LMFDB - Embedded newform 116.2.g.b.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [116,2,Mod(25,116)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(116, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([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("116.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 116 = 2^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	116.g (of order $7$, degree $6$, 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:	$0.926264663447$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
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} - 5 x^{11} + 12 x^{10} - 16 x^{9} + 22 x^{8} + 28 x^{7} + 71 x^{6} + 154 x^{5} + 442 x^{4} + \cdots + 841 $ x^12 - 5x^11 + 12x^10 - 16x^9 + 22x^8 + 28x^7 + 71x^6 + 154x^5 + 442x^4 + 555x^3 + 1573x^2 + 1363*x + 841
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			81.2
Root			$-0.366459 + 1.60556i$ of defining polynomial
Character	$\chi$	$=$	116.81
Dual form			116.2.g.b.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.588980 - 2.58049i) q^{3} +(-0.379425 + 0.475783i) q^{5} +(0.143938 - 0.630635i) q^{7} +(-3.60913 - 1.73806i) q^{9} +O(q^{10})$	\(q+(0.588980 - 2.58049i) q^{3} +(-0.379425 + 0.475783i) q^{5} +(0.143938 - 0.630635i) q^{7} +(-3.60913 - 1.73806i) q^{9} +(2.86324 - 1.37887i) q^{11} +(-4.97137 + 2.39409i) q^{13} +(1.00428 + 1.25933i) q^{15} +6.66330 q^{17} +(1.14602 + 5.02104i) q^{19} +(-1.54257 - 0.742863i) q^{21} +(1.01545 + 1.27333i) q^{23} +(1.03020 + 4.51359i) q^{25} +(-1.65990 + 2.08145i) q^{27} +(-5.38378 - 0.122066i) q^{29} +(-1.23153 + 1.54429i) q^{31} +(-1.87176 - 8.20070i) q^{33} +(0.245432 + 0.307762i) q^{35} +(-2.60003 - 1.25211i) q^{37} +(3.24988 + 14.2387i) q^{39} -9.83108 q^{41} +(-4.81739 - 6.04081i) q^{43} +(2.19633 - 1.05770i) q^{45} +(7.49675 - 3.61024i) q^{47} +(5.92980 + 2.85564i) q^{49} +(3.92455 - 17.1946i) q^{51} +(4.82640 - 6.05211i) q^{53} +(-0.430344 + 1.88546i) q^{55} +13.6317 q^{57} -1.12157 q^{59} +(-2.02019 + 8.85104i) q^{61} +(-1.61557 + 2.02587i) q^{63} +(0.747195 - 3.27367i) q^{65} +(-11.2641 - 5.42452i) q^{67} +(3.88390 - 1.87039i) q^{69} +(0.344508 - 0.165906i) q^{71} +(0.200048 + 0.250852i) q^{73} +12.2540 q^{75} +(-0.457430 - 2.00413i) q^{77} +(-15.5018 - 7.46526i) q^{79} +(-3.09926 - 3.88635i) q^{81} +(-1.91516 - 8.39086i) q^{83} +(-2.52822 + 3.17029i) q^{85} +(-3.48593 + 13.8209i) q^{87} +(-5.99640 + 7.51924i) q^{89} +(0.794224 + 3.47972i) q^{91} +(3.25968 + 4.08751i) q^{93} +(-2.82375 - 1.35985i) q^{95} +(1.95580 + 8.56894i) q^{97} -12.7304 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - q^{5} - 7 q^{7} + q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - q^5 - 7 * q^7 + q^9	$ 12 q - 3 q^{3} - q^{5} - 7 q^{7} + q^{9} + 3 q^{11} - 21 q^{13} + 29 q^{15} - 10 q^{17} + 17 q^{19} + 3 q^{21} - 19 q^{23} - 3 q^{25} + 9 q^{27} - 5 q^{29} - 27 q^{31} - 47 q^{33} + 27 q^{35} - 3 q^{37} - 37 q^{39} - 2 q^{41} - 9 q^{43} + 22 q^{45} + 19 q^{47} + 17 q^{49} + 2 q^{51} + 22 q^{53} + 49 q^{55} + 30 q^{57} + 36 q^{59} - 33 q^{61} + 9 q^{63} + 38 q^{65} - 3 q^{67} + 47 q^{69} - 35 q^{71} + 34 q^{73} - 44 q^{75} - 27 q^{77} - 19 q^{79} - 39 q^{81} - q^{83} - 34 q^{85} - 25 q^{87} - 11 q^{89} - 23 q^{91} + 7 q^{93} - 105 q^{95} + 38 q^{97} - 16 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - q^5 - 7 * q^7 + q^9 + 3 * q^11 - 21 * q^13 + 29 * q^15 - 10 * q^17 + 17 * q^19 + 3 * q^21 - 19 * q^23 - 3 * q^25 + 9 * q^27 - 5 * q^29 - 27 * q^31 - 47 * q^33 + 27 * q^35 - 3 * q^37 - 37 * q^39 - 2 * q^41 - 9 * q^43 + 22 * q^45 + 19 * q^47 + 17 * q^49 + 2 * q^51 + 22 * q^53 + 49 * q^55 + 30 * q^57 + 36 * q^59 - 33 * q^61 + 9 * q^63 + 38 * q^65 - 3 * q^67 + 47 * q^69 - 35 * q^71 + 34 * q^73 - 44 * q^75 - 27 * q^77 - 19 * q^79 - 39 * q^81 - q^83 - 34 * q^85 - 25 * q^87 - 11 * q^89 - 23 * q^91 + 7 * q^93 - 105 * q^95 + 38 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/116\mathbb{Z}\right)^\times$.

