476398	+	0.825146i	0.999634	−	0.0270417i	$-0.00860869\pi$
$83$	4.34020	+	7.51744i	0.476398	+	0.825146i	−0.523236	+	0.852188i	$0.675275\pi$
$84$		0			0
$85$	−0.379014	−	0.656472i	−0.0411099	−	0.0712044i
$86$	0.343259	−	0.594541i	0.0370145	−	0.0641110i
$87$		0			0
$88$	−1.94430	+	3.36763i	−0.207264	+	0.358991i
$89$	−6.25792	−	10.8390i	−0.663339	−	1.14894i	−0.979733	−	0.200308i	$-0.935806\pi$
$89$	−6.25792	−	10.8390i	−0.663339	−	1.14894i	0.316394	−	0.948628i	$-0.397528\pi$
$90$		0			0
$91$	−5.61747	+	0.215725i	−0.588871	+	0.0226141i
$92$	1.68465	+	2.91790i	0.175637	+	0.304212i
$93$		0			0
$94$	−2.96760			−0.306084
$95$	0.766870	+	1.32826i	0.0786792	+	0.136276i
$96$		0			0
$97$	6.57834			0.667929			0.333965	−	0.942586i	$-0.391613\pi$
$97$	6.57834			0.667929			0.333965	+	0.942586i	$0.391613\pi$
$98$	2.28452	−	3.95690i	0.230771	−	0.399708i
$99$		0			0
$100$	2.47882	−	4.29344i	0.247882	−	0.429344i
$101$	5.65246	−	9.79034i	0.562440	−	0.974175i	−0.434842	−	0.900507i	$-0.643196\pi$
$101$	5.65246	−	9.79034i	0.562440	−	0.974175i	0.997283	−	0.0736686i	$-0.0234707\pi$
$102$		0			0
$103$	9.34320	−	16.1829i	0.920613	−	1.59455i	0.122144	−	0.992512i	$-0.461023\pi$
$103$	9.34320	−	16.1829i	0.920613	−	1.59455i	0.798469	−	0.602036i	$-0.205644\pi$
$104$	3.60290	−	0.138360i	0.353293	−	0.0135673i
$105$		0			0
$106$	4.76149	−	8.24714i	0.462476	−	0.801033i
$107$	5.71380	+	9.89659i	0.552374	+	0.956739i	0.998103	+	0.0615712i	$0.0196111\pi$
$107$	5.71380	+	9.89659i	0.552374	+	0.956739i	−0.445729	+	0.895168i	$0.647056\pi$
$108$		0			0
$109$	−6.39848			−0.612863			−0.306432	−	0.951893i	$-0.599135\pi$
$109$	−6.39848			−0.612863			−0.306432	+	0.951893i	$0.599135\pi$
$110$	−0.800395			−0.0763147
$111$		0			0
$112$	0.779577	−	1.35027i	0.0736631	−	0.127588i
$113$	6.48841	+	11.2383i	0.610378	+	1.05721i	0.991177	+	0.132548i	$0.0423159\pi$
$113$	6.48841	+	11.2383i	0.610378	+	1.05721i	−0.380798	+	0.924658i	$0.624351\pi$
$114$		0			0
$115$	−0.346752	+	0.600592i	−0.0323348	+	0.0560055i
$116$	4.87634			0.452756
$117$		0			0
$118$	−6.60057			−0.607632
$119$	−2.87101	+	4.97273i	−0.263185	+	0.455850i
$120$		0			0
$121$	−2.06064	−	3.56913i	−0.187331	−	0.324466i
$122$	−2.67549	+	4.63408i	−0.242227	+	0.419550i
$123$		0			0
$124$	3.00370			0.269740
$125$	2.04959			0.183321
$126$		0			0
$127$	−5.60948	−	9.71591i	−0.497761	−	0.862147i	0.502236	−	0.864731i	$-0.332511\pi$
$127$	−5.60948	−	9.71591i	−0.497761	−	0.862147i	−0.999997	+	0.00258339i	$0.999178\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	0.395457	+	0.627993i	0.0346838	+	0.0550787i
$131$	−0.232322	+	0.402393i	−0.0202980	+	0.0351572i	−0.875996	−	0.482318i	$-0.839795\pi$
$131$	−0.232322	+	0.402393i	−0.0202980	+	0.0351572i	0.855698	+	0.517476i	$0.173128\pi$
$132$		0			0
$133$	5.80899	−	10.0615i	0.503703	−	0.872439i
$134$	1.51690	−	2.62734i	0.131040	−	0.226968i
$135$		0			0
$136$	1.84139	−	3.18938i	0.157898	−	0.273487i
$137$	15.3970			1.31545			0.657727	−	0.753256i	$-0.271518\pi$
$137$	15.3970			1.31545			0.657727	+	0.753256i	$0.271518\pi$
$138$		0			0
$139$	−2.40855	−	4.17173i	−0.204290	−	0.353841i	0.745616	−	0.666376i	$-0.232155\pi$
$139$	−2.40855	−	4.17173i	−0.204290	−	0.353841i	−0.949906	+	0.312534i	$0.898822\pi$
$140$	0.320922			0.0271228
$141$		0			0
$142$	1.39708	+	2.41982i	0.117241	+	0.203067i
$143$	−6.53918	+	12.4022i	−0.546834	+	1.03713i
$144$		0			0
$145$	0.501850	+	0.869229i	0.0416764	+	0.0721856i
$146$	7.66819	−	13.2817i	0.634624	−	1.09920i
$147$		0			0
$148$	4.38086	−	7.58788i	0.360105	−	0.623720i
$149$	−8.39889	−	14.5473i	−0.688064	−	1.19176i	−0.972463	−	0.233056i	$-0.925127\pi$
$149$	−8.39889	−	14.5473i	−0.688064	−	1.19176i	0.284399	−	0.958706i	$-0.408206\pi$
$150$		0			0
$151$	−0.315574	−	0.546591i	−0.0256811	−	0.0444809i	0.852899	−	0.522076i	$-0.174842\pi$
$151$	−0.315574	−	0.546591i	−0.0256811	−	0.0444809i	−0.878580	+	0.477595i	$0.841509\pi$
$152$	−3.72573	+	6.45316i	−0.302197	+	0.523420i
$153$		0			0
$154$	3.03147	+	5.25066i	0.244283	+	0.423110i
$155$	0.309127	+	0.535423i	0.0248297	+	0.0430062i
$156$		0			0
$157$	−8.62325	+	14.9359i	−0.688210	+	1.19202i	0.284206	+	0.958763i	$0.408270\pi$
$157$	−8.62325	+	14.9359i	−0.688210	+	1.19202i	−0.972416	+	0.233252i	$0.925063\pi$
$158$	−1.65891			−0.131976
$159$		0			0
$160$	−0.205831			−0.0162723
$161$	5.25325			0.414014
$162$		0			0
$163$	1.67055	−	2.89347i	0.130847	−	0.226634i	−0.793156	−	0.609018i	$-0.791564\pi$
$163$	1.67055	−	2.89347i	0.130847	−	0.226634i	0.924003	+	0.382384i	$0.124897\pi$
$164$	−1.74646	−	3.02496i	−0.136376	−	0.236209i
$165$		0			0
$166$	−8.68039			−0.673729
$167$	21.1610			1.63749			0.818744	−	0.574159i	$-0.194671\pi$
$167$	21.1610			1.63749			0.818744	+	0.574159i	$0.194671\pi$
$168$		0			0
$169$	12.9617	−	0.996996i	0.997055	−	0.0766920i
$170$	0.758029			0.0581381
$171$		0			0
$172$	0.343259	+	0.594541i	0.0261732	+	0.0453333i
$173$	22.5833			1.71698			0.858489	−	0.512832i	$-0.171404\pi$
$173$	22.5833			1.71698			0.858489	+	0.512832i	$0.171404\pi$
$174$		0			0
$175$	−3.86486	−	6.69413i	−0.292156	−	0.506029i
$176$	−1.94430	−	3.36763i	−0.146557	−	0.253845i
$177$		0			0
$178$	12.5158			0.938102
$179$	−5.40388	−	9.35979i	−0.403905	−	0.699584i	0.590289	−	0.807192i	$-0.299014\pi$
$179$	−5.40388	−	9.35979i	−0.403905	−	0.699584i	−0.994193	+	0.107609i	$0.965681\pi$
$180$		0			0
$181$	13.6295			1.01307			0.506536	−	0.862219i	$-0.330926\pi$
$181$	13.6295			1.01307			0.506536	+	0.862219i	$0.330926\pi$
$182$	2.62191	−	4.97273i	0.194349	−	0.368603i
$183$		0			0
$184$	−3.36930			−0.248388
$185$	1.80343			0.132591
$186$		0			0
$187$	7.16044	+	12.4022i	0.523623	+	0.906942i
$188$	1.48380	−	2.57002i	0.108217	−	0.187438i
$189$		0			0
$190$	−1.53374			−0.111269
$191$	−11.9124			−0.861954			−0.430977	−	0.902363i	$-0.641831\pi$
$191$	−11.9124			−0.861954			−0.430977	+	0.902363i	$0.641831\pi$
$192$		0			0
$193$	23.8109			1.71395			0.856973	−	0.515362i	$-0.172342\pi$
$193$	23.8109			1.71395			0.856973	+	0.515362i	$0.172342\pi$
$194$	−3.28917	+	5.69701i	−0.236149	+	0.409022i
$195$		0			0
$196$	2.28452	+	3.95690i	0.163180	+	0.282636i
$197$	3.84864	+	6.66603i	0.274204	+	0.474935i	0.969934	−	0.243368i	$-0.0782523\pi$
