LMFDB - Embedded newform 308.2.j.b.225.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(113,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("308.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.j (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 13x^{6} - 25x^{5} + 126x^{4} + 135x^{3} + 717x^{2} + 1068x + 7921 $ x^8 - x^7 + 13x^6 - 25x^5 + 126x^4 + 135x^3 + 717x^2 + 1068x + 7921
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			225.2
Root			$-1.17324 - 3.61085i$ of defining polynomial
Character	$\chi$	$=$	308.225
Dual form			308.2.j.b.141.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.11803 - 1.53884i) q^{3} +(1.17324 - 3.61085i) q^{5} +(0.809017 - 0.587785i) q^{7} +(1.19098 + 3.66547i) q^{9} +O(q^{10})$	\(q+(-2.11803 - 1.53884i) q^{3} +(1.17324 - 3.61085i) q^{5} +(0.809017 - 0.587785i) q^{7} +(1.19098 + 3.66547i) q^{9} +(-2.45354 + 2.23163i) q^{11} +(-0.482253 - 1.48422i) q^{13} +(-8.04148 + 5.84247i) q^{15} +(-0.107065 + 0.329514i) q^{17} +(-5.77892 - 4.19863i) q^{19} -2.61803 q^{21} +4.61803 q^{23} +(-7.61666 - 5.53382i) q^{25} +(0.690983 - 2.12663i) q^{27} +(-2.04285 + 1.48422i) q^{29} +(0.583918 + 1.79711i) q^{31} +(8.63079 - 0.951057i) q^{33} +(-1.17324 - 3.61085i) q^{35} +(8.23246 - 5.98123i) q^{37} +(-1.26255 + 3.88574i) q^{39} +(2.11803 + 1.53884i) q^{41} -12.9290 q^{43} +14.6328 q^{45} +(5.25021 + 3.81450i) q^{47} +(0.309017 - 0.951057i) q^{49} +(0.733838 - 0.533164i) q^{51} +(0.955767 + 2.94155i) q^{53} +(5.17949 + 11.4776i) q^{55} +(5.77892 + 17.7857i) q^{57} +(5.04285 - 3.66385i) q^{59} +(3.42567 - 10.5431i) q^{61} +(3.11803 + 2.26538i) q^{63} -5.92509 q^{65} +9.86490 q^{67} +(-9.78115 - 7.10642i) q^{69} +(3.09695 - 9.53143i) q^{71} +(-0.444798 + 0.323165i) q^{73} +(7.61666 + 23.4417i) q^{75} +(-0.673236 + 3.24758i) q^{77} +(-3.69638 - 11.3763i) q^{79} +(4.61803 - 3.35520i) q^{81} +(4.65215 - 14.3178i) q^{83} +(1.06421 + 0.773194i) q^{85} +6.61082 q^{87} -12.6480 q^{89} +(-1.26255 - 0.917299i) q^{91} +(1.52872 - 4.70490i) q^{93} +(-21.9407 + 15.9408i) q^{95} +(1.08460 + 3.33806i) q^{97} +(-11.1021 - 6.33553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} - q^{5} + 2 q^{7} + 14 q^{9}+O(q^{10}) $ 8 * q - 8 * q^3 - q^5 + 2 * q^7 + 14 * q^9	$ 8 q - 8 q^{3} - q^{5} + 2 q^{7} + 14 q^{9} - 5 q^{11} + 11 q^{13} - 4 q^{15} - 7 q^{17} - 5 q^{19} - 12 q^{21} + 28 q^{23} - 15 q^{25} + 10 q^{27} + 7 q^{29} + 3 q^{31} + q^{35} + 10 q^{37} + 9 q^{39} + 8 q^{41} - 44 q^{43} + 2 q^{45} + q^{47} - 2 q^{49} - 13 q^{51} - 6 q^{53} - 12 q^{55} + 5 q^{57} + 17 q^{59} - 23 q^{61} + 16 q^{63} - 80 q^{65} + 38 q^{67} - 38 q^{69} + 10 q^{71} - 5 q^{73} + 15 q^{75} + 5 q^{77} - 27 q^{79} + 28 q^{81} + 21 q^{83} + 38 q^{85} - 32 q^{87} + 26 q^{89} + 9 q^{91} + 12 q^{93} - 66 q^{95} - 28 q^{97} - 20 q^{99}+O(q^{100}) $ 8 * q - 8 * q^3 - q^5 + 2 * q^7 + 14 * q^9 - 5 * q^11 + 11 * q^13 - 4 * q^15 - 7 * q^17 - 5 * q^19 - 12 * q^21 + 28 * q^23 - 15 * q^25 + 10 * q^27 + 7 * q^29 + 3 * q^31 + q^35 + 10 * q^37 + 9 * q^39 + 8 * q^41 - 44 * q^43 + 2 * q^45 + q^47 - 2 * q^49 - 13 * q^51 - 6 * q^53 - 12 * q^55 + 5 * q^57 + 17 * q^59 - 23 * q^61 + 16 * q^63 - 80 * q^65 + 38 * q^67 - 38 * q^69 + 10 * q^71 - 5 * q^73 + 15 * q^75 + 5 * q^77 - 27 * q^79 + 28 * q^81 + 21 * q^83 + 38 * q^85 - 32 * q^87 + 26 * q^89 + 9 * q^91 + 12 * q^93 - 66 * q^95 - 28 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.11803	−	1.53884i	−1.22285	−	0.888451i	−0.226514	−	0.974008i	$-0.572733\pi$
$3$	−2.11803	−	1.53884i	−1.22285	−	0.888451i	−0.996333	+	0.0855571i	$0.972733\pi$
$4$		0			0
$5$	1.17324	−	3.61085i	0.524687	−	1.61482i	−0.240247	−	0.970712i	$-0.577229\pi$
$5$	1.17324	−	3.61085i	0.524687	−	1.61482i	0.764934	−	0.644109i	$-0.222771\pi$
$6$		0			0
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$		0			0
$9$	1.19098	+	3.66547i	0.396994	+	1.22182i
$10$		0			0
$11$	−2.45354	+	2.23163i	−0.739769	+	0.672861i
$11$	−2.45354	+	2.23163i	−0.739769	+	0.672861i
$12$		0			0
$13$	−0.482253	−	1.48422i	−0.133753	−	0.411649i	0.861641	−	0.507518i	$-0.169437\pi$
$13$	−0.482253	−	1.48422i	−0.133753	−	0.411649i	−0.995394	+	0.0958692i	$0.969437\pi$
$14$		0			0
$15$	−8.04148	+	5.84247i	−2.07630	+	1.50852i
$16$		0			0
$17$	−0.107065	+	0.329514i	−0.0259672	+	0.0799188i	−0.963200	−	0.268785i	$-0.913378\pi$
$17$	−0.107065	+	0.329514i	−0.0259672	+	0.0799188i	0.937233	+	0.348704i	$0.113378\pi$
$18$		0			0
$19$	−5.77892	−	4.19863i	−1.32578	−	0.963232i	−0.999841	−	0.0178403i	$-0.994321\pi$
$19$	−5.77892	−	4.19863i	−1.32578	−	0.963232i	−0.325935	−	0.945392i	$-0.605679\pi$
$20$		0			0
$21$	−2.61803			−0.571302
$22$		0			0
$23$	4.61803			0.962927			0.481463	−	0.876466i	$-0.340105\pi$
$23$	4.61803			0.962927			0.481463	+	0.876466i	$0.340105\pi$
$24$		0			0
$25$	−7.61666	−	5.53382i	−1.52333	−	1.10676i
$26$		0			0
$27$	0.690983	−	2.12663i	0.132980	−	0.409270i
$28$		0			0
$29$	−2.04285	+	1.48422i	−0.379349	+	0.275613i	−0.761077	−	0.648662i	$-0.775329\pi$
$29$	−2.04285	+	1.48422i	−0.379349	+	0.275613i	0.381728	+	0.924275i	$0.375329\pi$
$30$		0			0
$31$	0.583918	+	1.79711i	0.104875	+	0.322771i	0.989701	−	0.143150i	$-0.0457231\pi$
$31$	0.583918	+	1.79711i	0.104875	+	0.322771i	−0.884826	+	0.465921i	$0.845723\pi$
$32$		0			0
$33$	8.63079	−	0.951057i	1.50243	−	0.165558i
$34$		0			0
$35$	−1.17324	−	3.61085i	−0.198313	−	0.610345i
$36$		0			0
$37$	8.23246	−	5.98123i	1.35341	−	0.983308i	0.354574	−	0.935028i	$-0.384626\pi$
$37$	8.23246	−	5.98123i	1.35341	−	0.983308i	0.998834	−	0.0482806i	$-0.0153742\pi$
$38$		0			0
$39$	−1.26255	+	3.88574i	−0.202170	+	0.622216i
$40$		0			0
$41$	2.11803	+	1.53884i	0.330781	+	0.240327i	0.740762	−	0.671767i	$-0.234465\pi$
$41$	2.11803	+	1.53884i	0.330781	+	0.240327i	−0.409981	+	0.912094i	$0.634465\pi$
$42$		0			0
$43$	−12.9290			−1.97166			−0.985828	−	0.167760i	$-0.946347\pi$
$43$	−12.9290			−1.97166			−0.985828	+	0.167760i	$0.946347\pi$
$44$		0			0
$45$	14.6328			2.18132
$46$		0			0
$47$	5.25021	+	3.81450i	0.765821	+	0.556402i	0.900690	−	0.434462i	$-0.143061\pi$
$47$	5.25021	+	3.81450i	0.765821	+	0.556402i	−0.134869	+	0.990863i	$0.543061\pi$
$48$		0			0
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$		0			0
$51$	0.733838	−	0.533164i	0.102758	−	0.0746579i
$52$		0			0
$53$	0.955767	+	2.94155i	0.131285	+	0.404053i	0.994994	−	0.0999382i	$-0.0318645\pi$
$53$	0.955767	+	2.94155i	0.131285	+	0.404053i	−0.863709	+	0.503991i	$0.831865\pi$
$54$		0			0
$55$	5.17949	+	11.4776i	0.698402	+	1.54764i
$56$		0			0
$57$	5.77892	+	17.7857i	0.765437	+	2.35577i
$58$		0			0
$59$	5.04285	−	3.66385i	0.656524	−	0.476992i	−0.208963	−	0.977923i	$-0.567009\pi$
$59$	5.04285	−	3.66385i	0.656524	−	0.476992i	0.865487	+	0.500931i	$0.167009\pi$
$60$		0			0
$61$	3.42567	−	10.5431i	0.438612	−	1.34991i	−0.450727	−	0.892662i	$-0.648835\pi$