$n$	$59$	$89$
$\chi(n)$	$1$	$e\left(\frac{5}{7}\right)$

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			0
$2$		0			0
$3$	0.588980	−	2.58049i	0.340048	−	1.48985i	−0.458922	−	0.888476i	$-0.651764\pi$
$3$	0.588980	−	2.58049i	0.340048	−	1.48985i	0.798970	−	0.601371i	$-0.205378\pi$
$4$		0			0
$5$	−0.379425	+	0.475783i	−0.169684	+	0.212777i	−0.859401	−	0.511302i	$-0.829163\pi$
$5$	−0.379425	+	0.475783i	−0.169684	+	0.212777i	0.689717	+	0.724079i	$0.257735\pi$
$6$		0			0
$7$	0.143938	−	0.630635i	0.0544035	−	0.238357i	−0.940414	−	0.340031i	$-0.889562\pi$
$7$	0.143938	−	0.630635i	0.0544035	−	0.238357i	0.994818	+	0.101673i	$0.0324196\pi$
$8$		0			0
$9$	−3.60913	−	1.73806i	−1.20304	−	0.579355i
$10$		0			0
$11$	2.86324	−	1.37887i	0.863300	−	0.415744i	0.0508032	−	0.998709i	$-0.483822\pi$
$11$	2.86324	−	1.37887i	0.863300	−	0.415744i	0.812497	+	0.582965i	$0.198108\pi$
$12$		0			0
$13$	−4.97137	+	2.39409i	−1.37881	+	0.664001i	−0.968746	−	0.248056i	$-0.920208\pi$
$13$	−4.97137	+	2.39409i	−1.37881	+	0.664001i	−0.410065	+	0.912056i	$0.634494\pi$
$14$		0			0
$15$	1.00428	+	1.25933i	0.259304	+	0.325157i
$16$		0			0
$17$	6.66330			1.61609			0.808043	−	0.589123i	$-0.200527\pi$
$17$	6.66330			1.61609			0.808043	+	0.589123i	$0.200527\pi$
$18$		0			0
$19$	1.14602	+	5.02104i	0.262915	+	1.15190i	0.918073	+	0.396412i	$0.129745\pi$
$19$	1.14602	+	5.02104i	0.262915	+	1.15190i	−0.655158	+	0.755492i	$0.727398\pi$
$20$		0			0
$21$	−1.54257	−	0.742863i	−0.336616	−	0.162106i
$22$		0			0
$23$	1.01545	+	1.27333i	0.211735	+	0.265508i	0.876346	−	0.481682i	$-0.159974\pi$
$23$	1.01545	+	1.27333i	0.211735	+	0.265508i	−0.664611	+	0.747190i	$0.731403\pi$
$24$		0			0
$25$	1.03020	+	4.51359i	0.206040	+	0.902718i
$26$		0			0
$27$	−1.65990	+	2.08145i	−0.319449	+	0.400576i
$28$		0			0
$29$	−5.38378	−	0.122066i	−0.999743	−	0.0226671i
$29$	−5.38378	−	0.122066i	−0.999743	−	0.0226671i
$30$		0			0
$31$	−1.23153	+	1.54429i	−0.221190	+	0.277363i	−0.880028	−	0.474921i	$-0.842477\pi$
$31$	−1.23153	+	1.54429i	−0.221190	+	0.277363i	0.658839	+	0.752284i	$0.271048\pi$
$32$		0			0
$33$	−1.87176	−	8.20070i	−0.325831	−	1.42756i
$34$		0			0
$35$	0.245432	+	0.307762i	0.0414855	+	0.0520212i
$36$		0			0
$37$	−2.60003	−	1.25211i	−0.427442	−	0.205845i	0.207779	−	0.978176i	$-0.433377\pi$
$37$	−2.60003	−	1.25211i	−0.427442	−	0.205845i	−0.635221	+	0.772331i	$0.719091\pi$
$38$		0			0
$39$	3.24988	+	14.2387i	0.520397	+	2.28001i
$40$		0			0
$41$	−9.83108			−1.53536			−0.767678	−	0.640836i	$-0.778588\pi$
$41$	−9.83108			−1.53536			−0.767678	+	0.640836i	$0.778588\pi$
$42$		0			0
$43$	−4.81739	−	6.04081i	−0.734644	−	0.921215i	0.264422	−	0.964407i	$-0.414819\pi$
$43$	−4.81739	−	6.04081i	−0.734644	−	0.921215i	−0.999067	+	0.0431920i	$0.986247\pi$
$44$		0			0
$45$	2.19633	−	1.05770i	0.327410	−	0.157672i
$46$		0			0
$47$	7.49675	−	3.61024i	1.09351	−	0.526608i	0.201900	−	0.979406i	$-0.435288\pi$
$47$	7.49675	−	3.61024i	1.09351	−	0.526608i	0.891613	+	0.452798i	$0.149574\pi$
$48$		0			0
$49$	5.92980	+	2.85564i	0.847114	+	0.407949i
$50$		0			0
$51$	3.92455	−	17.1946i	0.549547	−	2.40772i
$52$		0			0
$53$	4.82640	−	6.05211i	0.662957	−	0.831321i	−0.330705	−	0.943734i	$-0.607287\pi$
$53$	4.82640	−	6.05211i	0.662957	−	0.831321i	0.993662	+	0.112413i	$0.0358580\pi$
$54$		0			0
$55$	−0.430344	+	1.88546i	−0.0580275	+	0.254235i
$56$		0			0
$57$	13.6317			1.80556
$58$		0			0
$59$	−1.12157			−0.146016			−0.0730082	−	0.997331i	$-0.523260\pi$
$59$	−1.12157			−0.146016			−0.0730082	+	0.997331i	$0.523260\pi$
$60$		0			0
$61$	−2.02019	+	8.85104i	−0.258659	+	1.13326i	0.664027	+	0.747708i	$0.268846\pi$
$61$	−2.02019	+	8.85104i	−0.258659	+	1.13326i	−0.922687	+	0.385551i	$0.874011\pi$
$62$		0			0
$63$	−1.61557	+	2.02587i	−0.203543	+	0.255235i
$64$		0			0
$65$	0.747195	−	3.27367i	0.0926781	−	0.406049i
$66$		0			0
$67$	−11.2641	−	5.42452i	−1.37613	−	0.662711i	−0.407961	−	0.912999i	$-0.633760\pi$
$67$	−11.2641	−	5.42452i	−1.37613	−	0.662711i	−0.968171	+	0.250289i	$0.919475\pi$
$68$		0			0
$69$	3.88390	−	1.87039i	0.467566	−	0.225168i
$70$		0			0
$71$	0.344508	−	0.165906i	0.0408855	−	0.0196894i	−0.413329	−	0.910582i	$-0.635634\pi$
$71$	0.344508	−	0.165906i	0.0408855	−	0.0196894i	0.454215	+	0.890892i	$0.349920\pi$
$72$		0			0
$73$	0.200048	+	0.250852i	0.0234139	+	0.0293601i	0.793401	−	0.608700i	$-0.208309\pi$