$197$	3.84864	+	6.66603i	0.274204	+	0.474935i	−0.695730	+	0.718303i	$0.744919\pi$
$198$		0			0
$199$	3.23845	−	5.60917i	0.229568	−	0.397623i	−0.728112	−	0.685458i	$-0.759602\pi$
$199$	3.23845	−	5.60917i	0.229568	−	0.397623i	0.957680	+	0.287835i	$0.0929354\pi$
$200$	2.47882	+	4.29344i	0.175279	+	0.303592i
$201$		0			0
$202$	5.65246	+	9.79034i	0.397705	+	0.688846i
$203$	3.80148	−	6.58435i	0.266812	−	0.462131i
$204$		0			0
$205$	0.359475	−	0.622629i	0.0251068	−	0.0434863i
$206$	9.34320	+	16.1829i	0.650972	+	1.12752i
$207$		0			0
$208$	−1.68162	+	3.18938i	−0.116600	+	0.221144i
$209$	−14.4879	−	25.0938i	−1.00215	−	1.73577i
$210$		0			0
$211$	−13.8149			−0.951059			−0.475530	−	0.879700i	$-0.657744\pi$
$211$	−13.8149			−0.951059			−0.475530	+	0.879700i	$0.657744\pi$
$212$	4.76149	+	8.24714i	0.327020	+	0.566416i
$213$		0			0
$214$	−11.4276			−0.781174
$215$	−0.0706531	+	0.122375i	−0.00481850	+	0.00834590i
$216$		0			0
$217$	2.34161	−	4.05580i	0.158959	−	0.275325i
$218$	3.19924	−	5.54125i	0.216680	−	0.375301i
$219$		0			0
$220$	0.400197	−	0.693162i	0.0269813	−	0.0467330i
$221$	6.19305	−	11.7458i	0.416590	−	0.790106i
$222$		0			0
$223$	−5.93420	+	10.2783i	−0.397383	+	0.688288i	−0.993402	−	0.114682i	$-0.963415\pi$
$223$	−5.93420	+	10.2783i	−0.397383	+	0.688288i	0.596019	+	0.802970i	$0.296748\pi$
$224$	0.779577	+	1.35027i	0.0520877	+	0.0902185i
$225$		0			0
$226$	−12.9768			−0.863205
$227$	−9.83394			−0.652701			−0.326351	−	0.945249i	$-0.605819\pi$
$227$	−9.83394			−0.652701			−0.326351	+	0.945249i	$0.605819\pi$
$228$		0			0
$229$	8.65591	−	14.9925i	0.571999	−	0.990731i	−0.424362	−	0.905493i	$-0.639502\pi$
$229$	8.65591	−	14.9925i	0.571999	−	0.990731i	0.996361	−	0.0852383i	$-0.0271652\pi$
$230$	−0.346752	−	0.600592i	−0.0228642	−	0.0396019i
$231$		0			0
$232$	−2.43817	+	4.22303i	−0.160074	+	0.277256i
$233$	−17.6548			−1.15660			−0.578301	−	0.815823i	$-0.696284\pi$
$233$	−17.6548			−1.15660			−0.578301	+	0.815823i	$0.696284\pi$
$234$		0			0
$235$	0.610823			0.0398457
$236$	3.30029	−	5.71626i	0.214830	−	0.372097i
$237$		0			0
$238$	−2.87101	−	4.97273i	−0.186100	−	0.322334i
$239$	0.631256	−	1.09337i	0.0408326	−	0.0707241i	−0.844887	−	0.534945i	$-0.820332\pi$
$239$	0.631256	−	1.09337i	0.0408326	−	0.0707241i	0.885719	+	0.464221i	$0.153666\pi$
$240$		0			0
$241$	−10.8891			−0.701428			−0.350714	−	0.936483i	$-0.614061\pi$
$241$	−10.8891			−0.701428			−0.350714	+	0.936483i	$0.614061\pi$
$242$	4.12128			0.264926
$243$		0			0
$244$	−2.67549	−	4.63408i	−0.171281	−	0.296667i
$245$	−0.470224	+	0.814452i	−0.0300415	+	0.0520335i
$246$		0			0
$247$	−12.5306	+	23.7655i	−0.797300	+	1.51217i
$248$	−1.50185	+	2.60128i	−0.0953676	+	0.165181i
$249$		0			0
$250$	−1.02479	+	1.77499i	−0.0648136	+	0.112260i
$251$	12.3336	−	21.3624i	0.778489	−	1.34838i	−0.154323	−	0.988020i	$-0.549320\pi$
$251$	12.3336	−	21.3624i	0.778489	−	1.34838i	0.932812	−	0.360362i	$-0.117347\pi$
$252$		0			0
$253$	6.55094	−	11.3466i	0.411854	−	0.713352i
$254$	11.2190			0.703940
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−25.5375			−1.59298			−0.796492	−	0.604649i	$-0.793313\pi$
$257$	−25.5375			−1.59298			−0.796492	+	0.604649i	$0.793313\pi$
$258$		0			0
$259$	−6.83044	−	11.8307i	−0.424423	−	0.735122i
$260$	−0.741586	+	0.0284788i	−0.0459912	+	0.00176618i
$261$		0			0
$262$	−0.232322	−	0.402393i	−0.0143529	−	0.0248599i
$263$	−6.20109	+	10.7406i	−0.382376	+	0.662294i	−0.991401	−	0.130857i	$-0.958227\pi$
$263$	−6.20109	+	10.7406i	−0.382376	+	0.662294i	0.609026	+	0.793150i	$0.291561\pi$
$264$		0			0
$265$	−0.980060	+	1.69751i	−0.0602046	+	0.104277i
$266$	5.80899	+	10.0615i	0.356172	+	0.616908i
$267$		0			0
$268$	1.51690	+	2.62734i	0.0926592	+	0.160490i
$269$	−2.46813	+	4.27492i	−0.150484	+	0.260646i	−0.931406	−	0.363983i	$-0.881417\pi$
$269$	−2.46813	+	4.27492i	−0.150484	+	0.260646i	0.780921	+	0.624629i	$0.214750\pi$
$270$		0			0
$271$	13.7565	+	23.8269i	0.835647	+	1.44738i	0.893503	+	0.449058i	$0.148240\pi$
$271$	13.7565	+	23.8269i	0.835647	+	1.44738i	−0.0578557	+	0.998325i	$0.518426\pi$
$272$	1.84139	+	3.18938i	0.111651	+	0.193385i
$273$		0			0
$274$	−7.69850	+	13.3342i	−0.465083	+	0.805548i
$275$	−19.2783			−1.16253
$276$		0			0
$277$	−2.66768			−0.160285			−0.0801425	−	0.996783i	$-0.525538\pi$
$277$	−2.66768			−0.160285			−0.0801425	+	0.996783i	$0.525538\pi$
$278$	4.81710			0.288910
$279$		0			0
$280$	−0.160461	+	0.277926i	−0.00958937	+	0.0166093i
$281$	5.51262	+	9.54813i	0.328855	+	0.569594i	0.982285	−	0.187393i	$-0.0600039\pi$
$281$	5.51262	+	9.54813i	0.328855	+	0.569594i	−0.653430	+	0.756987i	$0.726671\pi$
$282$		0			0
$283$	4.86782			0.289362			0.144681	−	0.989478i	$-0.453784\pi$
$283$	4.86782			0.289362			0.144681	+	0.989478i	$0.453784\pi$
$284$	−2.79417			−0.165803
$285$		0			0
$286$	−7.47107	−	11.8642i	−0.441774	−	0.701546i
$287$	−5.44600			−0.321467
$288$		0			0
$289$	1.71857	+	2.97666i	0.101093	+	0.175097i
$290$	−1.00370			−0.0589393
$291$		0			0
$292$	7.66819	+	13.2817i	0.448747	+	0.777252i
$293$	−4.24723	−	7.35642i	−0.248126	−	0.429767i	0.714880	−	0.699247i	$-0.246481\pi$
$293$	−4.24723	−	7.35642i	−0.248126	−	0.429767i	−0.963006	+	0.269480i	$0.913148\pi$
$294$		0			0
$295$	1.35860			0.0791008
$296$	4.38086	+	7.58788i	0.254633	+	0.441037i
$297$		0			0
$298$	16.7978			0.973070
$299$	−12.1392	+	0.466177i	−0.702029	+	0.0269597i
$300$		0			0
$301$	1.07039			0.0616960
$302$	0.631148			0.0363185
$303$		0			0
$304$	−3.72573	−	6.45316i	−0.213685	−	0.370114i
$305$	0.550698	−	0.953836i	0.0315328	−	0.0546165i
$306$		0			0
$307$	−14.0572			−0.802285			−0.401142	−	0.916016i	$-0.631387\pi$
$307$	−14.0572			−0.802285			−0.401142	+	0.916016i	$0.631387\pi$
$308$	−6.06294			−0.345468
$309$		0			0
$310$	−0.618254			−0.0351144
$311$	4.74354	−	8.21605i	0.268981	−	0.465890i	−0.699618	−	0.714517i	$-0.746646\pi$
$311$	4.74354	−	8.21605i	0.268981	−	0.465890i	0.968599	+	0.248628i	$0.0799796\pi$
$312$		0			0
$313$	−16.9273	−	29.3190i	−0.956790	−	1.65721i	−0.730217	−	0.683215i	$-0.760581\pi$
$313$	−16.9273	−	29.3190i	−0.956790	−	1.65721i	−0.226573	−	0.973994i	$-0.572752\pi$
$314$	−8.62325	−	14.9359i	−0.486638	−	0.842882i
$315$		0			0
$316$	0.829455	−	1.43666i	0.0466605	−	0.0808183i
$317$	3.53923	+	6.13013i	0.198783	+	0.344302i	0.948134	−	0.317871i	$-0.102968\pi$