$61$	3.42567	−	10.5431i	0.438612	−	1.34991i	0.889339	−	0.457248i	$-0.151165\pi$
$62$		0			0
$63$	3.11803	+	2.26538i	0.392835	+	0.285412i
$64$		0			0
$65$	−5.92509			−0.734917
$66$		0			0
$67$	9.86490			1.20519			0.602595	−	0.798047i	$-0.294134\pi$
$67$	9.86490			1.20519			0.602595	+	0.798047i	$0.294134\pi$
$68$		0			0
$69$	−9.78115	−	7.10642i	−1.17751	−	0.855513i
$70$		0			0
$71$	3.09695	−	9.53143i	0.367540	−	1.13117i	−0.580835	−	0.814021i	$-0.697274\pi$
$71$	3.09695	−	9.53143i	0.367540	−	1.13117i	0.948375	−	0.317151i	$-0.102726\pi$
$72$		0			0
$73$	−0.444798	+	0.323165i	−0.0520597	+	0.0378236i	−0.613511	−	0.789686i	$-0.710243\pi$
$73$	−0.444798	+	0.323165i	−0.0520597	+	0.0378236i	0.561451	+	0.827510i	$0.310243\pi$
$74$		0			0
$75$	7.61666	+	23.4417i	0.879496	+	2.70681i
$76$		0			0
$77$	−0.673236	+	3.24758i	−0.0767223	+	0.370096i
$78$		0			0
$79$	−3.69638	−	11.3763i	−0.415876	−	1.27993i	−0.911465	−	0.411377i	$-0.865048\pi$
$79$	−3.69638	−	11.3763i	−0.415876	−	1.27993i	0.495590	−	0.868557i	$-0.334952\pi$
$80$		0			0
$81$	4.61803	−	3.35520i	0.513115	−	0.372800i
$82$		0			0
$83$	4.65215	−	14.3178i	0.510640	−	1.57159i	−0.280438	−	0.959872i	$-0.590480\pi$
$83$	4.65215	−	14.3178i	0.510640	−	1.57159i	0.791078	−	0.611716i	$-0.209520\pi$
$84$		0			0
$85$	1.06421	+	0.773194i	0.115430	+	0.0838647i
$86$		0			0
$87$	6.61082			0.708754
$88$		0			0
$89$	−12.6480			−1.34069			−0.670343	−	0.742051i	$-0.733853\pi$
$89$	−12.6480			−1.34069			−0.670343	+	0.742051i	$0.733853\pi$
$90$		0			0
$91$	−1.26255	−	0.917299i	−0.132352	−	0.0961591i
$92$		0			0
$93$	1.52872	−	4.70490i	0.158520	−	0.487876i
$94$		0			0
$95$	−21.9407	+	15.9408i	−2.25106	+	1.63549i
$96$		0			0
$97$	1.08460	+	3.33806i	0.110125	+	0.338929i	0.990899	−	0.134607i	$-0.0429773\pi$
$97$	1.08460	+	3.33806i	0.110125	+	0.338929i	−0.880774	+	0.473536i	$0.842977\pi$
$98$		0			0
$99$	−11.1021	−	6.33553i	−1.11580	−	0.636745i
$100$		0			0
$101$	2.28502	+	7.03256i	0.227368	+	0.699766i	0.998043	+	0.0625373i	$0.0199193\pi$
$101$	2.28502	+	7.03256i	0.227368	+	0.699766i	−0.770675	+	0.637229i	$0.780081\pi$
$102$		0			0
$103$	3.60390	−	2.61838i	0.355102	−	0.257997i	−0.395904	−	0.918292i	$-0.629569\pi$
$103$	3.60390	−	2.61838i	0.355102	−	0.257997i	0.751006	+	0.660295i	$0.229569\pi$
$104$		0			0
$105$	−3.07157	+	9.45332i	−0.299755	+	0.922550i
$106$		0			0
$107$	12.4485	+	9.04440i	1.20345	+	0.874355i	0.994619	−	0.103597i	$-0.0330353\pi$
$107$	12.4485	+	9.04440i	1.20345	+	0.874355i	0.208827	+	0.977953i	$0.433035\pi$
$108$		0			0
$109$	0.108188			0.0103626			0.00518128	−	0.999987i	$-0.498351\pi$
$109$	0.108188			0.0103626			0.00518128	+	0.999987i	$0.498351\pi$
$110$		0			0
$111$	−26.6408			−2.52863
$112$		0			0
$113$	−1.38960	−	1.00960i	−0.130722	−	0.0949753i	0.520503	−	0.853860i	$-0.325745\pi$
$113$	−1.38960	−	1.00960i	−0.130722	−	0.0949753i	−0.651225	+	0.758885i	$0.725745\pi$
$114$		0			0
$115$	5.41804	−	16.6750i	0.505235	−	1.55495i
$116$		0			0
$117$	4.86601	−	3.53536i	0.449863	−	0.326844i
$118$		0			0
$119$	0.107065	+	0.329514i	0.00981468	+	0.0302065i
$120$		0			0
$121$	1.03968	−	10.9508i	0.0945168	−	0.995523i
$122$		0			0
$123$	−2.11803	−	6.51864i	−0.190977	−	0.587766i
$124$		0			0
$125$	−13.5601	+	9.85197i	−1.21285	+	0.881187i
$126$		0			0
$127$	5.54911	−	17.0784i	0.492404	−	1.51546i	−0.328561	−	0.944483i	$-0.606564\pi$
$127$	5.54911	−	17.0784i	0.492404	−	1.51546i	0.820964	−	0.570980i	$-0.193436\pi$
$128$		0			0
$129$	27.3841	+	19.8957i	2.41103	+	1.75172i
$130$		0			0
$131$	−4.51843			−0.394777			−0.197389	−	0.980325i	$-0.563246\pi$
$131$	−4.51843			−0.394777			−0.197389	+	0.980325i	$0.563246\pi$
$132$		0			0
$133$	−7.14314			−0.619389
$134$		0			0
$135$	−6.86824	−	4.99007i	−0.591124	−	0.429477i
$136$		0			0
$137$	−5.43664	+	16.7323i	−0.464484	+	1.42953i	0.395147	+	0.918618i	$0.370694\pi$
$137$	−5.43664	+	16.7323i	−0.464484	+	1.42953i	−0.859631	+	0.510916i	$0.829306\pi$
$138$		0			0
$139$	2.75021	−	1.99814i	0.233269	−	0.169480i	−0.465010	−	0.885305i	$-0.653949\pi$
$139$	2.75021	−	1.99814i	0.233269	−	0.169480i	0.698280	+	0.715825i	$0.253949\pi$
$140$		0			0
$141$	−5.25021	−	16.1585i	−0.442147	−	1.36079i
$142$		0			0
$143$	4.49545	+	2.56538i	0.375929	+	0.214528i
$144$		0			0
$145$	2.96255	+	9.11778i	0.246026	+	0.757190i
$146$		0			0
$147$	−2.11803	+	1.53884i	−0.174692	+	0.126922i
$148$		0			0
$149$	−5.90930	+	18.1870i	−0.484109	+	1.48993i	0.349158	+	0.937064i	$0.386468\pi$
$149$	−5.90930	+	18.1870i	−0.484109	+	1.48993i	−0.833267	+	0.552871i	$0.813532\pi$
$150$		0			0
$151$	−4.59155	−	3.33596i	−0.373655	−	0.271476i	0.385070	−	0.922887i	$-0.374177\pi$
$151$	−4.59155	−	3.33596i	−0.373655	−	0.271476i	−0.758725	+	0.651411i	$0.774177\pi$
$152$		0			0
$153$	−1.33534			−0.107955
$154$		0			0
$155$	7.17418			0.576244
$156$		0			0
$157$	2.77129	+	2.01346i	0.221173	+	0.160692i	0.692855	−	0.721077i	$-0.256353\pi$
$157$	2.77129	+	2.01346i	0.221173	+	0.160692i	−0.471681	+	0.881769i	$0.656353\pi$
$158$		0			0
$159$	2.50223	−	7.70107i	0.198440	−	0.610735i
$160$		0			0
$161$	3.73607	−	2.71441i	0.294443	−	0.213926i
$162$		0			0
$163$	5.57835	+	17.1684i	0.436930	+	1.34473i	0.891096	+	0.453815i	$0.149937\pi$
$163$	5.57835	+	17.1684i	0.436930	+	1.34473i	−0.454166	+	0.890917i	$0.650063\pi$
$164$		0			0
$165$	6.69183	−	32.2803i	0.520959	−	2.51302i
$166$		0			0
$167$	1.42620	+	4.38939i	0.110363	+	0.339661i	0.990952	−	0.134220i	$-0.0428528\pi$
$167$	1.42620	+	4.38939i	0.110363	+	0.339661i	−0.880589	+	0.473881i	$0.842853\pi$
$168$		0			0
$169$	8.54688	−	6.20967i	0.657452	−	0.477667i
$170$		0			0
$171$	8.50736	−	26.1830i	0.650574	−	2.00226i
$172$		0			0
$173$	−10.0778	−	7.32197i	−0.766203	−	0.556679i	0.134604	−	0.990899i	$-0.457024\pi$
$173$	−10.0778	−	7.32197i	−0.766203	−	0.556679i	−0.900807	+	0.434221i	$0.857024\pi$
$174$		0			0
$175$	−9.41470			−0.711685
$176$		0			0
$177$	−16.3190			−1.22661
$178$		0			0
$179$	−5.65077	−	4.10553i	−0.422359	−	0.306861i	0.356228	−	0.934399i	$-0.384063\pi$
$179$	−5.65077	−	4.10553i	−0.422359	−	0.306861i	−0.778586	+	0.627538i	$0.784063\pi$
$180$		0			0
$181$	−4.73331	+	14.5676i	−0.351824	+	1.08280i	0.606004	+	0.795462i	$0.292772\pi$
$181$	−4.73331	+	14.5676i	−0.351824	+	1.08280i	−0.957828	+	0.287342i	$0.907228\pi$
$182$		0			0
$183$	−23.4799	+	17.0592i	−1.73568	+	1.26105i
$184$		0			0
$185$	−11.9387	−	36.7436i	−0.877751	−	2.70144i
$186$		0			0
$187$	−0.472662	−	1.04740i	−0.0345645	−	0.0765938i
$188$		0			0
$189$	−0.690983	−	2.12663i	−0.0502616	−	0.154689i
$190$		0			0
$191$	4.36422	−	3.17079i	0.315784	−	0.229430i	−0.418590	−	0.908175i	$-0.637476\pi$
$191$	4.36422	−	3.17079i	0.315784	−	0.229430i	0.734374	+	0.678745i	$0.237476\pi$
$192$		0			0
$193$	2.64992	−	8.15562i	0.190745	−	0.587054i	−0.809254	−	0.587458i	$-0.800129\pi$