$73$	0.200048	+	0.250852i	0.0234139	+	0.0293601i	−0.769987	+	0.638060i	$0.779737\pi$
$74$		0			0
$75$	12.2540			1.41498
$76$		0			0
$77$	−0.457430	−	2.00413i	−0.0521290	−	0.228392i
$78$		0			0
$79$	−15.5018	−	7.46526i	−1.74408	−	0.839907i	−0.981103	−	0.193487i	$-0.938020\pi$
$79$	−15.5018	−	7.46526i	−1.74408	−	0.839907i	−0.762982	−	0.646420i	$-0.776265\pi$
$80$		0			0
$81$	−3.09926	−	3.88635i	−0.344362	−	0.431816i
$82$		0			0
$83$	−1.91516	−	8.39086i	−0.210216	−	0.921017i	−0.964420	−	0.264376i	$-0.914834\pi$
$83$	−1.91516	−	8.39086i	−0.210216	−	0.921017i	0.754204	−	0.656641i	$-0.228023\pi$
$84$		0			0
$85$	−2.52822	+	3.17029i	−0.274224	+	0.343866i
$86$		0			0
$87$	−3.48593	+	13.8209i	−0.373731	+	1.48176i
$88$		0			0
$89$	−5.99640	+	7.51924i	−0.635617	+	0.797038i	−0.990447	−	0.137892i	$-0.955967\pi$
$89$	−5.99640	+	7.51924i	−0.635617	+	0.797038i	0.354830	+	0.934931i	$0.384539\pi$
$90$		0			0
$91$	0.794224	+	3.47972i	0.0832573	+	0.364774i
$92$		0			0
$93$	3.25968	+	4.08751i	0.338013	+	0.423855i
$94$		0			0
$95$	−2.82375	−	1.35985i	−0.289711	−	0.139517i
$96$		0			0
$97$	1.95580	+	8.56894i	0.198582	+	0.870044i	0.971782	+	0.235882i	$0.0757978\pi$
$97$	1.95580	+	8.56894i	0.198582	+	0.870044i	−0.773200	+	0.634162i	$0.781345\pi$
$98$		0			0
$99$	−12.7304			−1.27945
$100$		0			0
$101$	9.08321	+	11.3900i	0.903814	+	1.13335i	0.990555	+	0.137116i	$0.0437832\pi$
$101$	9.08321	+	11.3900i	0.903814	+	1.13335i	−0.0867414	+	0.996231i	$0.527645\pi$
$102$		0			0
$103$	8.84897	−	4.26144i	0.871915	−	0.419892i	0.0562500	−	0.998417i	$-0.482086\pi$
$103$	8.84897	−	4.26144i	0.871915	−	0.419892i	0.815665	+	0.578525i	$0.196371\pi$
$104$		0			0
$105$	0.938731	−	0.452069i	0.0916107	−	0.0441174i
$106$		0			0
$107$	0.975441	+	0.469747i	0.0942994	+	0.0454122i	0.480439	−	0.877028i	$-0.340477\pi$
$107$	0.975441	+	0.469747i	0.0942994	+	0.0454122i	−0.386139	+	0.922440i	$0.626192\pi$
$108$		0			0
$109$	1.01089	−	4.42898i	0.0968252	−	0.424219i	−0.903162	−	0.429300i	$-0.858760\pi$
$109$	1.01089	−	4.42898i	0.0968252	−	0.424219i	0.999987	+	0.00508113i	$0.00161738\pi$
$110$		0			0
$111$	−4.76241	+	5.97188i	−0.452028	+	0.566826i
$112$		0			0
$113$	0.291733	−	1.27816i	0.0274439	−	0.120240i	−0.959351	−	0.282217i	$-0.908930\pi$
$113$	0.291733	−	1.27816i	0.0274439	−	0.120240i	0.986794	+	0.161978i	$0.0517873\pi$
$114$		0			0
$115$	−0.991116			−0.0924220
$116$		0			0
$117$	22.1034			2.04346
$118$		0			0
$119$	0.959103	−	4.20211i	0.0879208	−	0.385206i
$120$		0			0
$121$	−0.561495	+	0.704093i	−0.0510450	+	0.0640085i
$122$		0			0
$123$	−5.79031	+	25.3690i	−0.522094	+	2.28745i
$124$		0			0
$125$	−5.27980	−	2.54262i	−0.472239	−	0.227418i
$126$		0			0
$127$	8.84522	−	4.25963i	0.784886	−	0.377981i	0.00188260	−	0.999998i	$-0.499401\pi$
$127$	8.84522	−	4.25963i	0.784886	−	0.377981i	0.783004	+	0.622017i	$0.213686\pi$
$128$		0			0
$129$	−18.4256	+	8.87330i	−1.62228	+	0.781251i
$130$		0			0
$131$	1.30095	+	1.63134i	0.113665	+	0.142531i	0.835409	−	0.549629i	$-0.185231\pi$
$131$	1.30095	+	1.63134i	0.113665	+	0.142531i	−0.721744	+	0.692160i	$0.756659\pi$
$132$		0			0
$133$	3.33139			0.288869
$134$		0			0
$135$	−0.360513	−	1.57951i	−0.0310280	−	0.135943i
$136$		0			0
$137$	5.87422	+	2.82887i	0.501868	+	0.241687i	0.667650	−	0.744475i	$-0.267300\pi$
$137$	5.87422	+	2.82887i	0.501868	+	0.241687i	−0.165782	+	0.986163i	$0.553015\pi$
$138$		0			0
$139$	−2.48124	−	3.11138i	−0.210456	−	0.263904i	0.665388	−	0.746498i	$-0.268266\pi$
$139$	−2.48124	−	3.11138i	−0.210456	−	0.263904i	−0.875844	+	0.482594i	$0.839695\pi$
$140$		0			0
$141$	−4.90076	−	21.4716i	−0.412719	−	1.80824i
$142$		0			0
$143$	−10.9331	+	13.7097i	−0.914274	+	1.14646i
$144$		0			0
$145$	2.10082	−	2.51520i	0.174463	−	0.208876i
$146$		0			0
$147$	10.8615	−	13.6199i	0.895841	−	1.12335i
$148$		0			0
$149$	−2.45408	−	10.7520i	−0.201046	−	0.880840i	−0.970302	−	0.241898i	$-0.922230\pi$
$149$	−2.45408	−	10.7520i	−0.201046	−	0.880840i	0.769256	−	0.638941i	$-0.220627\pi$
$150$		0			0
$151$	5.08706	+	6.37897i	0.413979	+	0.519113i	0.944479	−	0.328572i	$-0.106567\pi$
$151$	5.08706	+	6.37897i	0.413979	+	0.519113i	−0.530500	+	0.847685i	$0.677996\pi$
$152$		0			0
$153$	−24.0487	−	11.5812i	−1.94422	−	0.936287i
$154$		0			0
$155$	−0.267475	−	1.17188i	−0.0214841	−	0.0941280i
$156$		0			0