$317$	3.53923	+	6.13013i	0.198783	+	0.344302i	−0.749351	+	0.662173i	$0.769634\pi$
$318$		0			0
$319$	−9.48108	−	16.4217i	−0.530839	−	0.919440i
$320$	0.102915	−	0.178255i	0.00575314	−	0.00996474i
$321$		0			0
$322$	−2.62662	+	4.54945i	−0.146376	+	0.253531i
$323$	13.7210	+	23.7655i	0.763459	+	1.32235i
$324$		0			0
$325$	9.52496	+	15.1258i	0.528350	+	0.839030i
$326$	1.67055	+	2.89347i	0.0925229	+	0.160254i
$327$		0			0
$328$	3.49292			0.192864
$329$	−2.31347	−	4.00705i	−0.127546	−	0.220916i
$330$		0			0
$331$	−12.9539			−0.712009			−0.356004	−	0.934484i	$-0.615861\pi$
$331$	−12.9539			−0.712009			−0.356004	+	0.934484i	$0.615861\pi$
$332$	4.34020	−	7.51744i	0.238199	−	0.412573i
$333$		0			0
$334$	−10.5805	+	18.3260i	−0.578939	+	1.00275i
$335$	−0.312224	+	0.540788i	−0.0170586	+	0.0295464i
$336$		0			0
$337$	9.11943	−	15.7953i	0.496767	−	0.860425i	−0.503226	−	0.864155i	$-0.667854\pi$
$337$	9.11943	−	15.7953i	0.496767	−	0.860425i	0.999993	+	0.00372930i	$0.00118707\pi$
$338$	−5.61743	+	11.7237i	−0.305548	+	0.637684i
$339$		0			0
$340$	−0.379014	+	0.656472i	−0.0205549	+	0.0356022i
$341$	−5.84011	−	10.1154i	−0.316259	−	0.547777i
$342$		0			0
$343$	18.0379			0.973956
$344$	−0.686517			−0.0370145
$345$		0			0
$346$	−11.2917	+	19.5577i	−0.607043	+	1.05143i
$347$	−6.24852	−	10.8228i	−0.335438	−	0.580996i	0.648131	−	0.761529i	$-0.275551\pi$
$347$	−6.24852	−	10.8228i	−0.335438	−	0.580996i	−0.983569	+	0.180533i	$0.942218\pi$
$348$		0			0
$349$	−1.00654	+	1.74337i	−0.0538787	+	0.0933206i	−0.891707	−	0.452613i	$-0.850492\pi$
$349$	−1.00654	+	1.74337i	−0.0538787	+	0.0933206i	0.837828	+	0.545934i	$0.183825\pi$
$350$	7.72971			0.413171
$351$		0			0
$352$	3.88861			0.207264
$353$	−18.0573	+	31.2761i	−0.961091	+	1.66466i	−0.241320	+	0.970446i	$0.577580\pi$
$353$	−18.0573	+	31.2761i	−0.961091	+	1.66466i	−0.719770	+	0.694212i	$0.755753\pi$
$354$		0			0
$355$	−0.287563	−	0.498074i	−0.0152623	−	0.0264350i
$356$	−6.25792	+	10.8390i	−0.331669	+	0.574468i
$357$		0			0
$358$	10.8078			0.571208
$359$	−34.3296			−1.81185			−0.905923	−	0.423442i	$-0.860822\pi$
$359$	−34.3296			−1.81185			−0.905923	+	0.423442i	$0.860822\pi$
$360$		0			0
$361$	−18.2621	−	31.6310i	−0.961165	−	1.66479i
$362$	−6.81475	+	11.8035i	−0.358175	+	0.620377i
$363$		0			0
$364$	2.99556	+	4.75701i	0.157010	+	0.249335i
$365$	−1.57835	+	2.73378i	−0.0826145	+	0.143093i
$366$		0			0
$367$	2.52885	−	4.38010i	0.132005	−	0.228640i	−0.792444	−	0.609944i	$-0.791192\pi$
$367$	2.52885	−	4.38010i	0.132005	−	0.228640i	0.924449	+	0.381305i	$0.124525\pi$
$368$	1.68465	−	2.91790i	0.0878183	−	0.152106i
$369$		0			0
$370$	−0.901716	+	1.56182i	−0.0468780	+	0.0811951i
$371$	14.8478			0.770858
$372$		0			0
$373$	13.5229	+	23.4224i	0.700191	+	1.21277i	0.968399	+	0.249406i	$0.0802353\pi$
$373$	13.5229	+	23.4224i	0.700191	+	1.21277i	−0.268208	+	0.963361i	$0.586431\pi$
$374$	−14.3209			−0.740515
$375$		0			0
$376$	1.48380	+	2.57002i	0.0765211	+	0.132538i
$377$	−8.20017	+	15.5525i	−0.422330	+	0.800994i
$378$		0			0
$379$	3.71240	+	6.43007i	0.190693	+	0.330290i	0.945480	−	0.325680i	$-0.105593\pi$
$379$	3.71240	+	6.43007i	0.190693	+	0.330290i	−0.754787	+	0.655970i	$0.772260\pi$
$380$	0.766870	−	1.32826i	0.0393396	−	0.0681382i
$381$		0			0
$382$	5.95622	−	10.3165i	0.304747	−	0.527837i
$383$	15.4542	+	26.7675i	0.789673	+	1.36775i	0.926167	+	0.377113i	$0.123083\pi$
$383$	15.4542	+	26.7675i	0.789673	+	1.36775i	−0.136494	+	0.990641i	$0.543584\pi$
$384$		0			0
$385$	−0.623969	−	1.08075i	−0.0318004	−	0.0550800i
$386$	−11.9054	+	20.6208i	−0.605971	+	1.04957i
$387$		0			0
$388$	−3.28917	−	5.69701i	−0.166982	−	0.289222i
$389$	4.51699	+	7.82366i	0.229020	+	0.396675i	0.957518	−	0.288373i	$-0.0931144\pi$
$389$	4.51699	+	7.82366i	0.229020	+	0.396675i	−0.728498	+	0.685048i	$0.759781\pi$
$390$		0			0
$391$	−6.20418	+	10.7460i	−0.313759	+	0.543447i
$392$	−4.56904			−0.230771
$393$		0			0
$394$	−7.69727			−0.387783
$395$	0.341455			0.0171804
$396$		0			0
$397$	7.41951	−	12.8510i	0.372374	−	0.644971i	−0.617556	−	0.786527i	$-0.711877\pi$
$397$	7.41951	−	12.8510i	0.372374	−	0.644971i	0.989930	+	0.141556i	$0.0452104\pi$
$398$	3.23845	+	5.60917i	0.162329	+	0.281162i
$399$		0			0
$400$	−4.95763			−0.247882
$401$	−16.1782			−0.807903			−0.403951	−	0.914780i	$-0.632363\pi$
$401$	−16.1782			−0.807903			−0.403951	+	0.914780i	$0.632363\pi$
$402$		0			0
$403$	−5.05109	+	9.57994i	−0.251613	+	0.477211i
$404$	−11.3049			−0.562440
$405$		0			0
$406$	3.80148	+	6.58435i	0.188664	+	0.326776i
$407$	−34.0709			−1.68883
$408$		0			0
$409$	−0.973364	−	1.68592i	−0.0481298	−	0.0833632i	0.840957	−	0.541102i	$-0.181993\pi$
$409$	−0.973364	−	1.68592i	−0.0481298	−	0.0833632i	−0.889087	+	0.457739i	$0.848659\pi$
$410$	0.359475	+	0.622629i	0.0177532	+	0.0307495i
$411$		0			0
$412$	−18.6864			−0.920613
$413$	−5.14565	−	8.91253i	−0.253201	−	0.438557i
$414$		0			0
$415$	1.78669			0.0877052
$416$	−1.92127	−	3.05102i	−0.0941981	−	0.149589i
$417$		0			0
$418$	28.9758			1.41725
$419$	−23.4899			−1.14756			−0.573778	−	0.819011i	$-0.694523\pi$
$419$	−23.4899			−1.14756			−0.573778	+	0.819011i	$0.694523\pi$
$420$		0			0
$421$	1.97408	+	3.41921i	0.0962108	+	0.166642i	0.910113	−	0.414360i	$-0.135994\pi$
$421$	1.97408	+	3.41921i	0.0962108	+	0.166642i	−0.813903	+	0.581001i	$0.802661\pi$
$422$	6.90747	−	11.9641i	0.336250	−	0.582403i
$423$		0			0
$424$	−9.52297			−0.462476
$425$	18.2579			0.885636
$426$		0			0
$427$	−8.34299			−0.403746
$428$	5.71380	−	9.89659i	0.276187	−	0.478370i
$429$		0			0
$430$	−0.0706531	−	0.122375i	−0.00340720	−	0.00590144i
$431$	14.3356	+	24.8300i	0.690522	+	1.19602i	0.971667	+	0.236354i	$0.0759525\pi$
$431$	14.3356	+	24.8300i	0.690522	+	1.19602i	−0.281145	+	0.959665i	$0.590714\pi$
$432$		0			0
$433$	−2.86328	+	4.95934i	−0.137600	+	0.238331i	−0.926588	−	0.376079i	$-0.877272\pi$
$433$	−2.86328	+	4.95934i	−0.137600	+	0.238331i	0.788988	+	0.614409i	$0.210606\pi$
$434$	2.34161	+	4.05580i	0.112401	+	0.194684i
$435$		0			0
$436$	3.19924	+	5.54125i	0.153216	+	0.265378i
$437$	12.5531	−	21.7426i	0.600496	−	1.04009i
$438$		0			0
$439$	−19.4991	+	33.7735i	−0.930642	+	1.61192i	−0.148415	+	0.988925i	$0.547417\pi$