$193$	2.64992	−	8.15562i	0.190745	−	0.587054i	1.00000		0.000404158i	$0.000128647\pi$
$194$		0			0
$195$	12.5495	+	9.11778i	0.898692	+	0.652938i
$196$		0			0
$197$	6.40803			0.456553			0.228277	−	0.973596i	$-0.426691\pi$
$197$	6.40803			0.456553			0.228277	+	0.973596i	$0.426691\pi$
$198$		0			0
$199$	−7.14760			−0.506680			−0.253340	−	0.967377i	$-0.581529\pi$
$199$	−7.14760			−0.506680			−0.253340	+	0.967377i	$0.581529\pi$
$200$		0			0
$201$	−20.8942	−	15.1805i	−1.47376	−	1.07075i
$202$		0			0
$203$	−0.780301	+	2.40152i	−0.0547664	+	0.168554i
$204$		0			0
$205$	8.04148	−	5.84247i	0.561641	−	0.408056i
$206$		0			0
$207$	5.50000	+	16.9273i	0.382276	+	1.17653i
$208$		0			0
$209$	23.5486	−	2.59490i	1.62889	−	0.179493i
$210$		0			0
$211$	4.71626	+	14.5151i	0.324681	+	0.999264i	0.971585	+	0.236693i	$0.0760634\pi$
$211$	4.71626	+	14.5151i	0.324681	+	0.999264i	−0.646904	+	0.762571i	$0.723937\pi$
$212$		0			0
$213$	−21.2268	+	15.4222i	−1.45444	+	1.05671i
$214$		0			0
$215$	−15.1688	+	46.6847i	−1.03450	+	3.18387i
$216$		0			0
$217$	1.52872	+	1.11068i	0.103776	+	0.0753977i
$218$		0			0
$219$	1.43940			0.0972655
$220$		0			0
$221$	0.540704			0.0363717
$222$		0			0
$223$	−12.3615	−	8.98113i	−0.827785	−	0.601421i	0.0911470	−	0.995837i	$-0.470947\pi$
$223$	−12.3615	−	8.98113i	−0.827785	−	0.601421i	−0.918932	+	0.394417i	$0.870947\pi$
$224$		0			0
$225$	11.2128	−	34.5093i	0.747517	−	2.30062i
$226$		0			0
$227$	5.10792	−	3.71112i	0.339024	−	0.246316i	−0.405226	−	0.914217i	$-0.632807\pi$
$227$	5.10792	−	3.71112i	0.339024	−	0.246316i	0.744250	+	0.667901i	$0.232807\pi$
$228$		0			0
$229$	−0.570886	−	1.75701i	−0.0377252	−	0.116106i	0.930420	−	0.366494i	$-0.119442\pi$
$229$	−0.570886	−	1.75701i	−0.0377252	−	0.116106i	−0.968146	+	0.250388i	$0.919442\pi$
$230$		0			0
$231$	6.42344	−	5.84247i	0.422631	−	0.384407i
$232$		0			0
$233$	4.80345	+	14.7835i	0.314684	+	0.968499i	0.975884	+	0.218289i	$0.0700476\pi$
$233$	4.80345	+	14.7835i	0.314684	+	0.968499i	−0.661200	+	0.750210i	$0.729952\pi$
$234$		0			0
$235$	19.9333	−	14.4824i	1.30031	−	0.944727i
$236$		0			0
$237$	−9.67726	+	29.7835i	−0.628605	+	1.93465i
$238$		0			0
$239$	17.1922	+	12.4909i	1.11207	+	0.807969i	0.982989	−	0.183664i	$-0.0587960\pi$
$239$	17.1922	+	12.4909i	1.11207	+	0.807969i	0.129085	+	0.991634i	$0.458796\pi$
$240$		0			0
$241$	−27.6283			−1.77969			−0.889847	−	0.456258i	$-0.849189\pi$
$241$	−27.6283			−1.77969			−0.889847	+	0.456258i	$0.849189\pi$
$242$		0			0
$243$	−21.6525			−1.38901
$244$		0			0
$245$	−3.07157	−	2.23163i	−0.196235	−	0.142573i
$246$		0			0
$247$	−3.44480	+	10.6020i	−0.219187	+	0.674589i
$248$		0			0
$249$	−31.8863	+	23.1668i	−2.02071	+	1.46813i
$250$		0			0
$251$	−3.02872	−	9.32143i	−0.191171	−	0.588363i	−1.00000		0.000319602i	$-0.999898\pi$
$251$	−3.02872	−	9.32143i	−0.191171	−	0.588363i	0.808829	−	0.588044i	$-0.200102\pi$
$252$		0			0
$253$	−11.3305	+	10.3057i	−0.712343	+	0.647916i
$254$		0			0
$255$	−1.06421	−	3.27530i	−0.0666435	−	0.205107i
$256$		0			0
$257$	19.4106	−	14.1026i	1.21080	−	0.879696i	0.215495	−	0.976505i	$-0.430863\pi$
$257$	19.4106	−	14.1026i	1.21080	−	0.879696i	0.995303	+	0.0968087i	$0.0308635\pi$
$258$		0			0
$259$	3.14452	−	9.67784i	0.195391	−	0.601351i
$260$		0			0
$261$	−7.87337	−	5.72034i	−0.487349	−	0.354080i
$262$		0			0
$263$	19.8086			1.22145			0.610726	−	0.791842i	$-0.290878\pi$
$263$	19.8086			1.22145			0.610726	+	0.791842i	$0.290878\pi$
$264$		0			0
$265$	11.7428			0.721356
$266$		0			0
$267$	26.7889	+	19.4633i	1.63946	+	1.19113i
$268$		0			0
$269$	0.834395	−	2.56800i	0.0508740	−	0.156574i	−0.922392	−	0.386255i	$-0.873768\pi$
$269$	0.834395	−	2.56800i	0.0508740	−	0.156574i	0.973266	+	0.229681i	$0.0737684\pi$
$270$		0			0
$271$	−1.21859	+	0.885358i	−0.0740242	+	0.0537817i	−0.624182	−	0.781279i	$-0.714568\pi$
$271$	−1.21859	+	0.885358i	−0.0740242	+	0.0537817i	0.550158	+	0.835061i	$0.314568\pi$
$272$		0			0
$273$	1.26255	+	3.88574i	0.0764132	+	0.235176i
$274$		0			0
$275$	31.0372	−	3.42009i	1.87161	−	0.206239i
$276$		0			0
$277$	0.896957	+	2.76055i	0.0538929	+	0.165865i	0.974380	−	0.224907i	$-0.0722079\pi$
$277$	0.896957	+	2.76055i	0.0538929	+	0.165865i	−0.920487	+	0.390773i	$0.872208\pi$
$278$		0			0
$279$	−5.89183	+	4.28066i	−0.352734	+	0.256277i
$280$		0			0
$281$	−6.11384	+	18.8165i	−0.364721	+	1.12250i	0.585434	+	0.810720i	$0.300924\pi$
$281$	−6.11384	+	18.8165i	−0.364721	+	1.12250i	−0.950155	+	0.311777i	$0.899076\pi$
$282$		0			0
$283$	12.9921	+	9.43932i	0.772301	+	0.561110i	0.902659	−	0.430358i	$-0.141613\pi$
$283$	12.9921	+	9.43932i	0.772301	+	0.561110i	−0.130358	+	0.991467i	$0.541613\pi$
$284$		0			0
$285$	71.0015			4.20576
$286$		0			0
$287$	2.61803			0.154538
$288$		0			0
$289$	13.6562	+	9.92179i	0.803304	+	0.583635i
$290$		0			0
$291$	2.83952	−	8.73916i	0.166456	−	0.512299i
$292$		0			0
$293$	19.8491	−	14.4212i	1.15960	−	0.842497i	0.169871	−	0.985466i	$-0.445665\pi$
$293$	19.8491	−	14.4212i	1.15960	−	0.842497i	0.989727	+	0.142969i	$0.0456650\pi$
$294$		0			0
$295$	−7.31314	−	22.5075i	−0.425788	−	1.31044i
$296$		0			0
$297$	3.05049	+	6.75977i	0.177007	+	0.392242i
$298$		0			0
$299$	−2.22706	−	6.85418i	−0.128794	−	0.396388i
$300$		0			0
$301$	−10.4598	+	7.59948i	−0.602892	+	0.438027i
$302$		0			0
$303$	5.98225	−	18.4115i	0.343671	−	1.05771i
$304$		0			0
$305$	−34.0505	−	24.7392i	−1.94973	−	1.41656i
$306$		0			0
$307$	8.73202			0.498363			0.249181	−	0.968457i	$-0.419838\pi$
$307$	8.73202			0.498363			0.249181	+	0.968457i	$0.419838\pi$
$308$		0			0
$309$	−11.6624			−0.663454
$310$		0			0
$311$	20.5013	+	14.8950i	1.16252	+	0.844620i	0.990095	−	0.140402i	$-0.0448396\pi$
$311$	20.5013	+	14.8950i	1.16252	+	0.844620i	0.172426	+	0.985023i	$0.444840\pi$
$312$		0			0
$313$	4.79376	−	14.7537i	0.270959	−	0.833926i	−0.719301	−	0.694698i	$-0.755538\pi$
$313$	4.79376	−	14.7537i	0.270959	−	0.833926i	0.990260	−	0.139228i	$-0.0444621\pi$
$314$		0			0
$315$	11.8381	−	8.60092i	0.667004	−	0.484607i
$316$		0			0
$317$	−0.0743274	−	0.228756i	−0.00417464	−	0.0128482i	0.948947	−	0.315434i	$-0.102150\pi$
$317$	−0.0743274	−	0.228756i	−0.00417464	−	0.0128482i	−0.953122	+	0.302586i	$0.902150\pi$
$318$		0			0
$319$	1.69999	−	8.20048i	0.0951813	−	0.459139i
$320$		0			0
$321$	−12.4485	−	38.3127i	−0.694810	−	2.13841i
$322$		0			0
$323$	2.00223	−	1.45471i	0.111407	−	0.0809420i
$324$		0			0
$325$	−4.54027	+	13.9735i	−0.251849	+	0.775110i
$326$		0			0
$327$	−0.229146	−	0.166485i	−0.0126718	−	0.00920662i
$328$		0			0
$329$	6.48961			0.357784
$330$		0			0
$331$	16.2480			0.893073			0.446536	−	0.894766i	$-0.352657\pi$
$331$	16.2480			0.893073			0.446536	+	0.894766i	$0.352657\pi$
$332$		0			0
$333$	31.7287	+	23.0523i	1.73872	+	1.26326i
$334$		0			0
$335$	11.5739	−	35.6207i	0.632347	−	1.94616i
$336$		0			0
$337$	−11.6436	+	8.45954i	−0.634265	+	0.460820i	−0.857875	−	0.513858i	$-0.828216\pi$