$157$	18.2828			1.45912			0.729562	−	0.683915i	$-0.239724\pi$
$157$	18.2828			1.45912			0.729562	+	0.683915i	$0.239724\pi$
$158$		0			0
$159$	−12.7748	−	16.0190i	−1.01310	−	1.27039i
$160$		0			0
$161$	0.949169	−	0.457095i	0.0748050	−	0.0360242i
$162$		0			0
$163$	−17.4871	+	8.42132i	−1.36969	+	0.659609i	−0.966775	−	0.255628i	$-0.917718\pi$
$163$	−17.4871	+	8.42132i	−1.36969	+	0.659609i	−0.402917	+	0.915237i	$0.632004\pi$
$164$		0			0
$165$	4.61194	+	2.22100i	0.359039	+	0.172904i
$166$		0			0
$167$	−5.31968	+	23.3070i	−0.411649	+	1.80355i	0.164695	+	0.986345i	$0.447336\pi$
$167$	−5.31968	+	23.3070i	−0.411649	+	1.80355i	−0.576344	+	0.817207i	$0.695521\pi$
$168$		0			0
$169$	10.8775	−	13.6400i	0.836734	−	1.04923i
$170$		0			0
$171$	4.59075	−	20.1134i	0.351064	−	1.53811i
$172$		0			0
$173$	1.03092			0.0783792			0.0391896	−	0.999232i	$-0.487522\pi$
$173$	1.03092			0.0783792			0.0391896	+	0.999232i	$0.487522\pi$
$174$		0			0
$175$	2.99471			0.226379
$176$		0			0
$177$	−0.660585	+	2.89421i	−0.0496526	+	0.217542i
$178$		0			0
$179$	10.8118	−	13.5575i	0.808109	−	1.01334i	−0.191385	−	0.981515i	$-0.561298\pi$
$179$	10.8118	−	13.5575i	0.808109	−	1.01334i	0.999494	−	0.0318212i	$-0.0101307\pi$
$180$		0			0
$181$	−0.754541	+	3.30586i	−0.0560846	+	0.245723i	−0.995198	−	0.0978856i	$-0.968792\pi$
$181$	−0.754541	+	3.30586i	−0.0560846	+	0.245723i	0.939113	+	0.343608i	$0.111649\pi$
$182$		0			0
$183$	21.6502	+	10.4262i	1.60043	+	0.770725i
$184$		0			0
$185$	1.58225	−	0.761969i	0.116329	−	0.0560211i
$186$		0			0
$187$	19.0786	−	9.18779i	1.39517	−	0.671878i
$188$		0			0
$189$	1.07371	+	1.34639i	0.0781012	+	0.0979358i
$190$		0			0
$191$	17.7442			1.28393			0.641963	−	0.766735i	$-0.278120\pi$
$191$	17.7442			1.28393			0.641963	+	0.766735i	$0.278120\pi$
$192$		0			0
$193$	−1.04550	−	4.58061i	−0.0752564	−	0.329720i	0.923260	−	0.384176i	$-0.125515\pi$
$193$	−1.04550	−	4.58061i	−0.0752564	−	0.329720i	−0.998516	+	0.0544565i	$0.982657\pi$
$194$		0			0
$195$	−8.00760	−	3.85626i	−0.573436	−	0.276152i
$196$		0			0
$197$	−9.15408	−	11.4788i	−0.652201	−	0.817834i	0.340268	−	0.940328i	$-0.389482\pi$
$197$	−9.15408	−	11.4788i	−0.652201	−	0.817834i	−0.992469	+	0.122494i	$0.960911\pi$
$198$		0			0
$199$	−2.99572	−	13.1251i	−0.212361	−	0.930414i	−0.962958	−	0.269653i	$-0.913091\pi$
$199$	−2.99572	−	13.1251i	−0.212361	−	0.930414i	0.750597	−	0.660761i	$-0.229766\pi$
$200$		0			0
$201$	−20.6323	+	25.8721i	−1.45529	+	1.82487i
$202$		0			0
$203$	−0.851911	+	3.37763i	−0.0597924	+	0.237063i
$204$		0			0
$205$	3.73015	−	4.67746i	0.260525	−	0.326688i
$206$		0			0
$207$	−1.45175	−	6.36053i	−0.100904	−	0.442087i
$208$		0			0
$209$	10.2047	+	12.7962i	0.705871	+	0.885134i
$210$		0			0
$211$	8.59368	+	4.13850i	0.591613	+	0.284906i	0.705639	−	0.708572i	$-0.250660\pi$
$211$	8.59368	+	4.13850i	0.591613	+	0.284906i	−0.114025	+	0.993478i	$0.536375\pi$
$212$		0			0
$213$	−0.225211	−	0.986714i	−0.0154312	−	0.0676086i
$214$		0			0
$215$	4.70195			0.320670
$216$		0			0
$217$	0.796620	+	0.998929i	0.0540781	+	0.0678117i
$218$		0			0
$219$	0.765147	−	0.368475i	0.0517038	−	0.0248992i
$220$		0			0
$221$	−33.1257	+	15.9525i	−2.22828	+	1.07308i
$222$		0			0
$223$	0.596162	+	0.287096i	0.0399219	+	0.0192254i	0.453738	−	0.891135i	$-0.350090\pi$
$223$	0.596162	+	0.287096i	0.0399219	+	0.0192254i	−0.413816	+	0.910360i	$0.635804\pi$
$224$		0			0
$225$	4.12680	−	18.0807i	0.275120	−	1.20538i
$226$		0			0
$227$	−0.697190	+	0.874248i	−0.0462741	+	0.0580259i	−0.804430	−	0.594047i	$-0.797529\pi$
$227$	−0.697190	+	0.874248i	−0.0462741	+	0.0580259i	0.758156	+	0.652073i	$0.226101\pi$
$228$		0			0
$229$	1.11130	−	4.86894i	0.0734370	−	0.321749i	−0.924845	−	0.380345i	$-0.875805\pi$
$229$	1.11130	−	4.86894i	0.0734370	−	0.321749i	0.998282	+	0.0585962i	$0.0186624\pi$
$230$		0			0
$231$	−5.44106			−0.357995
$232$		0			0
$233$	3.74324			0.245228			0.122614	−	0.992454i	$-0.460872\pi$
$233$	3.74324			0.245228			0.122614	+	0.992454i	$0.460872\pi$
$234$		0			0
$235$	−1.12676	+	4.93664i	−0.0735015	+	0.322031i
$236$		0			0
$237$	−28.3943	+	35.6053i	−1.84440	+	2.31281i
$238$		0			0
$239$	−3.58045	+	15.6870i	−0.231600	+	1.01470i	0.716713	+	0.697368i	$0.245646\pi$
$239$	−3.58045	+	15.6870i	−0.231600	+	1.01470i	−0.948313	+	0.317337i	$0.897211\pi$
$240$		0			0
$241$	19.9713	+	9.61765i	1.28646	+	0.619527i	0.947043	−	0.321108i	$-0.104055\pi$