$439$	−19.4991	+	33.7735i	−0.930642	+	1.61192i	−0.782227	+	0.622994i	$0.785916\pi$
$440$	0.400197	+	0.693162i	0.0190787	+	0.0330452i
$441$		0			0
$442$	7.07562	+	11.2362i	0.336553	+	0.534453i
$443$	−19.4094	−	33.6180i	−0.922167	−	1.59724i	−0.796055	−	0.605224i	$-0.793083\pi$
$443$	−19.4094	−	33.6180i	−0.922167	−	1.59724i	−0.126112	−	0.992016i	$-0.540250\pi$
$444$		0			0
$445$	−2.57615			−0.122121
$446$	−5.93420	−	10.2783i	−0.280993	−	0.486693i
$447$		0			0
$448$	−1.55915			−0.0736631
$449$	13.3263	−	23.0818i	0.628907	−	1.08930i	−0.358865	−	0.933390i	$-0.616836\pi$
$449$	13.3263	−	23.0818i	0.628907	−	1.08930i	0.987771	−	0.155909i	$-0.0498306\pi$
$450$		0			0
$451$	−6.79130	+	11.7629i	−0.319790	+	0.553892i
$452$	6.48841	−	11.2383i	0.305189	−	0.528603i
$453$		0			0
$454$	4.91697	−	8.51644i	0.230765	−	0.399696i
$455$	−0.539670	+	1.02354i	−0.0253001	+	0.0479843i
$456$		0			0
$457$	−5.64143	+	9.77124i	−0.263895	+	0.457079i	−0.967273	−	0.253736i	$-0.918341\pi$
$457$	−5.64143	+	9.77124i	−0.263895	+	0.457079i	0.703379	+	0.710815i	$0.251674\pi$
$458$	8.65591	+	14.9925i	0.404464	+	0.700553i
$459$		0			0
$460$	0.693504			0.0323348
$461$	7.76634			0.361714			0.180857	−	0.983509i	$-0.442113\pi$
$461$	7.76634			0.361714			0.180857	+	0.983509i	$0.442113\pi$
$462$		0			0
$463$	0.105633	−	0.182962i	0.00490918	−	0.00850295i	−0.863560	−	0.504245i	$-0.831771\pi$
$463$	0.105633	−	0.182962i	0.00490918	−	0.00850295i	0.868470	+	0.495742i	$0.165104\pi$
$464$	−2.43817	−	4.22303i	−0.113189	−	0.196049i
$465$		0			0
$466$	8.82738	−	15.2895i	0.408921	−	0.708271i
$467$	34.8916			1.61459			0.807294	−	0.590149i	$-0.200931\pi$
$467$	34.8916			1.61459			0.807294	+	0.590149i	$0.200931\pi$
$468$		0			0
$469$	4.73015			0.218418
$470$	−0.305411	+	0.528988i	−0.0140876	+	0.0244004i
$471$		0			0
$472$	3.30029	+	5.71626i	0.151908	+	0.263112i
$473$	1.33480	−	2.31194i	0.0613741	−	0.106303i
$474$		0			0
$475$	−36.9416			−1.69500
$476$	5.74202			0.263185
$477$		0			0
$478$	0.631256	+	1.09337i	0.0288730	+	0.0500095i
$479$	−3.72958	+	6.45981i	−0.170409	+	0.295156i	−0.938563	−	0.345109i	$-0.887842\pi$
$479$	−3.72958	+	6.45981i	−0.170409	+	0.295156i	0.768154	+	0.640265i	$0.221175\pi$
$480$		0			0
$481$	16.8337	+	26.7322i	0.767549	+	1.21888i
$482$	5.44455	−	9.43023i	0.247992	−	0.429535i
$483$		0			0
$484$	−2.06064	+	3.56913i	−0.0936654	+	0.162233i
$485$	0.677012	−	1.17262i	0.0307415	−	0.0532459i
$486$		0			0
$487$	21.2844	−	36.8657i	0.964489	−	1.67054i	0.253509	−	0.967333i	$-0.418415\pi$
$487$	21.2844	−	36.8657i	0.964489	−	1.67054i	0.710981	−	0.703211i	$-0.248251\pi$
$488$	5.35098			0.242227
$489$		0			0
$490$	−0.470224	−	0.814452i	−0.0212426	−	0.0367932i
$491$	33.4196			1.50821			0.754103	−	0.656756i	$-0.228072\pi$
$491$	33.4196			1.50821			0.754103	+	0.656756i	$0.228072\pi$
$492$		0			0
$493$	8.97923	+	15.5525i	0.404404	+	0.700449i
$494$	−14.3163	−	22.7346i	−0.644120	−	1.02288i
$495$		0			0
$496$	−1.50185	−	2.60128i	−0.0674350	−	0.116801i
$497$	−2.17827	+	3.77287i	−0.0977088	+	0.169237i
$498$		0			0
$499$	3.44081	−	5.95966i	0.154032	−	0.266791i	−0.778674	−	0.627428i	$-0.784107\pi$
$499$	3.44081	−	5.95966i	0.154032	−	0.266791i	0.932706	+	0.360637i	$0.117441\pi$
$500$	−1.02479	−	1.77499i	−0.0458301	−	0.0793801i
$501$		0			0
$502$	12.3336	+	21.3624i	0.550475	+	0.953450i
$503$	13.4441	−	23.2858i	0.599441	−	1.03826i	−0.393463	−	0.919340i	$-0.628723\pi$
$503$	13.4441	−	23.2858i	0.599441	−	1.03826i	0.992904	−	0.118921i	$-0.0379436\pi$
$504$		0			0
$505$	−1.16345	−	2.01515i	−0.0517728	−	0.0896731i
$506$	6.55094	+	11.3466i	0.291225	+	0.504416i
$507$		0			0
$508$	−5.60948	+	9.71591i	−0.248881	+	0.431074i
$509$	34.0371			1.50867			0.754335	−	0.656490i	$-0.227960\pi$
$509$	34.0371			1.50867			0.754335	+	0.656490i	$0.227960\pi$
$510$		0			0
$511$	23.9118			1.05779
$512$	1.00000			0.0441942
$513$		0			0
$514$	12.7687	−	22.1161i	0.563205	−	0.975499i
$515$	−1.92312	−	3.33094i	−0.0847427	−	0.146779i
$516$		0			0
$517$	−11.5398			−0.507521
$518$	13.6609			0.600225
$519$		0			0
$520$	0.346130	−	0.656472i	0.0151788	−	0.0287882i
$521$	−28.8015			−1.26182			−0.630909	−	0.775857i	$-0.717318\pi$
$521$	−28.8015			−1.26182			−0.630909	+	0.775857i	$0.717318\pi$
$522$		0			0
$523$	11.0647	+	19.1647i	0.483827	+	0.838013i	0.999827	−	0.0185751i	$-0.00591297\pi$
$523$	11.0647	+	19.1647i	0.483827	+	0.838013i	−0.516000	+	0.856588i	$0.672580\pi$
$524$	0.464643			0.0202980
$525$		0			0
$526$	−6.20109	−	10.7406i	−0.270380	−	0.468313i
$527$	5.53098	+	9.57994i	0.240933	+	0.417309i
$528$		0			0
$529$	−11.6479			−0.506428
$530$	−0.980060	−	1.69751i	−0.0425711	−	0.0737353i
$531$		0			0
$532$	−11.6180			−0.503703
$533$	12.5846	−	0.483282i	0.545101	−	0.0209332i
$534$		0			0
$535$	2.35215			0.101692
$536$	−3.03379			−0.131040
$537$		0			0
$538$	−2.46813	−	4.27492i	−0.106408	−	0.184305i
$539$	8.88360	−	15.3869i	0.382644	−	0.662759i
$540$		0			0
$541$	20.1937			0.868196			0.434098	−	0.900866i	$-0.357067\pi$
$541$	20.1937			0.868196			0.434098	+	0.900866i	$0.357067\pi$
$542$	−27.5130			−1.18178
$543$		0			0
$544$	−3.68278			−0.157898
$545$	−0.658502	+	1.14056i	−0.0282071	+	0.0488562i
$546$		0			0
$547$	−2.75008	−	4.76328i	−0.117585	−	0.203663i	0.801225	−	0.598363i	$-0.204182\pi$
$547$	−2.75008	−	4.76328i	−0.117585	−	0.203663i	−0.918810	+	0.394700i	$0.870849\pi$
$548$	−7.69850	−	13.3342i	−0.328864	−	0.569609i
$549$		0			0
$550$	9.63915	−	16.6955i	0.411015	−	0.711898i
$551$	−18.1679	−	31.4678i	−0.773979	−	1.34057i
$552$		0			0
$553$	−1.29325	−	2.23997i	−0.0549945	−	0.0952532i
$554$	1.33384	−	2.31027i	0.0566693	−	0.0981542i
$555$		0			0
$556$	−2.40855	+	4.17173i	−0.102145	+	0.176921i
$557$	12.6702	+	21.9455i	0.536856	+	0.929861i	0.999071	+	0.0430936i	$0.0137214\pi$
$557$	12.6702	+	21.9455i	0.536856	+	0.929861i	−0.462215	+	0.886768i	$0.652945\pi$
$558$		0			0
$559$	−2.47345	+	0.0949868i	−0.104616	+	0.00401751i
$560$	−0.160461	−	0.277926i	−0.00678071	−	0.0117445i
$561$		0			0
$562$	−11.0252			−0.465071
$563$	10.7828	+	18.6764i	0.454442	+	0.787117i	0.998656	−	0.0518299i	$-0.0165054\pi$
$563$	10.7828	+	18.6764i	0.454442	+	0.787117i	−0.544214	+	0.838946i	$0.683172\pi$
$564$		0			0
$565$	2.67103			0.112371
$566$	−2.43391	+	4.21565i	−0.102305	+	0.177197i