$337$	−11.6436	+	8.45954i	−0.634265	+	0.460820i	0.223610	+	0.974679i	$0.428216\pi$
$338$		0			0
$339$	1.38960	+	4.27674i	0.0754725	+	0.232281i
$340$		0			0
$341$	−5.44315	−	3.10620i	−0.294763	−	0.168210i
$342$		0			0
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$		0			0
$345$	−37.1358	+	26.9807i	−1.99932	+	1.45259i
$346$		0			0
$347$	0.479338	−	1.47525i	0.0257322	−	0.0791956i	−0.937366	−	0.348347i	$-0.886743\pi$
$347$	0.479338	−	1.47525i	0.0257322	−	0.0791956i	0.963098	+	0.269151i	$0.0867431\pi$
$348$		0			0
$349$	26.5297	+	19.2750i	1.42010	+	1.03177i	0.991755	+	0.128151i	$0.0409043\pi$
$349$	26.5297	+	19.2750i	1.42010	+	1.03177i	0.428348	+	0.903614i	$0.359096\pi$
$350$		0			0
$351$	−3.48961			−0.186262
$352$		0			0
$353$	3.46992			0.184685			0.0923426	−	0.995727i	$-0.470564\pi$
$353$	3.46992			0.184685			0.0923426	+	0.995727i	$0.470564\pi$
$354$		0			0
$355$	−30.7831	−	22.3652i	−1.63380	−	1.18702i
$356$		0			0
$357$	0.280301	−	0.862678i	0.0148351	−	0.0456578i
$358$		0			0
$359$	−17.7812	+	12.9188i	−0.938453	+	0.681826i	−0.948048	−	0.318128i	$-0.896946\pi$
$359$	−17.7812	+	12.9188i	−0.938453	+	0.681826i	0.00959451	+	0.999954i	$0.496946\pi$
$360$		0			0
$361$	9.89610	+	30.4571i	0.520848	+	1.60300i
$362$		0			0
$363$	−19.0536	+	21.5942i	−1.00005	+	1.13340i
$364$		0			0
$365$	0.645046	+	1.98525i	0.0337633	+	0.103913i
$366$		0			0
$367$	−19.3278	+	14.0424i	−1.00890	+	0.733009i	−0.963978	−	0.265981i	$-0.914304\pi$
$367$	−19.3278	+	14.0424i	−1.00890	+	0.733009i	−0.0449226	+	0.998990i	$0.514304\pi$
$368$		0			0
$369$	−3.11803	+	9.59632i	−0.162318	+	0.499565i
$370$		0			0
$371$	2.50223	+	1.81798i	0.129909	+	0.0943846i
$372$		0			0
$373$	−9.07767			−0.470024			−0.235012	−	0.971993i	$-0.575513\pi$
$373$	−9.07767			−0.470024			−0.235012	+	0.971993i	$0.575513\pi$
$374$		0			0
$375$	43.8813			2.26602
$376$		0			0
$377$	3.18808	+	2.31628i	0.164195	+	0.119294i
$378$		0			0
$379$	−2.64796	+	8.14959i	−0.136017	+	0.418616i	−0.995747	−	0.0921325i	$-0.970632\pi$
$379$	−2.64796	+	8.14959i	−0.136017	+	0.418616i	0.859730	+	0.510749i	$0.170632\pi$
$380$		0			0
$381$	−38.0341	+	27.6334i	−1.94855	+	1.41570i
$382$		0			0
$383$	4.69809	+	14.4592i	0.240061	+	0.738832i	0.996410	+	0.0846631i	$0.0269814\pi$
$383$	4.69809	+	14.4592i	0.240061	+	0.738832i	−0.756349	+	0.654169i	$0.773019\pi$
$384$		0			0
$385$	10.9366	+	6.24112i	0.557383	+	0.318077i
$386$		0			0
$387$	−15.3982	−	47.3909i	−0.782736	−	2.40901i
$388$		0			0
$389$	−15.8938	+	11.5475i	−0.805846	+	0.585481i	−0.912623	−	0.408802i	$-0.865947\pi$
$389$	−15.8938	+	11.5475i	−0.805846	+	0.585481i	0.106777	+	0.994283i	$0.465947\pi$
$390$		0			0
$391$	−0.494432	+	1.52171i	−0.0250045	+	0.0769559i
$392$		0			0
$393$	9.57019	+	6.95315i	0.482752	+	0.350740i
$394$		0			0
$395$	−45.4148			−2.28507
$396$		0			0
$397$	−7.52681			−0.377760			−0.188880	−	0.982000i	$-0.560486\pi$
$397$	−7.52681			−0.377760			−0.188880	+	0.982000i	$0.560486\pi$
$398$		0			0
$399$	15.1294	+	10.9922i	0.757418	+	0.550297i
$400$		0			0
$401$	4.59806	−	14.1514i	0.229616	−	0.706685i	−0.768174	−	0.640241i	$-0.778835\pi$
$401$	4.59806	−	14.1514i	0.229616	−	0.706685i	0.997790	−	0.0664444i	$-0.0211655\pi$
$402$		0			0
$403$	2.38572	−	1.73333i	0.118841	−	0.0863431i
$404$		0			0
$405$	−6.69707	−	20.6115i	−0.332780	−	1.02419i
$406$		0			0
$407$	−6.85076	+	33.0469i	−0.339580	+	1.63808i
$408$		0			0
$409$	2.01165	+	6.19123i	0.0994698	+	0.306137i	0.988393	−	0.151920i	$-0.0485456\pi$
$409$	2.01165	+	6.19123i	0.0994698	+	0.306137i	−0.888923	+	0.458057i	$0.848546\pi$
$410$		0			0
$411$	37.2633	−	27.0734i	1.83806	−	1.33543i
$412$		0			0
$413$	1.92620	−	5.92823i	0.0947821	−	0.291709i
$414$		0			0
$415$	−46.2415	−	33.5964i	−2.26991	−	1.64918i
$416$		0			0
$417$	−8.89986			−0.435828
$418$		0			0
$419$	−12.9129			−0.630837			−0.315418	−	0.948953i	$-0.602145\pi$
$419$	−12.9129			−0.630837			−0.315418	+	0.948953i	$0.602145\pi$
$420$		0			0
$421$	−19.8381	−	14.4133i	−0.966852	−	0.702459i	−0.0121201	−	0.999927i	$-0.503858\pi$
$421$	−19.8381	−	14.4133i	−0.966852	−	0.702459i	−0.954732	+	0.297467i	$0.903858\pi$
$422$		0			0
$423$	−7.72902	+	23.7875i	−0.375798	+	1.15659i
$424$		0			0
$425$	2.63895	−	1.91731i	0.128008	−	0.0930032i
$426$		0			0
$427$	−3.42567	−	10.5431i	−0.165780	−	0.510218i
$428$		0			0
$429$	−5.57380	−	12.3514i	−0.269106	−	0.596329i
$430$		0			0
$431$	−5.58794	−	17.1979i	−0.269162	−	0.828394i	−0.990705	−	0.136025i	$-0.956567\pi$
$431$	−5.58794	−	17.1979i	−0.269162	−	0.828394i	0.721544	−	0.692369i	$-0.243433\pi$
$432$		0			0
$433$	22.0627	−	16.0295i	1.06027	−	0.770329i	0.0861289	−	0.996284i	$-0.472550\pi$
$433$	22.0627	−	16.0295i	1.06027	−	0.770329i	0.974138	+	0.225955i	$0.0725503\pi$
$434$		0			0
$435$	7.75605	−	23.8707i	0.371874	−	1.14451i
$436$		0			0
$437$	−26.6873	−	19.3894i	−1.27662	−	0.927522i
$438$		0			0
$439$	−19.5604			−0.933566			−0.466783	−	0.884372i	$-0.654587\pi$
$439$	−19.5604			−0.933566			−0.466783	+	0.884372i	$0.654587\pi$
$440$		0			0
$441$	3.85410			0.183529
$442$		0			0
$443$	−12.6839	−	9.21543i	−0.602633	−	0.437838i	0.244180	−	0.969730i	$-0.421481\pi$
$443$	−12.6839	−	9.21543i	−0.602633	−	0.437838i	−0.846812	+	0.531892i	$0.821481\pi$
$444$		0			0
$445$	−14.8391	+	45.6701i	−0.703441	+	2.16497i
$446$		0			0
$447$	40.5030	−	29.4271i	1.91572	−	1.39186i
$448$		0			0
$449$	−6.66227	−	20.5043i	−0.314412	−	0.967660i	−0.975996	−	0.217789i	$-0.930116\pi$
$449$	−6.66227	−	20.5043i	−0.314412	−	0.967660i	0.661584	−	0.749871i	$-0.269884\pi$
$450$		0			0
$451$	−8.63079	+	0.951057i	−0.406408	+	0.0447835i
$452$		0			0
$453$	4.59155	+	14.1313i	0.215730	+	0.663948i
$454$		0			0
$455$	−4.79350	+	3.48268i	−0.224723	+	0.163271i
$456$		0			0
$457$	0.0823812	−	0.253543i	0.00385363	−	0.0118603i	−0.949111	−	0.314941i	$-0.898015\pi$
$457$	0.0823812	−	0.253543i	0.00385363	−	0.0118603i	0.952965	+	0.303081i	$0.0980152\pi$
$458$		0			0
$459$	0.626772	+	0.455377i	0.0292552	+	0.0212552i
$460$		0			0
$461$	−23.1709			−1.07918			−0.539588	−	0.841929i	$-0.681420\pi$
$461$	−23.1709			−1.07918			−0.539588	+	0.841929i	$0.681420\pi$
$462$		0			0
$463$	25.5690			1.18829			0.594146	−	0.804357i	$-0.297490\pi$
$463$	25.5690			1.18829			0.594146	+	0.804357i	$0.297490\pi$
$464$		0			0
$465$	−15.1951	−	11.0399i	−0.704658	−	0.511964i
$466$		0			0
$467$	−5.28020	+	16.2508i	−0.244338	+	0.751996i	0.751406	+	0.659840i	$0.229376\pi$
$467$	−5.28020	+	16.2508i	−0.244338	+	0.751996i	−0.995745	+	0.0921563i	$0.970624\pi$
$468$		0			0
$469$	7.98087	−	5.79844i	0.368523	−	0.267747i
$470$		0			0
$471$	−2.77129	−	8.52916i	−0.127694	−	0.393003i
$472$		0			0
$473$	31.7218	−	28.8527i	1.45857	−	1.32665i
$474$		0			0
$475$	20.7816	+	63.9591i	0.953524	+	2.93464i
$476$		0			0
$477$	−9.64385	+	7.00667i	−0.441562	+	0.320813i