$241$	19.9713	+	9.61765i	1.28646	+	0.619527i	0.339419	+	0.940635i	$0.389770\pi$
$242$		0			0
$243$	−19.0500	+	9.17398i	−1.22206	+	0.588511i
$244$		0			0
$245$	−3.60858	+	1.73780i	−0.230544	+	0.111024i
$246$		0			0
$247$	−17.7181	−	22.2178i	−1.12737	−	1.41368i
$248$		0			0
$249$	−22.7805			−1.44366
$250$		0			0
$251$	0.369520	+	1.61897i	0.0233239	+	0.102189i	0.985250	−	0.171121i	$-0.0547388\pi$
$251$	0.369520	+	1.61897i	0.0233239	+	0.102189i	−0.961926	+	0.273309i	$0.911882\pi$
$252$		0			0
$253$	4.66323	+	2.24569i	0.293175	+	0.141185i
$254$		0			0
$255$	6.69182	+	8.39128i	0.419058	+	0.525482i
$256$		0			0
$257$	−4.16162	−	18.2332i	−0.259595	−	1.13736i	−0.921686	−	0.387936i	$-0.873188\pi$
$257$	−4.16162	−	18.2332i	−0.259595	−	1.13736i	0.662092	−	0.749423i	$-0.269669\pi$
$258$		0			0
$259$	−1.16387	+	1.45944i	−0.0723191	+	0.0906852i
$260$		0			0
$261$	19.2186	+	9.79791i	1.18960	+	0.606475i
$262$		0			0
$263$	6.96230	−	8.73044i	0.429314	−	0.538342i	−0.519378	−	0.854544i	$-0.673836\pi$
$263$	6.96230	−	8.73044i	0.429314	−	0.538342i	0.948692	+	0.316202i	$0.102408\pi$
$264$		0			0
$265$	1.04824	+	4.59264i	0.0643929	+	0.282124i
$266$		0			0
$267$	15.8716	+	19.9023i	0.971325	+	1.21800i
$268$		0			0
$269$	−14.1318	−	6.80552i	−0.861632	−	0.414940i	−0.0497499	−	0.998762i	$-0.515842\pi$
$269$	−14.1318	−	6.80552i	−0.861632	−	0.414940i	−0.811882	+	0.583822i	$0.801557\pi$
$270$		0			0
$271$	−3.65527	−	16.0148i	−0.222042	−	0.972828i	−0.955938	−	0.293567i	$-0.905158\pi$
$271$	−3.65527	−	16.0148i	−0.222042	−	0.972828i	0.733897	−	0.679261i	$-0.237700\pi$
$272$		0			0
$273$	9.44717			0.571769
$274$		0			0
$275$	9.17334	+	11.5030i	0.553173	+	0.693657i
$276$		0			0
$277$	2.00027	−	0.963280i	0.120185	−	0.0578779i	−0.372825	−	0.927902i	$-0.621611\pi$
$277$	2.00027	−	0.963280i	0.120185	−	0.0578779i	0.493010	+	0.870024i	$0.335897\pi$
$278$		0			0
$279$	7.12883	−	3.43307i	0.426792	−	0.205532i
$280$		0			0
$281$	−4.54079	−	2.18673i	−0.270881	−	0.130449i	0.293513	−	0.955955i	$-0.405176\pi$
$281$	−4.54079	−	2.18673i	−0.270881	−	0.130449i	−0.564393	+	0.825506i	$0.690890\pi$
$282$		0			0
$283$	−2.73940	+	12.0021i	−0.162840	+	0.713449i	0.825901	+	0.563815i	$0.190667\pi$
$283$	−2.73940	+	12.0021i	−0.162840	+	0.713449i	−0.988741	+	0.149635i	$0.952190\pi$
$284$		0			0
$285$	−5.17221	+	6.48574i	−0.306375	+	0.384182i
$286$		0			0
$287$	−1.41507	+	6.19982i	−0.0835288	+	0.365964i
$288$		0			0
$289$	27.3995			1.61174
$290$		0			0
$291$	23.2640			1.36376
$292$		0			0
$293$	−4.95946	+	21.7288i	−0.289735	+	1.26941i	0.595155	+	0.803611i	$0.297091\pi$
$293$	−4.95946	+	21.7288i	−0.289735	+	1.26941i	−0.884890	+	0.465801i	$0.845766\pi$
$294$		0			0
$295$	0.425553	−	0.533626i	0.0247766	−	0.0310689i
$296$		0			0
$297$	−1.88267	+	8.24850i	−0.109243	+	0.478626i
$298$		0			0
$299$	−8.09664	−	3.89914i	−0.468241	−	0.225493i
$300$		0			0
$301$	−4.50295	+	2.16851i	−0.259546	+	0.124991i
$302$		0			0
$303$	34.7416	−	16.7307i	1.99585	−	0.961152i
$304$		0			0
$305$	−3.44467	−	4.31947i	−0.197241	−	0.247332i
$306$		0			0
$307$	13.1298			0.749360			0.374680	−	0.927154i	$-0.377753\pi$
$307$	13.1298			0.749360			0.374680	+	0.927154i	$0.377753\pi$
$308$		0			0
$309$	−5.78474	−	25.3446i	−0.329082	−	1.44180i
$310$		0			0
$311$	−26.8389	−	12.9249i	−1.52189	−	0.732905i	−0.528637	−	0.848848i	$-0.677297\pi$
$311$	−26.8389	−	12.9249i	−1.52189	−	0.732905i	−0.993256	+	0.115943i	$0.963011\pi$
$312$		0			0
$313$	−16.6866	−	20.9243i	−0.943181	−	1.18271i	−0.983019	−	0.183506i	$-0.941255\pi$
$313$	−16.6866	−	20.9243i	−0.943181	−	1.18271i	0.0398375	−	0.999206i	$-0.487316\pi$
$314$		0			0
$315$	−0.350885	−	1.53733i	−0.0197701	−	0.0866186i
$316$		0			0
$317$	19.0006	−	23.8259i	1.06718	−	1.33820i	0.129155	−	0.991624i	$-0.458773\pi$
$317$	19.0006	−	23.8259i	1.06718	−	1.33820i	0.938023	−	0.346574i	$-0.112655\pi$
$318$		0			0
$319$	−15.5834	+	7.07400i	−0.872502	+	0.396068i
$320$		0			0
$321$	1.78669	−	2.24044i	0.0997235	−	0.125049i
$322$		0			0
$323$	7.63626	+	33.4566i	0.424893	+	1.86158i
$324$		0			0
$325$	−15.9274	−	19.9724i	−0.883495	−	1.10787i
$326$		0			0
$327$	−10.8335	−	5.21716i	−0.599096	−	0.288510i
$328$		0			0
$329$	−1.19768	−	5.24736i	−0.0660300	−	0.289296i
$330$		0			0
$331$	−8.87712			−0.487931			−0.243965	−	0.969784i	$-0.578448\pi$