$567$		0			0
$568$	1.39708	−	2.41982i	0.0586204	−	0.101533i
$569$	−0.285919	+	0.495226i	−0.0119864	+	0.0207610i	−0.871956	−	0.489584i	$-0.837149\pi$
$569$	−0.285919	+	0.495226i	−0.0119864	+	0.0207610i	0.859970	+	0.510345i	$0.170482\pi$
$570$		0			0
$571$	−5.02115	+	8.69689i	−0.210129	+	0.363953i	−0.951755	−	0.306860i	$-0.900722\pi$
$571$	−5.02115	+	8.69689i	−0.210129	+	0.363953i	0.741626	+	0.670814i	$0.234055\pi$
$572$	14.0103	−	0.538029i	0.585798	−	0.0224961i
$573$		0			0
$574$	2.72300	−	4.71637i	0.113656	−	0.196858i
$575$	−8.35187	−	14.4659i	−0.348297	−	0.603268i
$576$		0			0
$577$	−16.7133			−0.695785			−0.347892	−	0.937534i	$-0.613103\pi$
$577$	−16.7133			−0.695785			−0.347892	+	0.937534i	$0.613103\pi$
$578$	−3.43715			−0.142966
$579$		0			0
$580$	0.501850	−	0.869229i	0.0208382	−	0.0360928i
$581$	−6.76703	−	11.7208i	−0.280744	−	0.486263i
$582$		0			0
$583$	18.5156	−	32.0699i	0.766836	−	1.32820i
$584$	−15.3364			−0.634624
$585$		0			0
$586$	8.49447			0.350903
$587$	0.968663	−	1.67777i	0.0399810	−	0.0692491i	−0.845342	−	0.534225i	$-0.820604\pi$
$587$	0.968663	−	1.67777i	0.0399810	−	0.0692491i	0.885323	+	0.464976i	$0.153937\pi$
$588$		0			0
$589$	−11.1910	−	19.3833i	−0.461116	−	0.798677i
$590$	−0.679300	+	1.17658i	−0.0279663	+	0.0484391i
$591$		0			0
$592$	−8.76173			−0.360105
$593$	−45.4544			−1.86659			−0.933294	−	0.359113i	$-0.883079\pi$
$593$	−45.4544			−1.86659			−0.933294	+	0.359113i	$0.883079\pi$
$594$		0			0
$595$	0.590942	+	1.02354i	0.0242262	+	0.0419611i
$596$	−8.39889	+	14.5473i	−0.344032	+	0.595881i
$597$		0			0
$598$	5.66589	−	10.7460i	0.231695	−	0.439435i
$599$	−11.8317	+	20.4932i	−0.483431	+	0.837327i	−0.999819	−	0.0190274i	$-0.993943\pi$
$599$	−11.8317	+	20.4932i	−0.483431	+	0.837327i	0.516388	+	0.856355i	$0.327276\pi$
$600$		0			0
$601$	16.6831	−	28.8960i	0.680519	−	1.17869i	−0.294304	−	0.955712i	$-0.595088\pi$
$601$	16.6831	−	28.8960i	0.680519	−	1.17869i	0.974823	−	0.222981i	$-0.0715789\pi$
$602$	−0.535193	+	0.926981i	−0.0218128	+	0.0377809i
$603$		0			0
$604$	−0.315574	+	0.546591i	−0.0128405	+	0.0222405i
$605$	−0.848285			−0.0344877
$606$		0			0
$607$	14.5018	+	25.1178i	0.588610	+	1.01950i	0.994415	+	0.105542i	$0.0336578\pi$
$607$	14.5018	+	25.1178i	0.588610	+	1.01950i	−0.405805	+	0.913960i	$0.633009\pi$
$608$	7.45146			0.302197
$609$		0			0
$610$	0.550698	+	0.953836i	0.0222971	+	0.0386197i
$611$	5.70156	+	9.05420i	0.230661	+	0.366294i
$612$		0			0
$613$	−2.55168	−	4.41964i	−0.103061	−	0.178507i	0.809883	−	0.586591i	$-0.199530\pi$
$613$	−2.55168	−	4.41964i	−0.103061	−	0.178507i	−0.912944	+	0.408084i	$0.866197\pi$
$614$	7.02858	−	12.1739i	0.283651	−	0.491297i
$615$		0			0
$616$	3.03147	−	5.25066i	0.122141	−	0.211555i
$617$	4.56228	+	7.90210i	0.183671	+	0.318127i	0.943128	−	0.332431i	$-0.107869\pi$
$617$	4.56228	+	7.90210i	0.183671	+	0.318127i	−0.759457	+	0.650557i	$0.774535\pi$
$618$		0			0
$619$	4.97487	+	8.61673i	0.199957	+	0.346336i	0.948514	−	0.316734i	$-0.102586\pi$
$619$	4.97487	+	8.61673i	0.199957	+	0.346336i	−0.748557	+	0.663070i	$0.769253\pi$
$620$	0.309127	−	0.535423i	0.0124148	−	0.0215031i
$621$		0			0
$622$	4.74354	+	8.21605i	0.190199	+	0.329434i
$623$	9.75707	+	16.8997i	0.390909	+	0.677073i
$624$		0			0
$625$	−12.1832	+	21.1018i	−0.487326	+	0.844073i
$626$	33.8547			1.35311
$627$		0			0
$628$	17.2465			0.688210
$629$	32.2675			1.28659
$630$		0			0
$631$	22.5331	−	39.0284i	0.897027	−	1.55370i	0.0657504	−	0.997836i	$-0.479056\pi$
$631$	22.5331	−	39.0284i	0.897027	−	1.55370i	0.831276	−	0.555860i	$-0.187611\pi$
$632$	0.829455	+	1.43666i	0.0329939	+	0.0571472i
$633$		0			0
$634$	−7.07846			−0.281122
$635$	−2.30921			−0.0916381
$636$		0			0
$637$	−16.4618	+	0.632174i	−0.652239	+	0.0250476i
$638$	18.9622			0.750719
$639$		0			0
$640$	0.102915	+	0.178255i	0.00406809	+	0.00704613i
$641$	36.5673			1.44432			0.722160	−	0.691726i	$-0.243149\pi$
$641$	36.5673			1.44432			0.722160	+	0.691726i	$0.243149\pi$
$642$		0			0
$643$	12.6078	+	21.8373i	0.497201	+	0.861178i	0.999995	−	0.00322872i	$-0.00102773\pi$
$643$	12.6078	+	21.8373i	0.497201	+	0.861178i	−0.502794	+	0.864407i	$0.667694\pi$
$644$	−2.62662	−	4.54945i	−0.103504	−	0.179273i
$645$		0			0
$646$	−27.4421			−1.07969
$647$	−0.159617	−	0.276465i	−0.00627519	−	0.0108689i	0.862871	−	0.505425i	$-0.168664\pi$
$647$	−0.159617	−	0.276465i	−0.00627519	−	0.0108689i	−0.869146	+	0.494556i	$0.835331\pi$
$648$		0			0
$649$	−25.6670			−1.00752
$650$	−17.8618	+	0.685940i	−0.700599	+	0.0269048i
$651$		0			0
$652$	−3.34109			−0.130847
$653$	39.4731			1.54470			0.772350	−	0.635197i	$-0.219081\pi$
$653$	39.4731			1.54470			0.772350	+	0.635197i	$0.219081\pi$
$654$		0			0
$655$	0.0478189	+	0.0828248i	0.00186844	+	0.00323623i
$656$	−1.74646	+	3.02496i	−0.0681878	+	0.118105i
$657$		0			0
$658$	4.62694			0.180377
$659$	42.1963			1.64373			0.821866	−	0.569680i	$-0.192933\pi$
$659$	42.1963			1.64373			0.821866	+	0.569680i	$0.192933\pi$
$660$		0			0
$661$	29.3289			1.14076			0.570380	−	0.821381i	$-0.306796\pi$
$661$	29.3289			1.14076			0.570380	+	0.821381i	$0.306796\pi$
$662$	6.47693	−	11.2184i	0.251733	−	0.436015i
$663$		0			0
$664$	4.34020	+	7.51744i	0.168432	+	0.291733i
$665$	−1.19567	−	2.07096i	−0.0463660	−	0.0803083i
$666$		0			0
$667$	8.21491	−	14.2286i	0.318083	−	0.550935i
$668$	−10.5805	−	18.3260i	−0.409372	−	0.709053i
$669$		0			0
$670$	−0.312224	−	0.540788i	−0.0120623	−	0.0208925i
$671$	−10.4039	+	18.0201i	−0.401639	+	0.695659i
$672$		0			0
$673$	22.1964	−	38.4452i	0.855607	−	1.48195i	−0.0204745	−	0.999790i	$-0.506518\pi$
$673$	22.1964	−	38.4452i	0.855607	−	1.48195i	0.876081	−	0.482164i	$-0.160149\pi$
$674$	9.11943	+	15.7953i	0.351267	+	0.608413i
$675$		0			0
$676$	−7.34428	−	10.7267i	−0.282472	−	0.412564i
$677$	0.870301	+	1.50741i	0.0334484	+	0.0579343i	0.882265	−	0.470753i	$-0.156018\pi$
$677$	0.870301	+	1.50741i	0.0334484	+	0.0579343i	−0.848817	+	0.528687i	$0.822684\pi$
$678$		0			0
$679$	−10.2566			−0.393614
$680$	−0.379014	−	0.656472i	−0.0145345	−	0.0251746i
$681$		0			0
$682$	11.6802			0.447258
$683$	−7.31521	+	12.6703i	−0.279909	+	0.484816i	−0.971362	−	0.237605i	$-0.923638\pi$
$683$	−7.31521	+	12.6703i	−0.279909	+	0.484816i	0.691453	+	0.722421i	$0.256971\pi$