$478$		0			0
$479$	−4.68506	+	14.4191i	−0.214066	+	0.658826i	0.785153	+	0.619302i	$0.212584\pi$
$479$	−4.68506	+	14.4191i	−0.214066	+	0.658826i	−0.999219	+	0.0395245i	$0.987416\pi$
$480$		0			0
$481$	−12.8476	−	9.33432i	−0.585800	−	0.425609i
$482$		0			0
$483$	−12.0902			−0.550122
$484$		0			0
$485$	13.3257			0.605090
$486$		0			0
$487$	2.55203	+	1.85416i	0.115644	+	0.0840200i	0.644104	−	0.764938i	$-0.277230\pi$
$487$	2.55203	+	1.85416i	0.115644	+	0.0840200i	−0.528460	+	0.848958i	$0.677230\pi$
$488$		0			0
$489$	14.6043	−	44.9474i	0.660430	−	2.03259i
$490$		0			0
$491$	15.5688	−	11.3114i	0.702611	−	0.510477i	−0.178171	−	0.984000i	$-0.557018\pi$
$491$	15.5688	−	11.3114i	0.702611	−	0.510477i	0.880781	+	0.473523i	$0.157018\pi$
$492$		0			0
$493$	−0.270352	−	0.832057i	−0.0121760	−	0.0374740i
$494$		0			0
$495$	−35.9020	+	32.6548i	−1.61367	+	1.46773i
$496$		0			0
$497$	−3.09695	−	9.53143i	−0.138917	−	0.427543i
$498$		0			0
$499$	15.9739	−	11.6057i	0.715091	−	0.519544i	−0.169721	−	0.985492i	$-0.554287\pi$
$499$	15.9739	−	11.6057i	0.715091	−	0.519544i	0.884812	+	0.465948i	$0.154287\pi$
$500$		0			0
$501$	3.73384	−	11.4916i	0.166816	−	0.513406i
$502$		0			0
$503$	−24.1390	−	17.5380i	−1.07631	−	0.781981i	−0.0992701	−	0.995061i	$-0.531651\pi$
$503$	−24.1390	−	17.5380i	−1.07631	−	0.781981i	−0.977035	+	0.213079i	$0.931651\pi$
$504$		0			0
$505$	28.0744			1.24929
$506$		0			0
$507$	−27.6583			−1.22835
$508$		0			0
$509$	1.59445	+	1.15843i	0.0706727	+	0.0513467i	0.622561	−	0.782572i	$-0.286092\pi$
$509$	1.59445	+	1.15843i	0.0706727	+	0.0513467i	−0.551888	+	0.833918i	$0.686092\pi$
$510$		0			0
$511$	−0.169898	+	0.522892i	−0.00751584	+	0.0231314i
$512$		0			0
$513$	−12.9221	+	9.38843i	−0.570523	+	0.414509i
$514$		0			0
$515$	−5.22636	−	16.0851i	−0.230301	−	0.708794i
$516$		0			0
$517$	−21.3941	+	2.35749i	−0.940912	+	0.103682i
$518$		0			0
$519$	10.0778	+	31.0164i	0.442367	+	1.36147i
$520$		0			0
$521$	−4.59806	+	3.34068i	−0.201445	+	0.146358i	−0.683934	−	0.729544i	$-0.739733\pi$
$521$	−4.59806	+	3.34068i	−0.201445	+	0.146358i	0.482490	+	0.875902i	$0.339733\pi$
$522$		0			0
$523$	5.00796	−	15.4129i	0.218983	−	0.673959i	−0.779864	−	0.625949i	$-0.784712\pi$
$523$	5.00796	−	15.4129i	0.218983	−	0.673959i	0.998847	−	0.0480105i	$-0.0152881\pi$
$524$		0			0
$525$	19.9407	+	14.4877i	0.870282	+	0.632297i
$526$		0			0
$527$	−0.654691			−0.0285188
$528$		0			0
$529$	−1.67376			−0.0727723
$530$		0			0
$531$	19.4357	+	14.1208i	0.843437	+	0.612792i
$532$		0			0
$533$	1.26255	−	3.88574i	0.0546873	−	0.168310i
$534$		0			0
$535$	47.2630	−	34.3386i	2.04336	−	1.48459i
$536$		0			0
$537$	5.65077	+	17.3913i	0.243849	+	0.750489i
$538$		0			0
$539$	1.36422	+	3.02306i	0.0587611	+	0.130213i
$540$		0			0
$541$	0.967158	+	2.97661i	0.0415814	+	0.127974i	0.969692	−	0.244330i	$-0.0785679\pi$
$541$	0.967158	+	2.97661i	0.0415814	+	0.127974i	−0.928111	+	0.372304i	$0.878568\pi$
$542$		0			0
$543$	32.4426	−	23.5709i	1.39225	−	1.01153i
$544$		0			0
$545$	0.126930	−	0.390651i	0.00543709	−	0.0167337i
$546$		0			0
$547$	−6.21747	−	4.51726i	−0.265840	−	0.193144i	0.446878	−	0.894595i	$-0.352536\pi$
$547$	−6.21747	−	4.51726i	−0.265840	−	0.193144i	−0.712718	+	0.701451i	$0.752536\pi$
$548$		0			0
$549$	42.7255			1.82348
$550$		0			0
$551$	18.0372			0.768410
$552$		0			0
$553$	−9.67726	−	7.03094i	−0.411519	−	0.298986i
$554$		0			0
$555$	−31.2559	+	96.1959i	−1.32674	+	4.08329i
$556$		0			0
$557$	11.8043	−	8.57633i	0.500164	−	0.363391i	−0.308915	−	0.951090i	$-0.599966\pi$
$557$	11.8043	−	8.57633i	0.500164	−	0.363391i	0.809080	+	0.587699i	$0.199966\pi$
$558$		0			0
$559$	6.23505	+	19.1895i	0.263714	+	0.811630i
$560$		0			0
$561$	−0.610674	+	2.94579i	−0.0257827	+	0.124371i
$562$		0			0
$563$	−1.12868	−	3.47371i	−0.0475681	−	0.146399i	0.924451	−	0.381300i	$-0.124524\pi$
$563$	−1.12868	−	3.47371i	−0.0475681	−	0.146399i	−0.972019	+	0.234901i	$0.924524\pi$
$564$		0			0
$565$	−5.27584	+	3.83312i	−0.221956	+	0.161261i
$566$		0			0
$567$	1.76393	−	5.42882i	0.0740782	−	0.227989i
$568$		0			0
$569$	29.0090	+	21.0763i	1.21612	+	0.883564i	0.995772	−	0.0918564i	$-0.0292801\pi$
$569$	29.0090	+	21.0763i	1.21612	+	0.883564i	0.220350	+	0.975421i	$0.429280\pi$
$570$		0			0
$571$	−21.4344			−0.897003			−0.448501	−	0.893782i	$-0.648042\pi$
$571$	−21.4344			−0.897003			−0.448501	+	0.893782i	$0.648042\pi$
$572$		0			0
$573$	−14.1229			−0.589993
$574$		0			0
$575$	−35.1740	−	25.5554i	−1.46686	−	1.06573i
$576$		0			0
$577$	−5.49545	+	16.9133i	−0.228779	+	0.704108i	0.769107	+	0.639120i	$0.220701\pi$
$577$	−5.49545	+	16.9133i	−0.228779	+	0.704108i	−0.997886	+	0.0649886i	$0.979299\pi$
$578$		0			0
$579$	−18.1628	+	13.1961i	−0.754821	+	0.548410i
$580$		0			0
$581$	−4.65215	−	14.3178i	−0.193004	−	0.594004i
$582$		0			0
$583$	−8.90945	−	5.08428i	−0.368992	−	0.210569i
$584$		0			0
$585$	−7.05668	−	21.7182i	−0.291758	−	0.897939i
$586$		0			0
$587$	−26.1922	+	19.0298i	−1.08107	+	0.785443i	−0.977869	−	0.209217i	$-0.932908\pi$
$587$	−26.1922	+	19.0298i	−1.08107	+	0.785443i	−0.103201	+	0.994661i	$0.532908\pi$
$588$		0			0
$589$	4.17101	−	12.8370i	0.171863	−	0.528941i
$590$		0			0
$591$	−13.5724	−	9.86094i	−0.558295	−	0.405625i
$592$		0			0
$593$	20.3600			0.836086			0.418043	−	0.908427i	$-0.362716\pi$
$593$	20.3600			0.836086			0.418043	+	0.908427i	$0.362716\pi$
$594$		0			0
$595$	1.31544			0.0539277
$596$		0			0
$597$	15.1389	+	10.9990i	0.619592	+	0.450160i
$598$		0			0
$599$	−0.371421	+	1.14311i	−0.0151758	+	0.0467064i	−0.958358	−	0.285571i	$-0.907817\pi$
$599$	−0.371421	+	1.14311i	−0.0151758	+	0.0467064i	0.943182	+	0.332277i	$0.107817\pi$
$600$		0			0
$601$	6.43289	−	4.67377i	0.262403	−	0.190647i	−0.448803	−	0.893631i	$-0.648149\pi$
$601$	6.43289	−	4.67377i	0.262403	−	0.190647i	0.711206	+	0.702984i	$0.248149\pi$
$602$		0			0
$603$	11.7489	+	36.1595i	0.478453	+	1.47253i
$604$		0			0
$605$	−38.3217	−	16.6020i	−1.55800	−	0.674966i
$606$		0			0
$607$	7.60310	+	23.3999i	0.308600	+	0.949774i	0.978309	+	0.207150i	$0.0664189\pi$
$607$	7.60310	+	23.3999i	0.308600	+	0.949774i	−0.669709	+	0.742624i	$0.733581\pi$
$608$		0			0
$609$	5.34826	−	3.88574i	0.216723	−	0.157458i
$610$		0			0
$611$	3.12963	−	9.63202i	0.126611	−	0.389670i
$612$		0			0
$613$	10.6359	+	7.72745i	0.429581	+	0.312109i	0.781481	−	0.623929i	$-0.214464\pi$
$613$	10.6359	+	7.72745i	0.429581	+	0.312109i	−0.351900	+	0.936037i	$0.614464\pi$
$614$		0			0
$615$	−26.0228			−1.04934
$616$		0			0
$617$	10.7365			0.432234			0.216117	−	0.976367i	$-0.430661\pi$
$617$	10.7365			0.432234			0.216117	+	0.976367i	$0.430661\pi$
$618$		0			0
$619$	−2.75742	−	2.00339i	−0.110830	−	0.0805229i	0.530990	−	0.847378i	$-0.321820\pi$
$619$	−2.75742	−	2.00339i	−0.110830	−	0.0805229i	−0.641820	+	0.766855i	$0.721820\pi$
$620$		0			0