$331$	−8.87712			−0.487931			−0.243965	+	0.969784i	$0.578448\pi$
$332$		0			0
$333$	7.20758	+	9.03802i	0.394973	+	0.495281i
$334$		0			0
$335$	6.85478	−	3.30109i	0.374517	−	0.180358i
$336$		0			0
$337$	6.72814	−	3.24010i	0.366505	−	0.176500i	−0.241561	−	0.970386i	$-0.577660\pi$
$337$	6.72814	−	3.24010i	0.366505	−	0.176500i	0.608067	+	0.793886i	$0.291945\pi$
$338$		0			0
$339$	−3.12646	−	1.50563i	−0.169806	−	0.0817744i
$340$		0			0
$341$	−1.39680	+	6.11980i	−0.0756412	+	0.331406i
$342$		0			0
$343$	5.47753	−	6.86861i	0.295759	−	0.370870i
$344$		0			0
$345$	−0.583747	+	2.55756i	−0.0314279	+	0.137695i
$346$		0			0
$347$	−35.4169			−1.90128			−0.950639	−	0.310299i	$-0.899571\pi$
$347$	−35.4169			−1.90128			−0.950639	+	0.310299i	$0.899571\pi$
$348$		0			0
$349$	−20.1279			−1.07742			−0.538712	−	0.842490i	$-0.681089\pi$
$349$	−20.1279			−1.07742			−0.538712	+	0.842490i	$0.681089\pi$
$350$		0			0
$351$	3.26882	−	14.3216i	0.174477	−	0.764433i
$352$		0			0
$353$	18.5997	−	23.3233i	0.989964	−	1.24138i	0.0195804	−	0.999808i	$-0.493767\pi$
$353$	18.5997	−	23.3233i	0.989964	−	1.24138i	0.970384	−	0.241568i	$-0.0776616\pi$
$354$		0			0
$355$	−0.0517793	+	0.226860i	−0.00274816	+	0.0120405i
$356$		0			0
$357$	−10.2786	−	4.94991i	−0.544001	−	0.261977i
$358$		0			0
$359$	21.6181	−	10.4107i	1.14096	−	0.549458i	0.234655	−	0.972079i	$-0.424604\pi$
$359$	21.6181	−	10.4107i	1.14096	−	0.549458i	0.906307	+	0.422620i	$0.138890\pi$
$360$		0			0
$361$	−6.77903	+	3.26461i	−0.356791	+	0.171821i
$362$		0			0
$363$	1.48620	+	1.86363i	0.0780050	+	0.0978152i
$364$		0			0
$365$	−0.195255			−0.0102201
$366$		0			0
$367$	0.447103	+	1.95889i	0.0233386	+	0.102253i	0.985256	−	0.171088i	$-0.0547283\pi$
$367$	0.447103	+	1.95889i	0.0233386	+	0.102253i	−0.961917	+	0.273341i	$0.911871\pi$
$368$		0			0
$369$	35.4816	+	17.0870i	1.84710	+	0.889516i
$370$		0			0
$371$	−3.12197	−	3.91482i	−0.162084	−	0.203247i
$372$		0			0
$373$	−1.42888	−	6.26031i	−0.0739844	−	0.324147i	0.924370	−	0.381498i	$-0.124592\pi$
$373$	−1.42888	−	6.26031i	−0.0739844	−	0.324147i	−0.998354	+	0.0573512i	$0.981735\pi$
$374$		0			0
$375$	−9.67089	+	12.1269i	−0.499403	+	0.626231i
$376$		0			0
$377$	27.0570	−	12.2824i	1.39351	−	0.632576i
$378$		0			0
$379$	−7.98938	+	10.0184i	−0.410387	+	0.514609i	−0.943472	−	0.331453i	$-0.892461\pi$
$379$	−7.98938	+	10.0184i	−0.410387	+	0.514609i	0.533085	+	0.846062i	$0.321033\pi$
$380$		0			0
$381$	−5.78229	−	25.3338i	−0.296235	−	1.29789i
$382$		0			0
$383$	−14.1165	−	17.7016i	−0.721320	−	0.904507i	0.277092	−	0.960844i	$-0.410629\pi$
$383$	−14.1165	−	17.7016i	−0.721320	−	0.904507i	−0.998412	+	0.0563364i	$0.982058\pi$
$384$		0			0
$385$	1.12709	+	0.542779i	0.0574420	+	0.0276626i
$386$		0			0
$387$	6.88724	+	30.1750i	0.350098	+	1.53388i
$388$		0			0
$389$	8.34460			0.423088			0.211544	−	0.977368i	$-0.432151\pi$
$389$	8.34460			0.423088			0.211544	+	0.977368i	$0.432151\pi$
$390$		0			0
$391$	6.76623	+	8.48458i	0.342183	+	0.429084i
$392$		0			0
$393$	4.97590	−	2.39627i	0.251001	−	0.120876i
$394$		0			0
$395$	9.43359	−	4.54298i	0.474656	−	0.228582i
$396$		0			0
$397$	15.2601	+	7.34888i	0.765883	+	0.368830i	0.775683	−	0.631122i	$-0.217405\pi$
$397$	15.2601	+	7.34888i	0.765883	+	0.368830i	−0.00980058	+	0.999952i	$0.503120\pi$
$398$		0			0
$399$	1.96213	−	8.59663i	0.0982291	−	0.430370i
$400$		0			0
$401$	−10.6691	+	13.3786i	−0.532789	+	0.668096i	−0.973269	−	0.229666i	$-0.926237\pi$
$401$	−10.6691	+	13.3786i	−0.532789	+	0.668096i	0.440481	+	0.897762i	$0.354808\pi$
$402$		0			0
$403$	2.42524	−	10.6257i	0.120810	−	0.529301i
$404$		0			0
$405$	3.02499			0.150313
$406$		0			0
$407$	−9.17099			−0.454589
$408$		0			0
$409$	−2.91969	+	12.7920i	−0.144369	+	0.632523i	0.850021	+	0.526749i	$0.176589\pi$
$409$	−2.91969	+	12.7920i	−0.144369	+	0.632523i	−0.994390	+	0.105774i	$0.966268\pi$
$410$		0			0
$411$	10.7597	−	13.4922i	0.530736	−	0.665522i
$412$		0			0
$413$	−0.161437	+	0.707303i	−0.00794381	+	0.0348041i
$414$		0			0
$415$	4.71889	+	2.27250i	0.231641	+	0.111553i
$416$		0			0
$417$	−9.49030	+	4.57029i	−0.464742	+	0.223808i
$418$		0			0
$419$	−8.68443	+	4.18220i	−0.424262	+	0.204314i	−0.633817	−	0.773483i	$-0.718513\pi$
$419$	−8.68443	+	4.18220i	−0.424262	+	0.204314i	0.209555	+	0.977797i	$0.432799\pi$
$420$		0			0
$421$	14.3621	+	18.0096i	0.699968	+	0.877732i	0.997021	−	0.0771289i	$-0.0245753\pi$