$684$		0			0
$685$	1.58459	−	2.74459i	0.0605440	−	0.104865i
$686$	−9.01896	+	15.6213i	−0.344345	+	0.596424i
$687$		0			0
$688$	0.343259	−	0.594541i	0.0130866	−	0.0226667i
$689$	−34.3103	+	1.31760i	−1.30712	+	0.0501966i
$690$		0			0
$691$	9.02749	−	15.6361i	0.343422	−	0.594824i	−0.641644	−	0.767003i	$-0.721747\pi$
$691$	9.02749	−	15.6361i	0.343422	−	0.594824i	0.985066	+	0.172178i	$0.0550806\pi$
$692$	−11.2917	−	19.5577i	−0.429244	−	0.743473i
$693$		0			0
$694$	12.4970			0.474381
$695$	−0.991506			−0.0376100
$696$		0			0
$697$	6.43182	−	11.1402i	0.243623	−	0.421967i
$698$	−1.00654	−	1.74337i	−0.0380980	−	0.0659876i
$699$		0			0
$700$	−3.86486	+	6.69413i	−0.146078	+	0.253014i
$701$	20.6019			0.778122			0.389061	−	0.921212i	$-0.372799\pi$
$701$	20.6019			0.778122			0.389061	+	0.921212i	$0.372799\pi$
$702$		0			0
$703$	−65.2877			−2.46237
$704$	−1.94430	+	3.36763i	−0.0732787	+	0.126922i
$705$		0			0
$706$	−18.0573	−	31.2761i	−0.679594	−	1.17709i
$707$	−8.81305	+	15.2646i	−0.331449	+	0.574086i
$708$		0			0
$709$	−19.6723			−0.738808			−0.369404	−	0.929269i	$-0.620438\pi$
$709$	−19.6723			−0.738808			−0.369404	+	0.929269i	$0.620438\pi$
$710$	0.575126			0.0215841
$711$		0			0
$712$	−6.25792	−	10.8390i	−0.234526	−	0.406210i
$713$	5.06018	−	8.76448i	0.189505	−	0.328232i
$714$		0			0
$715$	1.53778	+	2.44202i	0.0575096	+	0.0913264i
$716$	−5.40388	+	9.35979i	−0.201952	+	0.349792i
$717$		0			0
$718$	17.1648	−	29.7303i	0.640585	−	1.10952i
$719$	15.9912	−	27.6975i	0.596370	−	1.03294i	−0.396982	−	0.917827i	$-0.629942\pi$
$719$	15.9912	−	27.6975i	0.596370	−	1.03294i	0.993352	−	0.115117i	$-0.0367244\pi$
$720$		0			0
$721$	−14.5675	+	25.2316i	−0.542521	+	0.939675i
$722$	36.5243			1.35929
$723$		0			0
$724$	−6.81475	−	11.8035i	−0.253268	−	0.438673i
$725$	−24.1751			−0.897840
$726$		0			0
$727$	−3.26856	−	5.66131i	−0.121224	−	0.209966i	0.799027	−	0.601296i	$-0.205349\pi$
$727$	−3.26856	−	5.66131i	−0.121224	−	0.209966i	−0.920251	+	0.391329i	$0.872015\pi$
$728$	−5.61747	+	0.215725i	−0.208197	+	0.00799530i
$729$		0			0
$730$	−1.57835	−	2.73378i	−0.0584173	−	0.101182i
$731$	−1.26415	+	2.18956i	−0.0467561	+	0.0809839i
$732$		0			0
$733$	−2.15768	+	3.73721i	−0.0796956	+	0.138037i	−0.903119	−	0.429391i	$-0.858728\pi$
$733$	−2.15768	+	3.73721i	−0.0796956	+	0.138037i	0.823423	+	0.567428i	$0.192062\pi$
$734$	2.52885	+	4.38010i	0.0933417	+	0.161673i
$735$		0			0
$736$	1.68465	+	2.91790i	0.0620969	+	0.107555i
$737$	5.89862	−	10.2167i	0.217278	−	0.376337i
$738$		0			0
$739$	−4.64539	−	8.04606i	−0.170884	−	0.295979i	0.767845	−	0.640635i	$-0.221329\pi$
$739$	−4.64539	−	8.04606i	−0.170884	−	0.295979i	−0.938729	+	0.344656i	$0.887996\pi$
$740$	−0.901716	−	1.56182i	−0.0331477	−	0.0574136i
$741$		0			0
$742$	−7.42389	+	12.8586i	−0.272540	+	0.472052i
$743$	2.95653			0.108464			0.0542322	−	0.998528i	$-0.482729\pi$
$743$	2.95653			0.108464			0.0542322	+	0.998528i	$0.482729\pi$
$744$		0			0
$745$	−3.45750			−0.126673
$746$	−27.0459			−0.990220
$747$		0			0
$748$	7.16044	−	12.4022i	0.261812	−	0.453471i
$749$	−8.90869	−	15.4303i	−0.325516	−	0.563811i
$750$		0			0
$751$	19.7803			0.721792			0.360896	−	0.932606i	$-0.382471\pi$
$751$	19.7803			0.721792			0.360896	+	0.932606i	$0.382471\pi$
$752$	−2.96760			−0.108217
$753$		0			0
$754$	−9.36877	−	14.8778i	−0.341190	−	0.541817i
$755$	−0.129910			−0.00472790
$756$		0			0
$757$	17.1539	+	29.7115i	0.623470	+	1.07988i	0.988835	+	0.149017i	$0.0476109\pi$
$757$	17.1539	+	29.7115i	0.623470	+	1.07988i	−0.365365	+	0.930864i	$0.619056\pi$
$758$	−7.42480			−0.269681
$759$		0			0
$760$	0.766870	+	1.32826i	0.0278173	+	0.0481810i
$761$	−3.08031	−	5.33526i	−0.111661	−	0.193403i	0.804779	−	0.593575i	$-0.202284\pi$
$761$	−3.08031	−	5.33526i	−0.111661	−	0.193403i	−0.916440	+	0.400172i	$0.868950\pi$
$762$		0			0
$763$	9.97621			0.361163
$764$	5.95622	+	10.3165i	0.215488	+	0.373237i
$765$		0			0
$766$	−30.9084			−1.11677
$767$	12.6815	+	20.1385i	0.457902	+	0.727158i
$768$		0			0
$769$	−30.2498			−1.09084			−0.545418	−	0.838164i	$-0.683629\pi$
$769$	−30.2498			−1.09084			−0.545418	+	0.838164i	$0.683629\pi$
$770$	1.24794			0.0449726
$771$		0			0
$772$	−11.9054	−	20.6208i	−0.428486	−	0.742160i
$773$	−24.3047	+	42.0971i	−0.874181	+	1.51413i	−0.0165485	+	0.999863i	$0.505268\pi$
$773$	−24.3047	+	42.0971i	−0.874181	+	1.51413i	−0.857633	+	0.514263i	$0.828066\pi$
$774$		0			0
$775$	−14.8912			−0.534909
$776$	6.57834			0.236149
$777$		0			0
$778$	−9.03398			−0.323884
$779$	−13.0137	+	22.5404i	−0.466263	+	0.807592i
$780$		0			0
$781$	5.43272	+	9.40974i	0.194398	+	0.336707i
$782$	−6.20418	−	10.7460i	−0.221861	−	0.384275i
$783$		0			0
$784$	2.28452	−	3.95690i	0.0815900	−	0.141318i
$785$	1.77493	+	3.07427i	0.0633500	+	0.109725i
$786$		0			0
$787$	17.7768	+	30.7903i	0.633673	+	1.09755i	0.986795	+	0.161977i	$0.0517870\pi$
$787$	17.7768	+	30.7903i	0.633673	+	1.09755i	−0.353121	+	0.935578i	$0.614880\pi$
$788$	3.84864	−	6.66603i	0.137102	−	0.237468i
$789$		0			0
$790$	−0.170727	+	0.295708i	−0.00607420	+	0.0105208i
$791$	−10.1164	−	17.5222i	−0.359699	−	0.623017i
$792$		0			0
$793$	19.2790	−	0.740363i	0.684618	−	0.0262911i
$794$	7.41951	+	12.8510i	0.263308	+	0.456064i
$795$		0			0
$796$	−6.47691			−0.229568
$797$	12.5860	+	21.7996i	0.445818	+	0.772180i	0.998109	−	0.0614717i	$-0.0195794\pi$
$797$	12.5860	+	21.7996i	0.445818	+	0.772180i	−0.552290	+	0.833652i	$0.686246\pi$
$798$		0			0
$799$	10.9290			0.386640
$800$	2.47882	−	4.29344i	0.0876394	−	0.151796i
$801$		0			0
$802$	8.08912	−	14.0108i	0.285637	−	0.494737i
$803$	29.8186	−	51.6473i	1.05227	−	1.82259i
$804$		0			0
$805$	0.540640	−	0.936416i	0.0190551	−	0.0330043i
$806$	−5.77092	−	9.16434i	−0.203272	−	0.322800i
$807$		0			0
$808$	5.65246	−	9.79034i	0.198853	−	0.344423i
$809$	6.11750	+	10.5958i	0.215080	+	0.372529i	0.953297	−	0.302034i	$-0.0976655\pi$
$809$	6.11750	+	10.5958i	0.215080	+	0.372529i	−0.738217	+	0.674563i	$0.764332\pi$
$810$		0			0
$811$	28.9188			1.01548			0.507739	−	0.861511i	$-0.330481\pi$
$811$	28.9188			1.01548			0.507739	+	0.861511i	$0.330481\pi$
$812$	−7.60296			−0.266812
$813$		0			0
$814$	17.0355	−	29.5063i	0.597093	−	1.03420i
$815$	−0.343849	−	0.595565i	−0.0120445	−	0.0208617i