$621$	3.19098	−	9.82084i	0.128050	−	0.394097i
$622$		0			0
$623$	−10.2325	+	7.43432i	−0.409955	+	0.297850i
$624$		0			0
$625$	5.11829	+	15.7525i	0.204732	+	0.630099i
$626$		0			0
$627$	−53.8698	−	30.7415i	−2.15135	−	1.22770i
$628$		0			0
$629$	1.08949	+	3.35309i	0.0434406	+	0.133697i
$630$		0			0
$631$	1.46811	−	1.06665i	0.0584447	−	0.0424625i	−0.558179	−	0.829720i	$-0.688500\pi$
$631$	1.46811	−	1.06665i	0.0584447	−	0.0424625i	0.616624	+	0.787258i	$0.288500\pi$
$632$		0			0
$633$	12.3473	−	38.0012i	0.490762	−	1.51041i
$634$		0			0
$635$	−55.1571	−	40.0740i	−2.18884	−	1.59029i
$636$		0			0
$637$	−1.56060			−0.0618333
$638$		0			0
$639$	38.6256			1.52800
$640$		0			0
$641$	10.1311	+	7.36065i	0.400153	+	0.290728i	0.769603	−	0.638522i	$-0.220454\pi$
$641$	10.1311	+	7.36065i	0.400153	+	0.290728i	−0.369450	+	0.929250i	$0.620454\pi$
$642$		0			0
$643$	−10.4921	+	32.2914i	−0.413768	+	1.27345i	0.499580	+	0.866268i	$0.333488\pi$
$643$	−10.4921	+	32.2914i	−0.413768	+	1.27345i	−0.913348	+	0.407179i	$0.866512\pi$
$644$		0			0
$645$	103.968	−	75.5374i	4.09375	−	2.97428i
$646$		0			0
$647$	8.10166	+	24.9343i	0.318509	+	0.980270i	0.974286	+	0.225315i	$0.0723412\pi$
$647$	8.10166	+	24.9343i	0.318509	+	0.980270i	−0.655777	+	0.754955i	$0.727659\pi$
$648$		0			0
$649$	−4.19649	+	20.2432i	−0.164727	+	0.794613i
$650$		0			0
$651$	−1.52872	−	4.70490i	−0.0599151	−	0.184400i
$652$		0			0
$653$	4.12316	−	2.99565i	0.161352	−	0.117229i	−0.504179	−	0.863599i	$-0.668205\pi$
$653$	4.12316	−	2.99565i	0.161352	−	0.117229i	0.665531	+	0.746370i	$0.268205\pi$
$654$		0			0
$655$	−5.30119	+	16.3154i	−0.207134	+	0.637494i
$656$		0			0
$657$	−1.71430	−	1.24551i	−0.0668811	−	0.0485920i
$658$		0			0
$659$	31.3038			1.21942			0.609711	−	0.792624i	$-0.291286\pi$
$659$	31.3038			1.21942			0.609711	+	0.792624i	$0.291286\pi$
$660$		0			0
$661$	5.57757			0.216942			0.108471	−	0.994100i	$-0.465405\pi$
$661$	5.57757			0.216942			0.108471	+	0.994100i	$0.465405\pi$
$662$		0			0
$663$	−1.14523	−	0.832057i	−0.0444770	−	0.0323144i
$664$		0			0
$665$	−8.38059	+	25.7928i	−0.324985	+	1.00020i
$666$		0			0
$667$	−9.43397	+	6.85418i	−0.365285	+	0.265395i
$668$		0			0
$669$	12.3615	+	38.0447i	0.477922	+	1.47089i
$670$		0			0
$671$	15.1233	+	33.5128i	0.583830	+	1.29375i
$672$		0			0
$673$	−6.33900	−	19.5094i	−0.244350	−	0.752033i	−0.995743	−	0.0921774i	$-0.970617\pi$
$673$	−6.33900	−	19.5094i	−0.244350	−	0.752033i	0.751392	−	0.659856i	$-0.229383\pi$
$674$		0			0
$675$	−17.0314	+	12.3740i	−0.655537	+	0.476276i
$676$		0			0
$677$	14.7225	−	45.3112i	0.565832	−	1.74145i	−0.0996358	−	0.995024i	$-0.531768\pi$
$677$	14.7225	−	45.3112i	0.565832	−	1.74145i	0.665467	−	0.746427i	$-0.268232\pi$
$678$		0			0
$679$	2.83952	+	2.06304i	0.108971	+	0.0791720i
$680$		0			0
$681$	−16.5296			−0.633414
$682$		0			0
$683$	36.0977			1.38124			0.690620	−	0.723218i	$-0.257338\pi$
$683$	36.0977			1.38124			0.690620	+	0.723218i	$0.257338\pi$
$684$		0			0
$685$	54.0392	+	39.2618i	2.06473	+	1.50012i
$686$		0			0
$687$	−1.49460	+	4.59990i	−0.0570225	+	0.175497i
$688$		0			0
$689$	3.90499	−	2.83714i	0.148768	−	0.108086i
$690$		0			0
$691$	−1.19759	−	3.68582i	−0.0455586	−	0.140215i	0.925690	−	0.378284i	$-0.123486\pi$
$691$	−1.19759	−	3.68582i	−0.0455586	−	0.140215i	−0.971248	+	0.238069i	$0.923486\pi$
$692$		0			0
$693$	−12.7057	+	1.40008i	−0.482650	+	0.0531848i
$694$		0			0
$695$	−3.98835	−	12.2749i	−0.151287	−	0.465612i
$696$		0			0
$697$	−0.733838	+	0.533164i	−0.0277961	+	0.0201950i
$698$		0			0
$699$	12.5756	−	38.7037i	0.475653	−	1.46391i
$700$		0			0
$701$	3.75354	+	2.72711i	0.141769	+	0.103002i	0.656409	−	0.754405i	$-0.272074\pi$
$701$	3.75354	+	2.72711i	0.141769	+	0.103002i	−0.514640	+	0.857406i	$0.672074\pi$
$702$		0			0
$703$	−72.6877			−2.74147
$704$		0			0
$705$	−64.5055			−2.42942
$706$		0			0
$707$	5.98225	+	4.34636i	0.224986	+	0.163462i
$708$		0			0
$709$	−8.05510	+	24.7910i	−0.302516	+	0.931047i	0.678077	+	0.734991i	$0.262814\pi$
$709$	−8.05510	+	24.7910i	−0.302516	+	0.931047i	−0.980593	+	0.196056i	$0.937186\pi$
$710$		0			0
$711$	37.2971	−	27.0980i	1.39875	−	1.01625i
$712$		0			0
$713$	2.69655	+	8.29913i	0.100987	+	0.310805i
$714$		0			0
$715$	14.5374	−	13.2226i	0.543669	−	0.494497i
$716$		0			0
$717$	−17.1922	−	52.9123i	−0.642056	−	1.97605i
$718$		0			0
$719$	−8.13328	+	5.90917i	−0.303320	+	0.220375i	−0.729025	−	0.684487i	$-0.760026\pi$
$719$	−8.13328	+	5.90917i	−0.303320	+	0.220375i	0.425705	+	0.904862i	$0.360026\pi$
$720$		0			0
$721$	1.37657	−	4.23663i	0.0512660	−	0.157780i
$722$		0			0
$723$	58.5177	+	42.5156i	2.17630	+	1.58117i
$724$		0			0
$725$	23.7731			0.882912
$726$		0			0
$727$	9.14590			0.339203			0.169601	−	0.985513i	$-0.445752\pi$
$727$	9.14590			0.339203			0.169601	+	0.985513i	$0.445752\pi$
$728$		0			0
$729$	32.0066	+	23.2541i	1.18543	+	0.861264i
$730$		0			0
$731$	1.38425	−	4.26029i	0.0511984	−	0.157572i
$732$		0			0
$733$	−6.79975	+	4.94031i	−0.251155	+	0.182474i	−0.706238	−	0.707974i	$-0.749609\pi$
$733$	−6.79975	+	4.94031i	−0.251155	+	0.182474i	0.455084	+	0.890449i	$0.349609\pi$
$734$		0			0
$735$	3.07157	+	9.45332i	0.113297	+	0.348691i
$736$		0			0
$737$	−24.2039	+	22.0148i	−0.891562	+	0.810925i
$738$		0			0
$739$	−1.50720	−	4.63869i	−0.0554433	−	0.170637i	0.919500	−	0.393090i	$-0.128594\pi$
$739$	−1.50720	−	4.63869i	−0.0554433	−	0.170637i	−0.974944	+	0.222453i	$0.928594\pi$
$740$		0			0
$741$	23.6110	−	17.1544i	0.867372	−	0.630182i
$742$		0			0
$743$	−2.00954	+	6.18471i	−0.0737227	+	0.226895i	−0.981127	−	0.193363i	$-0.938060\pi$
$743$	−2.00954	+	6.18471i	−0.0737227	+	0.226895i	0.907405	+	0.420258i	$0.138060\pi$
$744$		0			0
$745$	58.7374	+	42.6752i	2.15197	+	1.56350i
$746$		0			0
$747$	58.0223			2.12292
$748$		0			0
$749$	15.3873			0.562238
$750$		0			0
$751$	−27.5154	−	19.9911i	−1.00405	−	0.729486i	−0.0410983	−	0.999155i	$-0.513086\pi$
$751$	−27.5154	−	19.9911i	−1.00405	−	0.729486i	−0.962953	+	0.269669i	$0.913086\pi$
$752$		0			0
$753$	−7.92928	+	24.4038i	−0.288959	+	0.889325i
$754$		0			0
$755$	−17.4326	+	12.6655i	−0.634437	+	0.460946i
$756$		0			0
$757$	−4.94103	−	15.2069i	−0.179585	−	0.552705i	0.820228	−	0.572036i	$-0.193846\pi$
$757$	−4.94103	−	15.2069i	−0.179585	−	0.552705i	−0.999813	+	0.0193310i	$0.993846\pi$
$758$		0			0
$759$	39.8573	−	4.39201i	1.44673	−	0.159420i
$760$		0			0
$761$	16.2231	+	49.9296i	0.588088	+	1.80995i	0.586500	+	0.809949i	$0.300506\pi$
$761$	16.2231	+	49.9296i	0.588088	+	1.80995i	0.00158813	+	0.999999i	$0.499494\pi$
$762$		0			0
$763$	0.0875261	−	0.0635914i	0.00316866	−	0.00230216i
$764$		0			0
$765$	−1.56666	+	4.82169i	−0.0566428	+	0.174329i
$766$		0			0
$767$	−7.86989	−	5.71781i	−0.284165	−	0.206458i
$768$		0			0
$769$	24.1109			0.869461			0.434731	−	0.900561i	$-0.356844\pi$
$769$	24.1109			0.869461			0.434731	+	0.900561i	$0.356844\pi$