$421$	14.3621	+	18.0096i	0.699968	+	0.877732i	−0.297053	+	0.954861i	$0.596004\pi$
$422$		0			0
$423$	−33.3316			−1.62064
$424$		0			0
$425$	6.86451	+	30.0754i	0.332978	+	1.45887i
$426$		0			0
$427$	5.29099	+	2.54801i	0.256049	+	0.123307i
$428$		0			0
$429$	28.9384	+	36.2876i	1.39716	+	1.75198i
$430$		0			0
$431$	2.01619	+	8.83352i	0.0971166	+	0.425496i	0.999990	−	0.00441028i	$-0.00140384\pi$
$431$	2.01619	+	8.83352i	0.0971166	+	0.425496i	−0.902874	+	0.429906i	$0.858547\pi$
$432$		0			0
$433$	1.20618	−	1.51250i	0.0579653	−	0.0726862i	−0.752004	−	0.659159i	$-0.770912\pi$
$433$	1.20618	−	1.51250i	0.0579653	−	0.0726862i	0.809969	+	0.586473i	$0.199484\pi$
$434$		0			0
$435$	−5.25311	−	6.90254i	−0.251867	−	0.330951i
$436$		0			0
$437$	−5.22972	+	6.55786i	−0.250171	+	0.313705i
$438$		0			0
$439$	0.490574	+	2.14935i	0.0234138	+	0.102583i	0.985285	−	0.170921i	$-0.0546744\pi$
$439$	0.490574	+	2.14935i	0.0234138	+	0.102583i	−0.961871	+	0.273504i	$0.911817\pi$
$440$		0			0
$441$	−16.4381	−	20.6127i	−0.782767	−	0.981559i
$442$		0			0
$443$	1.03099	+	0.496499i	0.0489839	+	0.0235894i	0.458215	−	0.888841i	$-0.348489\pi$
$443$	1.03099	+	0.496499i	0.0489839	+	0.0235894i	−0.409231	+	0.912431i	$0.634203\pi$
$444$		0			0
$445$	−1.30235	−	5.70597i	−0.0617373	−	0.270489i
$446$		0			0
$447$	−29.1909			−1.38068
$448$		0			0
$449$	−5.33964	−	6.69570i	−0.251993	−	0.315990i	0.639704	−	0.768621i	$-0.279057\pi$
$449$	−5.33964	−	6.69570i	−0.251993	−	0.315990i	−0.891698	+	0.452631i	$0.850485\pi$
$450$		0			0
$451$	−28.1488	+	13.5557i	−1.32547	+	0.638314i
$452$		0			0
$453$	19.4571	−	9.37002i	0.914172	−	0.440242i
$454$		0			0
$455$	−1.95694	−	0.942414i	−0.0917428	−	0.0441810i
$456$		0			0
$457$	−4.52455	+	19.8233i	−0.211649	+	0.927296i	0.751797	+	0.659395i	$0.229187\pi$
$457$	−4.52455	+	19.8233i	−0.211649	+	0.927296i	−0.963446	+	0.267902i	$0.913670\pi$
$458$		0			0
$459$	−11.0604	+	13.8693i	−0.516257	+	0.647366i
$460$		0			0
$461$	−3.56144	+	15.6037i	−0.165873	+	0.726735i	0.821745	+	0.569855i	$0.193001\pi$
$461$	−3.56144	+	15.6037i	−0.165873	+	0.726735i	−0.987618	+	0.156880i	$0.949856\pi$
$462$		0			0
$463$	−6.22178			−0.289151			−0.144575	−	0.989494i	$-0.546182\pi$
$463$	−6.22178			−0.289151			−0.144575	+	0.989494i	$0.546182\pi$
$464$		0			0
$465$	−3.18157			−0.147542
$466$		0			0
$467$	5.86388	−	25.6913i	0.271348	−	1.18885i	−0.637076	−	0.770801i	$-0.719856\pi$
$467$	5.86388	−	25.6913i	0.271348	−	1.18885i	0.908423	−	0.418051i	$-0.137287\pi$
$468$		0			0
$469$	−5.04223	+	6.32276i	−0.232829	+	0.291958i
$470$		0			0
$471$	10.7682	−	47.1785i	0.496172	−	2.17387i
$472$		0			0
$473$	−22.1228	−	10.6538i	−1.01721	−	0.489862i
$474$		0			0
$475$	−21.4823	+	10.3453i	−0.985674	+	0.474676i
$476$		0			0
$477$	−27.9380	+	13.4542i	−1.27919	+	0.616028i
$478$		0			0
$479$	24.2468	+	30.4045i	1.10786	+	1.38922i	0.912791	+	0.408427i	$0.133923\pi$
$479$	24.2468	+	30.4045i	1.10786	+	1.38922i	0.195072	+	0.980789i	$0.437506\pi$
$480$		0			0
$481$	15.9234			0.726043
$482$		0			0
$483$	−0.620489	−	2.71854i	−0.0282332	−	0.123698i
$484$		0			0
$485$	−4.81904	−	2.32073i	−0.218821	−	0.105379i
$486$		0			0
$487$	−12.6125	−	15.8156i	−0.571527	−	0.716672i	0.409115	−	0.912483i	$-0.365838\pi$
$487$	−12.6125	−	15.8156i	−0.571527	−	0.716672i	−0.980642	+	0.195811i	$0.937266\pi$
$488$		0			0
$489$	11.4316	+	50.0852i	0.516956	+	2.26493i
$490$		0			0
$491$	13.9463	−	17.4882i	0.629389	−	0.789229i	−0.360242	−	0.932859i	$-0.617306\pi$
$491$	13.9463	−	17.4882i	0.629389	−	0.789229i	0.989632	+	0.143629i	$0.0458773\pi$
$492$		0			0
$493$	−35.8737	−	0.813361i	−1.61567	−	0.0366319i
$494$		0			0
$495$	4.83021	−	6.05690i	0.217102	−	0.272237i
$496$		0			0
$497$	−0.0550383	−	0.241139i	−0.00246881	−	0.0108166i
$498$		0			0
$499$	22.6465	+	28.3979i	1.01380	+	1.27126i	0.962128	+	0.272598i	$0.0878830\pi$
$499$	22.6465	+	28.3979i	1.01380	+	1.27126i	0.0516701	+	0.998664i	$0.483546\pi$
$500$		0			0
$501$	57.0104	+	27.4548i	2.54704	+	1.22659i
$502$		0			0
$503$	1.30663	+	5.72473i	0.0582598	+	0.255253i	0.995668	−	0.0929795i	$-0.0296391\pi$
$503$	1.30663	+	5.72473i	0.0582598	+	0.255253i	−0.937408	+	0.348233i	$0.886782\pi$
$504$		0			0
$505$	−8.86556			−0.394512
$506$		0			0
$507$	−28.7913	−	36.1031i	−1.27866	−	1.60339i
$508$		0			0