$816$		0			0
$817$	2.55778	−	4.43020i	0.0894853	−	0.154993i
$818$	1.94673			0.0680658
$819$		0			0
$820$	−0.718950			−0.0251068
$821$	−1.00461	+	1.74004i	−0.0350611	+	0.0607277i	−0.883024	−	0.469329i	$-0.844496\pi$
$821$	−1.00461	+	1.74004i	−0.0350611	+	0.0607277i	0.847962	+	0.530056i	$0.177829\pi$
$822$		0			0
$823$	−18.7352	−	32.4503i	−0.653067	−	1.13114i	−0.982375	−	0.186922i	$-0.940149\pi$
$823$	−18.7352	−	32.4503i	−0.653067	−	1.13114i	0.329308	−	0.944223i	$-0.393185\pi$
$824$	9.34320	−	16.1829i	0.325486	−	0.563758i
$825$		0			0
$826$	10.2913			0.358080
$827$	−14.0136			−0.487299			−0.243650	−	0.969863i	$-0.578345\pi$
$827$	−14.0136			−0.487299			−0.243650	+	0.969863i	$0.578345\pi$
$828$		0			0
$829$	−5.74472	−	9.95015i	−0.199522	−	0.345583i	0.748851	−	0.662738i	$-0.230606\pi$
$829$	−5.74472	−	9.95015i	−0.199522	−	0.345583i	−0.948374	+	0.317155i	$0.897272\pi$
$830$	−0.893345	+	1.54732i	−0.0310085	+	0.0537083i
$831$		0			0
$832$	3.60290	−	0.138360i	0.124908	−	0.00479678i
$833$	−8.41338	+	14.5724i	−0.291506	+	0.504904i
$834$		0			0
$835$	2.17779	−	3.77205i	0.0753656	−	0.130537i
$836$	−14.4879	+	25.0938i	−0.501075	+	0.867887i
$837$		0			0
$838$	11.7449	−	20.3428i	0.405722	−	0.702731i
$839$	−30.9451			−1.06834			−0.534172	−	0.845376i	$-0.679377\pi$
$839$	−30.9451			−1.06834			−0.534172	+	0.845376i	$0.679377\pi$
$840$		0			0
$841$	2.61067	+	4.52182i	0.0900232	+	0.155925i
$842$	−3.94816			−0.136063
$843$		0			0
$844$	6.90747	+	11.9641i	0.237765	+	0.411821i
$845$	1.15624	−	2.41309i	0.0397759	−	0.0830129i
$846$		0			0
$847$	3.21285	+	5.56482i	0.110395	+	0.191210i
$848$	4.76149	−	8.24714i	0.163510	−	0.283208i
$849$		0			0
$850$	−9.12893	+	15.8118i	−0.313120	+	0.542339i
$851$	−14.7604	−	25.5658i	−0.505981	−	0.876384i
$852$		0			0
$853$	19.1080	+	33.0960i	0.654246	+	1.13319i	0.982082	+	0.188452i	$0.0603471\pi$
$853$	19.1080	+	33.0960i	0.654246	+	1.13319i	−0.327837	+	0.944734i	$0.606320\pi$
$854$	4.17150	−	7.22525i	0.142746	−	0.247243i
$855$		0			0
$856$	5.71380	+	9.89659i	0.195294	+	0.338258i
$857$	1.95053	+	3.37842i	0.0666289	+	0.115405i	0.897415	−	0.441187i	$-0.145442\pi$
$857$	1.95053	+	3.37842i	0.0666289	+	0.115405i	−0.830786	+	0.556591i	$0.812109\pi$
$858$		0			0
$859$	5.64034	−	9.76935i	0.192446	−	0.333326i	−0.753614	−	0.657317i	$-0.771691\pi$
$859$	5.64034	−	9.76935i	0.192446	−	0.333326i	0.946060	+	0.323991i	$0.105025\pi$
$860$	0.141306			0.00481850
$861$		0			0
$862$	−28.6712			−0.976546
$863$	31.5354			1.07348			0.536739	−	0.843749i	$-0.319656\pi$
$863$	31.5354			1.07348			0.536739	+	0.843749i	$0.319656\pi$
$864$		0			0
$865$	2.32417	−	4.02558i	0.0790241	−	0.136874i
$866$	−2.86328	−	4.95934i	−0.0972981	−	0.168525i
$867$		0			0
$868$	−4.68323			−0.158959
$869$	−6.45085			−0.218830
$870$		0			0
$871$	−10.9304	+	0.419757i	−0.370364	+	0.0142229i
$872$	−6.39848			−0.216680
$873$		0			0
$874$	12.5531	+	21.7426i	0.424615	+	0.735454i
$875$	−3.19562			−0.108032
$876$		0			0
$877$	1.54424	+	2.67470i	0.0521452	+	0.0903182i	0.890920	−	0.454161i	$-0.150061\pi$
$877$	1.54424	+	2.67470i	0.0521452	+	0.0903182i	−0.838775	+	0.544479i	$0.816727\pi$
$878$	−19.4991	−	33.7735i	−0.658063	−	1.13980i
$879$		0			0
$880$	−0.800395			−0.0269813
$881$	10.9208	+	18.9154i	0.367932	+	0.637277i	0.989242	−	0.146288i	$-0.0467326\pi$
$881$	10.9208	+	18.9154i	0.367932	+	0.637277i	−0.621310	+	0.783565i	$0.713399\pi$
$882$		0			0
$883$	−53.5887			−1.80340			−0.901701	−	0.432359i	$-0.857681\pi$
$883$	−53.5887			−1.80340			−0.901701	+	0.432359i	$0.857681\pi$
$884$	−13.2687	+	0.509550i	−0.446273	+	0.0171380i
$885$		0			0
$886$	38.8187			1.30414
$887$	28.3532			0.952006			0.476003	−	0.879444i	$-0.342085\pi$
$887$	28.3532			0.952006			0.476003	+	0.879444i	$0.342085\pi$
$888$		0			0
$889$	8.74605	+	15.1486i	0.293333	+	0.508068i
$890$	1.28807	−	2.23101i	0.0431763	−	0.0747835i
$891$		0			0
$892$	11.8684			0.397383
$893$	−22.1129			−0.739982
$894$		0			0
$895$	−2.22457			−0.0743591
$896$	0.779577	−	1.35027i	0.0260438	−	0.0451092i
$897$		0			0
$898$	13.3263	+	23.0818i	0.444704	+	0.770250i
$899$	−7.32352	−	12.6847i	−0.244253	−	0.423059i
$900$		0			0
$901$	−17.5355	+	30.3724i	−0.584192	+	1.01185i
$902$	−6.79130	−	11.7629i	−0.226125	−	0.391661i
$903$		0			0
$904$	6.48841	+	11.2383i	0.215801	+	0.373779i
$905$	1.40268	−	2.42952i	0.0466268	−	0.0807600i
$906$		0			0
$907$	−2.33306	+	4.04097i	−0.0774679	+	0.134178i	−0.902157	−	0.431408i	$-0.858017\pi$
$907$	−2.33306	+	4.04097i	−0.0774679	+	0.134178i	0.824689	+	0.565587i	$0.191350\pi$
$908$	4.91697	+	8.51644i	0.163175	+	0.282628i
$909$		0			0
$910$	−0.616578	−	0.979138i	−0.0204394	−	0.0324581i
$911$	−11.4290	−	19.7956i	−0.378660	−	0.655858i	0.612208	−	0.790697i	$-0.290282\pi$
$911$	−11.4290	−	19.7956i	−0.378660	−	0.655858i	−0.990868	+	0.134839i	$0.956948\pi$
$912$		0			0
$913$	−33.7546			−1.11712
$914$	−5.64143	−	9.77124i	−0.186602	−	0.323204i
$915$		0			0
$916$	−17.3118			−0.571999
$917$	0.362225	−	0.627393i	0.0119617	−	0.0207183i
$918$		0			0
$919$	−24.5610	+	42.5410i	−0.810194	+	1.40330i	0.102534	+	0.994729i	$0.467305\pi$
$919$	−24.5610	+	42.5410i	−0.810194	+	1.40330i	−0.912728	+	0.408568i	$0.866028\pi$
$920$	−0.346752	+	0.600592i	−0.0114321	+	0.0198009i
$921$		0			0
$922$	−3.88317	+	6.72585i	−0.127885	+	0.221504i
$923$	4.69874	−	8.91167i	0.154661	−	0.293331i
$924$		0			0
$925$	−21.7187	+	37.6179i	−0.714107	+	1.23687i
$926$	0.105633	+	0.182962i	0.00347132	+	0.00601250i
$927$		0			0
$928$	4.87634			0.160074
$929$	6.12850			0.201069			0.100535	−	0.994934i	$-0.467945\pi$
$929$	6.12850			0.201069			0.100535	+	0.994934i	$0.467945\pi$
$930$		0			0
$931$	17.0230	−	29.4847i	0.557907	−	0.966323i
$932$	8.82738	+	15.2895i	0.289151	+	0.500823i
$933$		0			0
$934$	−17.4458	+	30.2170i	−0.570843	+	0.988730i
$935$	2.94768			0.0963993
$936$		0			0
$937$	25.2006			0.823267			0.411634	−	0.911349i	$-0.364958\pi$
$937$	25.2006			0.823267			0.411634	+	0.911349i	$0.364958\pi$
$938$	−2.36508	+	4.09643i	−0.0772224	+	0.133753i
$939$		0			0
$940$	−0.305411	−	0.528988i	−0.00996142	−	0.0172537i
$941$	4.42221	−	7.65949i	0.144160	−	0.249692i	−0.784899	−	0.619623i	$-0.787285\pi$
$941$	4.42221	−	7.65949i	0.144160	−	0.249692i	0.929059	+	0.369931i	$0.120619\pi$