$770$		0			0
$771$	−62.8139			−2.26219
$772$		0			0
$773$	−3.83052	−	2.78303i	−0.137774	−	0.100099i	0.516764	−	0.856128i	$-0.327137\pi$
$773$	−3.83052	−	2.78303i	−0.137774	−	0.100099i	−0.654538	+	0.756029i	$0.727137\pi$
$774$		0			0
$775$	5.49741	−	16.9193i	0.197473	−	0.607759i
$776$		0			0
$777$	−21.5529	+	15.6591i	−0.773204	+	0.561766i
$778$		0			0
$779$	−5.77892	−	17.7857i	−0.207051	−	0.637239i
$780$		0			0
$781$	13.6721	+	30.2969i	0.489227	+	1.08411i
$782$		0			0
$783$	1.74481	+	5.36996i	0.0623543	+	0.191907i
$784$		0			0
$785$	10.5217	−	7.64445i	0.375535	−	0.272842i
$786$		0			0
$787$	−11.9852	+	36.8867i	−0.427227	+	1.31487i	0.473619	+	0.880730i	$0.342948\pi$
$787$	−11.9852	+	36.8867i	−0.427227	+	1.31487i	−0.900846	+	0.434140i	$0.857052\pi$
$788$		0			0
$789$	−41.9554	−	30.4824i	−1.49365	−	1.08520i
$790$		0			0
$791$	−1.71764			−0.0610721
$792$		0			0
$793$	−17.3004			−0.614355
$794$		0			0
$795$	−24.8717	−	18.0703i	−0.882108	−	0.640889i
$796$		0			0
$797$	−0.384029	+	1.18192i	−0.0136030	+	0.0418657i	−0.957628	−	0.288009i	$-0.907007\pi$
$797$	−0.384029	+	1.18192i	−0.0136030	+	0.0418657i	0.944025	+	0.329875i	$0.107007\pi$
$798$		0			0
$799$	−1.81905	+	1.32161i	−0.0643532	+	0.0467553i
$800$		0			0
$801$	−15.0636	−	46.3609i	−0.532245	−	1.63808i
$802$		0			0
$803$	0.370146	−	1.78552i	0.0130622	−	0.0630097i
$804$		0			0
$805$	−5.41804	−	16.6750i	−0.190961	−	0.587717i
$806$		0			0
$807$	−5.71903	+	4.15512i	−0.201319	+	0.146267i
$808$		0			0
$809$	−6.43775	+	19.8134i	−0.226339	+	0.696600i	0.771814	+	0.635849i	$0.219350\pi$
$809$	−6.43775	+	19.8134i	−0.226339	+	0.696600i	−0.998153	+	0.0607517i	$0.980650\pi$
$810$		0			0
$811$	−6.53831	−	4.75036i	−0.229591	−	0.166808i	0.467042	−	0.884235i	$-0.345320\pi$
$811$	−6.53831	−	4.75036i	−0.229591	−	0.166808i	−0.696633	+	0.717427i	$0.745320\pi$
$812$		0			0
$813$	3.94344			0.138303
$814$		0			0
$815$	68.5372			2.40075
$816$		0			0
$817$	74.7158	+	54.2842i	2.61397	+	1.89916i
$818$		0			0
$819$	1.85865	−	5.72034i	0.0649465	−	0.199885i
$820$		0			0
$821$	−0.861988	+	0.626271i	−0.0300836	+	0.0218570i	−0.602725	−	0.797949i	$-0.705919\pi$
$821$	−0.861988	+	0.626271i	−0.0300836	+	0.0218570i	0.572642	+	0.819806i	$0.305919\pi$
$822$		0			0
$823$	−3.98851	−	12.2754i	−0.139031	−	0.427892i	0.857165	−	0.515043i	$-0.172224\pi$
$823$	−3.98851	−	12.2754i	−0.139031	−	0.427892i	−0.996195	+	0.0871505i	$0.972224\pi$
$824$		0			0
$825$	−71.0008	−	40.5174i	−2.47193	−	1.41064i
$826$		0			0
$827$	−2.17795	−	6.70305i	−0.0757348	−	0.233088i	0.906021	−	0.423232i	$-0.139104\pi$
$827$	−2.17795	−	6.70305i	−0.0757348	−	0.233088i	−0.981756	+	0.190144i	$0.939104\pi$
$828$		0			0
$829$	28.8086	−	20.9307i	1.00057	−	0.726953i	0.0383559	−	0.999264i	$-0.487788\pi$
$829$	28.8086	−	20.9307i	1.00057	−	0.726953i	0.962209	+	0.272311i	$0.0877879\pi$
$830$		0			0
$831$	2.34826	−	7.22721i	0.0814603	−	0.250709i
$832$		0			0
$833$	0.280301	+	0.203651i	0.00971186	+	0.00705608i
$834$		0			0
$835$	17.5227			0.606398
$836$		0			0
$837$	4.22527			0.146047
$838$		0			0
$839$	−5.56145	−	4.04063i	−0.192003	−	0.139498i	0.487631	−	0.873050i	$-0.337861\pi$
$839$	−5.56145	−	4.04063i	−0.192003	−	0.139498i	−0.679634	+	0.733552i	$0.737861\pi$
$840$		0			0
$841$	−6.99115	+	21.5165i	−0.241074	+	0.741950i
$842$		0			0
$843$	41.9049	−	30.4457i	1.44328	−	1.04861i
$844$		0			0
$845$	−12.3947	−	38.1469i	−0.426390	−	1.31229i
$846$		0			0
$847$	−5.59557	−	9.47046i	−0.192266	−	0.325409i
$848$		0			0
$849$	−12.9921	−	39.9856i	−0.445888	−	1.37230i
$850$		0			0
$851$	38.0178	−	27.6215i	1.30323	−	0.946854i
$852$		0			0
$853$	−11.4768	+	35.3221i	−0.392960	+	1.20941i	0.537580	+	0.843213i	$0.319339\pi$
$853$	−11.4768	+	35.3221i	−0.392960	+	1.20941i	−0.930539	+	0.366192i	$0.880661\pi$
$854$		0			0
$855$	−84.5616	−	61.4376i	−2.89194	−	2.10112i
$856$		0			0
$857$	17.5856			0.600714			0.300357	−	0.953827i	$-0.402894\pi$
$857$	17.5856			0.600714			0.300357	+	0.953827i	$0.402894\pi$
$858$		0			0
$859$	−53.7716			−1.83466			−0.917331	−	0.398125i	$-0.869661\pi$
$859$	−53.7716			−1.83466			−0.917331	+	0.398125i	$0.869661\pi$
$860$		0			0
$861$	−5.54508	−	4.02874i	−0.188976	−	0.137299i
$862$		0			0
$863$	16.1294	−	49.6412i	0.549052	−	1.68981i	−0.162105	−	0.986774i	$-0.551828\pi$
$863$	16.1294	−	49.6412i	0.549052	−	1.68981i	0.711156	−	0.703034i	$-0.248172\pi$
$864$		0			0
$865$	−38.2622	+	27.7991i	−1.30095	+	0.945198i
$866$		0			0
$867$	−13.6562	−	42.0294i	−0.463788	−	1.42739i
$868$		0			0
$869$	34.4569	+	19.6632i	1.16887	+	0.667029i
$870$		0			0
$871$	−4.75738	−	14.6417i	−0.161198	−	0.496115i
$872$		0			0
$873$	−10.9438	+	7.95115i	−0.370392	+	0.269106i
$874$		0			0
$875$	−5.17949	+	15.9408i	−0.175099	+	0.538898i
$876$		0			0
$877$	−46.6950	−	33.9259i	−1.57678	−	1.14560i	−0.920273	−	0.391277i	$-0.872034\pi$
$877$	−46.6950	−	33.9259i	−1.57678	−	1.14560i	−0.656506	−	0.754321i	$-0.727966\pi$
$878$		0			0
$879$	−64.2331			−2.16653
$880$		0			0
$881$	−19.5301			−0.657985			−0.328993	−	0.944333i	$-0.606709\pi$
$881$	−19.5301			−0.657985			−0.328993	+	0.944333i	$0.606709\pi$
$882$		0			0
$883$	−25.8870	−	18.8080i	−0.871167	−	0.632940i	0.0597327	−	0.998214i	$-0.480975\pi$
$883$	−25.8870	−	18.8080i	−0.871167	−	0.632940i	−0.930900	+	0.365274i	$0.880975\pi$
$884$		0			0
$885$	−19.1461	+	58.9255i	−0.643588	+	1.98076i
$886$		0			0
$887$	11.0233	−	8.00891i	0.370127	−	0.268913i	−0.387137	−	0.922022i	$-0.626536\pi$
$887$	11.0233	−	8.00891i	0.370127	−	0.268913i	0.757263	+	0.653110i	$0.226536\pi$
$888$		0			0
$889$	−5.54911	−	17.0784i	−0.186111	−	0.572791i
$890$		0			0
$891$	−3.84297	+	18.5378i	−0.128744	+	0.621041i
$892$		0			0
$893$	−14.3249	−	44.0874i	−0.479363	−	1.47533i
$894$		0			0
$895$	−21.4541	+	15.5873i	−0.717132	+	0.521027i
$896$		0			0
$897$	−5.83052	+	17.9445i	−0.194675	+	0.599149i
$898$		0			0
$899$	−3.86017	−	2.80458i	−0.128744	−	0.0935379i
$900$		0			0
$901$	−1.07161			−0.0357005
$902$		0			0
$903$	33.8486			1.12641
$904$		0			0
$905$	47.0482	+	34.1825i	1.56394	+	1.13627i
$906$		0			0
$907$	−7.45577	+	22.9465i	−0.247565	+	0.761926i	0.747639	+	0.664105i	$0.231187\pi$
$907$	−7.45577	+	22.9465i	−0.247565	+	0.761926i	−0.995204	+	0.0978208i	$0.968813\pi$
$908$		0			0
$909$	−23.0562	+	16.7513i	−0.764726	+	0.555606i
$910$		0			0
$911$	7.84905	+	24.1569i	0.260051	+	0.800354i	0.992792	+	0.119847i	$0.0382403\pi$
$911$	7.84905	+	24.1569i	0.260051	+	0.800354i	−0.732742	+	0.680507i	$0.761760\pi$
$912$		0			0
$913$	20.5379	+	45.5112i	0.679704	+	1.50620i
$914$		0			0
$915$	34.0505	+	104.797i	1.12568	+	3.46447i
$916$		0			0
$917$	−3.65549	+	2.65587i	−0.120715	+	0.0877045i
$918$		0			0
$919$	4.37355	−	13.4604i	0.144270	−	0.444017i	−0.852646	−	0.522488i	$-0.825004\pi$
$919$	4.37355	−	13.4604i	0.144270	−	0.444017i	0.996916	+	0.0784710i	$0.0250038\pi$
$920$		0			0
$921$	−18.4947	−	13.4372i	−0.609422	−	0.442771i
$922$		0			0
$923$	−15.6403			−0.514805
$924$		0			0
$925$	−95.8029			−3.14998
$926$		0			0
$927$	13.8898	+	10.0915i	0.456200	+	0.331449i
$928$		0			0
$929$	14.6896	−	45.2100i	0.481950	−	1.48329i	−0.354399	−	0.935094i	$-0.615315\pi$
$929$	14.6896	−	45.2100i	0.481950	−	1.48329i	0.836350	−	0.548196i	$-0.184685\pi$
$930$		0			0
$931$	−5.77892	+	4.19863i	−0.189397	+	0.137605i
$932$		0			0
$933$	−20.5013	−	63.0964i	−0.671181	−	2.06568i
$934$		0			0
$935$	−4.33656	+	0.477860i	−0.141821	+	0.0156277i
$936$		0			0
$937$	−3.70857	−	11.4138i	−0.121154	−	0.372873i	0.872027	−	0.489458i	$-0.162805\pi$
$937$	−3.70857	−	11.4138i	−0.121154	−	0.372873i	−0.993181	+	0.116585i	$0.962805\pi$
$938$		0			0
$939$	−32.8569	+	23.8719i	−1.07224	+	0.779031i
$940$		0			0
$941$	−16.0409	+	49.3688i	−0.522918	+	1.60938i	0.245479	+	0.969402i	$0.421055\pi$
$941$	−16.0409	+	49.3688i	−0.522918	+	1.60938i	−0.768397	+	0.639974i	$0.778945\pi$
$942$		0			0
$943$	9.78115	+	7.10642i	0.318518	+	0.231417i
$944$		0			0
$945$	−8.48961			−0.276167
$946$		0			0
$947$	33.0847			1.07511			0.537553	−	0.843230i	$-0.319349\pi$
$947$	33.0847			1.07511			0.537553	+	0.843230i	$0.319349\pi$
$948$		0			0
$949$	0.694153	+	0.504332i	0.0225332	+	0.0163713i
$950$		0			0
$951$	−0.194592	+	0.598891i	−0.00631006	+	0.0194204i
$952$		0			0
$953$	−40.9949	+	29.7845i	−1.32796	+	0.964816i	−0.328159	+	0.944623i	$0.606428\pi$
$953$	−40.9949	+	29.7845i	−1.32796	+	0.964816i	−0.999796	+	0.0201933i	$0.993572\pi$
$954$		0			0
$955$	−6.32899	−	19.4786i	−0.204801	−	0.630313i
$956$		0			0
$957$	−16.2199	+	14.7529i	−0.524314	+	0.476893i
$958$		0			0
$959$	5.43664	+	16.7323i	0.175558	+	0.540313i
$960$		0			0
$961$	22.1909	−	16.1226i	0.715835	−	0.520084i
$962$		0			0
$963$	−18.3260	+	56.4015i	−0.590546	+	1.81751i
$964$		0			0
$965$	−26.3397	−	19.1369i	−0.847905	−	0.616039i
$966$		0			0
$967$	51.7030			1.66266			0.831329	−	0.555781i	$-0.187581\pi$
$967$	51.7030			1.66266			0.831329	+	0.555781i	$0.187581\pi$
$968$		0			0
$969$	−6.47935			−0.208147
$970$		0			0
$971$	27.3663	+	19.8828i	0.878228	+	0.638070i	0.932782	−	0.360441i	$-0.117374\pi$
$971$	27.3663	+	19.8828i	0.878228	+	0.638070i	−0.0545544	+	0.998511i	$0.517374\pi$
$972$		0			0
$973$	1.05049	−	3.23306i	0.0336770	−	0.103647i
$974$		0			0
$975$	31.1194	−	22.6096i	0.996620	−	0.724087i
$976$		0			0
$977$	−12.6496	−	38.9313i	−0.404695	−	1.24552i	−0.921149	−	0.389209i	$-0.872748\pi$
$977$	−12.6496	−	38.9313i	−0.404695	−	1.24552i	0.516454	−	0.856315i	$-0.327252\pi$
$978$		0			0
$979$	31.0324	−	28.2256i	0.991799	−	0.902096i
$980$		0			0
$981$	0.128850	+	0.396561i	0.00411387	+	0.0126612i
$982$		0			0
$983$	−15.5152	+	11.2724i	−0.494857	+	0.359535i	−0.807049	−	0.590484i	$-0.798937\pi$
$983$	−15.5152	+	11.2724i	−0.494857	+	0.359535i	0.312192	+	0.950019i	$0.398937\pi$
$984$		0			0
$985$	7.51813	−	23.1384i	0.239547	−	0.737251i
$986$		0			0
$987$	−13.7452	−	9.98649i	−0.437515	−	0.317873i
$988$		0			0
$989$	−59.7066			−1.89856
$990$		0			0
$991$	16.3423			0.519131			0.259566	−	0.965725i	$-0.416421\pi$
$991$	16.3423			0.519131			0.259566	+	0.965725i	$0.416421\pi$
$992$		0			0
$993$	−34.4139	−	25.0031i	−1.09209	−	0.793451i
$994$		0			0
$995$	−8.38582	+	25.8089i	−0.265848	+	0.818197i
$996$		0			0
$997$	14.6624	−	10.6529i	0.464363	−	0.337380i	−0.330877	−	0.943674i	$-0.607345\pi$
$997$	14.6624	−	10.6529i	0.464363	−	0.337380i	0.795240	+	0.606294i	$0.207345\pi$
$998$		0			0
$999$	−7.03136	−	21.6403i	−0.222462	−	0.684669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.j.b.225.2	yes	8
11.3	even	5		3388.2.a.r.1.4		4
11.8	odd	10		3388.2.a.s.1.4		4
11.9	even	5	inner	308.2.j.b.141.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.j.b.141.2	✓	8	11.9	even	5	inner
308.2.j.b.225.2	yes	8	1.1	even	1	trivial
3388.2.a.r.1.4		4	11.3	even	5
3388.2.a.s.1.4		4	11.8	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.11803 - 1.53884i) q^{3} +(1.17324 - 3.61085i) q^{5} +(0.809017 - 0.587785i) q^{7} +(1.19098 + 3.66547i) q^{9} +O(q^{10})\)	\(q+(-2.11803 - 1.53884i) q^{3} +(1.17324 - 3.61085i) q^{5} +(0.809017 - 0.587785i) q^{7} +(1.19098 + 3.66547i) q^{9} +(-2.45354 + 2.23163i) q^{11} +(-0.482253 - 1.48422i) q^{13} +(-8.04148 + 5.84247i) q^{15} +(-0.107065 + 0.329514i) q^{17} +(-5.77892 - 4.19863i) q^{19} -2.61803 q^{21} +4.61803 q^{23} +(-7.61666 - 5.53382i) q^{25} +(0.690983 - 2.12663i) q^{27} +(-2.04285 + 1.48422i) q^{29} +(0.583918 + 1.79711i) q^{31} +(8.63079 - 0.951057i) q^{33} +(-1.17324 - 3.61085i) q^{35} +(8.23246 - 5.98123i) q^{37} +(-1.26255 + 3.88574i) q^{39} +(2.11803 + 1.53884i) q^{41} -12.9290 q^{43} +14.6328 q^{45} +(5.25021 + 3.81450i) q^{47} +(0.309017 - 0.951057i) q^{49} +(0.733838 - 0.533164i) q^{51} +(0.955767 + 2.94155i) q^{53} +(5.17949 + 11.4776i) q^{55} +(5.77892 + 17.7857i) q^{57} +(5.04285 - 3.66385i) q^{59} +(3.42567 - 10.5431i) q^{61} +(3.11803 + 2.26538i) q^{63} -5.92509 q^{65} +9.86490 q^{67} +(-9.78115 - 7.10642i) q^{69} +(3.09695 - 9.53143i) q^{71} +(-0.444798 + 0.323165i) q^{73} +(7.61666 + 23.4417i) q^{75} +(-0.673236 + 3.24758i) q^{77} +(-3.69638 - 11.3763i) q^{79} +(4.61803 - 3.35520i) q^{81} +(4.65215 - 14.3178i) q^{83} +(1.06421 + 0.773194i) q^{85} +6.61082 q^{87} -12.6480 q^{89} +(-1.26255 - 0.917299i) q^{91} +(1.52872 - 4.70490i) q^{93} +(-21.9407 + 15.9408i) q^{95} +(1.08460 + 3.33806i) q^{97} +(-11.1021 - 6.33553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} - q^{5} + 2 q^{7} + 14 q^{9}+O(q^{10}) \) 8 * q - 8 * q^3 - q^5 + 2 * q^7 + 14 * q^9	\( 8 q - 8 q^{3} - q^{5} + 2 q^{7} + 14 q^{9} - 5 q^{11} + 11 q^{13} - 4 q^{15} - 7 q^{17} - 5 q^{19} - 12 q^{21} + 28 q^{23} - 15 q^{25} + 10 q^{27} + 7 q^{29} + 3 q^{31} + q^{35} + 10 q^{37} + 9 q^{39} + 8 q^{41} - 44 q^{43} + 2 q^{45} + q^{47} - 2 q^{49} - 13 q^{51} - 6 q^{53} - 12 q^{55} + 5 q^{57} + 17 q^{59} - 23 q^{61} + 16 q^{63} - 80 q^{65} + 38 q^{67} - 38 q^{69} + 10 q^{71} - 5 q^{73} + 15 q^{75} + 5 q^{77} - 27 q^{79} + 28 q^{81} + 21 q^{83} + 38 q^{85} - 32 q^{87} + 26 q^{89} + 9 q^{91} + 12 q^{93} - 66 q^{95} - 28 q^{97} - 20 q^{99}+O(q^{100}) \) 8 * q - 8 * q^3 - q^5 + 2 * q^7 + 14 * q^9 - 5 * q^11 + 11 * q^13 - 4 * q^15 - 7 * q^17 - 5 * q^19 - 12 * q^21 + 28 * q^23 - 15 * q^25 + 10 * q^27 + 7 * q^29 + 3 * q^31 + q^35 + 10 * q^37 + 9 * q^39 + 8 * q^41 - 44 * q^43 + 2 * q^45 + q^47 - 2 * q^49 - 13 * q^51 - 6 * q^53 - 12 * q^55 + 5 * q^57 + 17 * q^59 - 23 * q^61 + 16 * q^63 - 80 * q^65 + 38 * q^67 - 38 * q^69 + 10 * q^71 - 5 * q^73 + 15 * q^75 + 5 * q^77 - 27 * q^79 + 28 * q^81 + 21 * q^83 + 38 * q^85 - 32 * q^87 + 26 * q^89 + 9 * q^91 + 12 * q^93 - 66 * q^95 - 28 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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