$942$		0			0
$943$	−11.7687			−0.383241
$944$	−6.60057			−0.214830
$945$		0			0
$946$	1.33480	+	2.31194i	0.0433980	+	0.0751676i
$947$	−18.0475	+	31.2593i	−0.586466	+	1.01579i	0.408225	+	0.912881i	$0.366148\pi$
$947$	−18.0475	+	31.2593i	−0.586466	+	1.01579i	−0.994691	+	0.102908i	$0.967185\pi$
$948$		0			0
$949$	−55.2553	+	2.12195i	−1.79366	+	0.0688813i
$950$	18.4708	−	31.9924i	0.599272	−	1.03797i
$951$		0			0
$952$	−2.87101	+	4.97273i	−0.0930499	+	0.161167i
$953$	−11.1990	+	19.3973i	−0.362772	+	0.628340i	−0.988416	−	0.151769i	$-0.951503\pi$
$953$	−11.1990	+	19.3973i	−0.362772	+	0.628340i	0.625644	+	0.780109i	$0.284836\pi$
$954$		0			0
$955$	−1.22597	+	2.12345i	−0.0396715	+	0.0687131i
$956$	−1.26251			−0.0408326
$957$		0			0
$958$	−3.72958	−	6.45981i	−0.120497	−	0.208707i
$959$	−24.0063			−0.775204
$960$		0			0
$961$	10.9889	+	19.0333i	0.354480	+	0.613978i
$962$	−31.5676	+	1.21228i	−1.01778	+	0.0390853i
$963$		0			0
$964$	5.44455	+	9.43023i	0.175357	+	0.303727i
$965$	2.45051	−	4.24440i	0.0788846	−	0.136632i
$966$		0			0
$967$	16.9168	−	29.3008i	0.544008	−	0.942249i	−0.454661	−	0.890665i	$-0.650240\pi$
$967$	16.9168	−	29.3008i	0.544008	−	0.942249i	0.998669	−	0.0515845i	$-0.0164271\pi$
$968$	−2.06064	−	3.56913i	−0.0662314	−	0.114716i
$969$		0			0
$970$	0.677012	+	1.17262i	0.0217376	+	0.0376506i
$971$	−6.05561	+	10.4886i	−0.194334	+	0.336596i	−0.946682	−	0.322170i	$-0.895588\pi$
$971$	−6.05561	+	10.4886i	−0.194334	+	0.336596i	0.752348	+	0.658766i	$0.228921\pi$
$972$		0			0
$973$	3.75530	+	6.50437i	0.120389	+	0.208520i
$974$	21.2844	+	36.8657i	0.681997	+	1.18125i
$975$		0			0
$976$	−2.67549	+	4.63408i	−0.0856403	+	0.148333i
$977$	6.34927			0.203131			0.101566	−	0.994829i	$-0.467615\pi$
$977$	6.34927			0.203131			0.101566	+	0.994829i	$0.467615\pi$
$978$		0			0
$979$	48.6692			1.55548
$980$	0.940449			0.0300415
$981$		0			0
$982$	−16.7098	+	28.9423i	−0.533232	+	0.923584i
$983$	−2.80169	−	4.85267i	−0.0893601	−	0.154776i	0.817881	−	0.575388i	$-0.195149\pi$
$983$	−2.80169	−	4.85267i	−0.0893601	−	0.154776i	−0.907241	+	0.420612i	$0.861816\pi$
$984$		0			0
$985$	1.58433			0.0504811
$986$	−17.9585			−0.571914
$987$		0			0
$988$	26.8468	−	1.03099i	0.854112	−	0.0328001i
$989$	2.31308			0.0735516
$990$		0			0
$991$	7.05719	+	12.2234i	0.224179	+	0.388290i	0.956073	−	0.293129i	$-0.0946966\pi$
$991$	7.05719	+	12.2234i	0.224179	+	0.388290i	−0.731894	+	0.681419i	$0.761363\pi$
$992$	3.00370			0.0953676
$993$		0			0
$994$	−2.17827	−	3.77287i	−0.0690905	−	0.119668i
$995$	−0.666573	−	1.15454i	−0.0211318	−	0.0366013i
$996$		0			0
$997$	43.6668			1.38294			0.691471	−	0.722404i	$-0.256963\pi$
$997$	43.6668			1.38294			0.691471	+	0.722404i	$0.256963\pi$
$998$	3.44081	+	5.95966i	0.108917	+	0.188650i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.g.c.523.3		12
3.2	odd	2		234.2.g.d.211.5	yes	12
9.2	odd	6		234.2.f.c.133.1	✓	12
9.7	even	3		702.2.f.d.289.3		12
13.9	even	3		702.2.f.d.685.3		12
39.35	odd	6		234.2.f.c.139.1	yes	12
117.61	even	3	inner	702.2.g.c.451.3		12
117.74	odd	6		234.2.g.d.61.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.f.c.133.1	✓	12	9.2	odd	6
234.2.f.c.139.1	yes	12	39.35	odd	6
234.2.g.d.61.5	yes	12	117.74	odd	6
234.2.g.d.211.5	yes	12	3.2	odd	2
702.2.f.d.289.3		12	9.7	even	3
702.2.f.d.685.3		12	13.9	even	3
702.2.g.c.451.3		12	117.61	even	3	inner
702.2.g.c.523.3		12	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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.102915 - 0.178255i) q^{5} -1.55915 q^{7} +1.00000 q^{8} +(0.102915 + 0.178255i) q^{10} +(-1.94430 + 3.36763i) q^{11} +(3.60290 - 0.138360i) q^{13} +(0.779577 - 1.35027i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.84139 - 3.18938i) q^{17} +(-3.72573 + 6.45316i) q^{19} -0.205831 q^{20} +(-1.94430 - 3.36763i) q^{22} -3.36930 q^{23} +(2.47882 + 4.29344i) q^{25} +(-1.68162 + 3.18938i) q^{26} +(0.779577 + 1.35027i) q^{28} +(-2.43817 + 4.22303i) q^{29} +(-1.50185 + 2.60128i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.84139 + 3.18938i) q^{34} +(-0.160461 + 0.277926i) q^{35} +(4.38086 + 7.58788i) q^{37} +(-3.72573 - 6.45316i) q^{38} +(0.102915 - 0.178255i) q^{40} +3.49292 q^{41} -0.686517 q^{43} +3.88861 q^{44} +(1.68465 - 2.91790i) q^{46} +(1.48380 + 2.57002i) q^{47} -4.56904 q^{49} -4.95763 q^{50} +(-1.92127 - 3.05102i) q^{52} -9.52297 q^{53} +(0.400197 + 0.693162i) q^{55} -1.55915 q^{56} +(-2.43817 - 4.22303i) q^{58} +(3.30029 + 5.71626i) q^{59} +5.35098 q^{61} +(-1.50185 - 2.60128i) q^{62} +1.00000 q^{64} +(0.346130 - 0.656472i) q^{65} -3.03379 q^{67} -3.68278 q^{68} +(-0.160461 - 0.277926i) q^{70} +(1.39708 - 2.41982i) q^{71} -15.3364 q^{73} -8.76173 q^{74} +7.45146 q^{76} +(3.03147 - 5.25066i) q^{77} +(0.829455 + 1.43666i) q^{79} +(0.102915 + 0.178255i) q^{80} +(-1.74646 + 3.02496i) q^{82} +(4.34020 + 7.51744i) q^{83} +(-0.379014 - 0.656472i) q^{85} +(0.343259 - 0.594541i) q^{86} +(-1.94430 + 3.36763i) q^{88} +(-6.25792 - 10.8390i) q^{89} +(-5.61747 + 0.215725i) q^{91} +(1.68465 + 2.91790i) q^{92} -2.96760 q^{94} +(0.766870 + 1.32826i) q^{95} +6.57834 q^{97} +(2.28452 - 3.95690i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} + 3 q^{5} - 2 q^{7} + 12 q^{8} + 3 q^{10} - 4 q^{11} + 4 q^{13} + q^{14} - 6 q^{16} + q^{17} + 9 q^{19} - 6 q^{20} - 4 q^{22} + 14 q^{23} - q^{25} - 5 q^{26} + q^{28} - q^{29}+ \cdots - 27 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 + 3 * q^5 - 2 * q^7 + 12 * q^8 + 3 * q^10 - 4 * q^11 + 4 * q^13 + q^14 - 6 * q^16 + q^17 + 9 * q^19 - 6 * q^20 - 4 * q^22 + 14 * q^23 - q^25 - 5 * q^26 + q^28 - q^29 + 8 * q^31 - 6 * q^32 + q^34 + 3 * q^35 + 15 * q^37 + 9 * q^38 + 3 * q^40 - 38 * q^41 + 4 * q^43 + 8 * q^44 - 7 * q^46 + 23 * q^47 + 54 * q^49 + 2 * q^50 + q^52 + 4 * q^53 + 24 * q^55 - 2 * q^56 - q^58 + 4 * q^59 + 16 * q^61 + 8 * q^62 + 12 * q^64 + 35 * q^65 - 28 * q^67 - 2 * q^68 + 3 * q^70 + 15 * q^71 - 90 * q^73 - 30 * q^74 - 18 * q^76 - 4 * q^77 - 12 * q^79 + 3 * q^80 + 19 * q^82 - 24 * q^83 + 7 * q^85 - 2 * q^86 - 4 * q^88 - 23 * q^89 + 8 * q^91 - 7 * q^92 - 46 * q^94 + 7 * q^95 + 8 * q^97 - 27 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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