$509$	−2.06644	+	0.995143i	−0.0915932	+	0.0441090i	−0.479119	−	0.877750i	$-0.659044\pi$
$509$	−2.06644	+	0.995143i	−0.0915932	+	0.0441090i	0.387526	+	0.921859i	$0.373330\pi$
$510$		0			0
$511$	0.186991	−	0.0900500i	0.00827199	−	0.00398358i
$512$		0			0
$513$	−12.3533	−	5.94905i	−0.545413	−	0.262657i
$514$		0			0
$515$	−1.32999	+	5.82709i	−0.0586066	+	0.256772i
$516$		0			0
$517$	16.4870	−	20.6740i	0.725096	−	0.909242i
$518$		0			0
$519$	0.607190	−	2.66027i	0.0266527	−	0.116773i
$520$		0			0
$521$	28.1445			1.23303			0.616517	−	0.787342i	$-0.288543\pi$
$521$	28.1445			1.23303			0.616517	+	0.787342i	$0.288543\pi$
$522$		0			0
$523$	−22.9140			−1.00196			−0.500980	−	0.865459i	$-0.667027\pi$
$523$	−22.9140			−1.00196			−0.500980	+	0.865459i	$0.667027\pi$
$524$		0			0
$525$	1.76383	−	7.72783i	0.0769797	−	0.337270i
$526$		0			0
$527$	−8.20606	+	10.2901i	−0.357462	+	0.448243i
$528$		0			0
$529$	4.52774	−	19.8373i	0.196858	−	0.862493i
$530$		0			0
$531$	4.04790	+	1.94937i	0.175664	+	0.0845953i
$532$		0			0
$533$	48.8740	−	23.5365i	2.11697	−	1.01948i
$534$		0			0
$535$	−0.593604	+	0.285865i	−0.0256637	+	0.0123590i
$536$		0			0
$537$	−28.6171	−	35.8847i	−1.23492	−	1.54854i
$538$		0			0
$539$	20.9160			0.900916
$540$		0			0
$541$	6.29296	+	27.5713i	0.270556	+	1.18538i	0.909359	+	0.416012i	$0.136573\pi$
$541$	6.29296	+	27.5713i	0.270556	+	1.18538i	−0.638803	+	0.769370i	$0.720570\pi$
$542$		0			0
$543$	8.08633	+	3.89417i	0.347018	+	0.167115i
$544$		0			0
$545$	1.72368	+	2.16143i	0.0738343	+	0.0925853i
$546$		0			0
$547$	10.1039	+	44.2679i	0.432010	+	1.89276i	0.450208	+	0.892924i	$0.351350\pi$
$547$	10.1039	+	44.2679i	0.432010	+	1.89276i	−0.0181984	+	0.999834i	$0.505793\pi$
$548$		0			0
$549$	22.6748	−	28.4333i	0.967737	−	1.21350i
$550$		0			0
$551$	−5.55702	−	27.1720i	−0.236737	−	1.15757i
$552$		0			0
$553$	−6.93915	+	8.70141i	−0.295082	+	0.370022i
$554$		0			0
$555$	−1.03434	−	4.53175i	−0.0439054	−	0.192362i
$556$		0			0
$557$	−8.86884	−	11.1212i	−0.375785	−	0.471219i	0.557593	−	0.830114i	$-0.311725\pi$
$557$	−8.86884	−	11.1212i	−0.375785	−	0.471219i	−0.933378	+	0.358895i	$0.883154\pi$
$558$		0			0
$559$	38.4113	+	18.4979i	1.62462	+	0.782377i
$560$		0			0
$561$	−12.4721	−	54.6437i	−0.526571	−	2.30706i
$562$		0			0
$563$	33.6042			1.41625			0.708124	−	0.706088i	$-0.249542\pi$
$563$	33.6042			1.41625			0.708124	+	0.706088i	$0.249542\pi$
$564$		0			0
$565$	0.497439	+	0.623768i	0.0209274	+	0.0262421i
$566$		0			0
$567$	−2.89697	+	1.39511i	−0.121661	+	0.0585889i
$568$		0			0
$569$	15.1015	−	7.27249i	0.633087	−	0.304879i	−0.0896797	−	0.995971i	$-0.528584\pi$
$569$	15.1015	−	7.27249i	0.633087	−	0.304879i	0.722767	+	0.691092i	$0.242870\pi$
$570$		0			0
$571$	−6.53857	−	3.14881i	−0.273631	−	0.131774i	0.292037	−	0.956407i	$-0.405667\pi$
$571$	−6.53857	−	3.14881i	−0.273631	−	0.131774i	−0.565667	+	0.824634i	$0.691381\pi$
$572$		0			0
$573$	10.4510	−	45.7888i	0.436597	−	1.91285i
$574$		0			0
$575$	−4.70119	+	5.89510i	−0.196053	+	0.245843i
$576$		0			0
$577$	−9.66876	+	42.3616i	−0.402516	+	1.76354i	0.214637	+	0.976694i	$0.431143\pi$
$577$	−9.66876	+	42.3616i	−0.402516	+	1.76354i	−0.617153	+	0.786844i	$0.711714\pi$
$578$		0			0
$579$	−12.4360			−0.516823
$580$		0			0
$581$	−5.56723			−0.230968
$582$		0			0
$583$	5.47410	−	23.9836i	0.226714	−	0.993300i
$584$		0			0
$585$	−8.38657	+	10.5164i	−0.346742	+	0.434801i
$586$		0			0
$587$	7.24630	−	31.7481i	0.299087	−	1.31039i	−0.572403	−	0.819972i	$-0.693989\pi$
$587$	7.24630	−	31.7481i	0.299087	−	1.31039i	0.871490	−	0.490413i	$-0.163154\pi$
$588$		0			0
$589$	−9.16530	−	4.41378i	−0.377650	−	0.181867i
$590$		0			0
$591$	−35.0126	+	16.8612i	−1.44023	+	0.693577i
$592$		0			0
$593$	−23.6346	+	11.3818i	−0.970555	+	0.467394i	−0.850846	−	0.525415i	$-0.823910\pi$
$593$	−23.6346	+	11.3818i	−0.970555	+	0.467394i	−0.119708	+	0.992809i	$0.538196\pi$
$594$		0			0
$595$	1.63538	+	2.05071i	0.0670442	+	0.0840708i
$596$		0			0
$597$	−35.6336			−1.45839
$598$		0			0
$599$	−3.61237	−	15.8268i	−0.147597	−	0.646666i	−0.993549	−	0.113406i	$-0.963824\pi$
$599$	−3.61237	−	15.8268i	−0.147597	−	0.646666i	0.845951	−	0.533260i	$-0.179033\pi$
$600$		0			0
$601$	−13.4796	−	6.49142i	−0.549843	−	0.264790i	0.138269	−	0.990395i	$-0.455846\pi$
$601$	−13.4796	−	6.49142i	−0.549843	−	0.264790i	−0.688112	+	0.725604i	$0.741560\pi$
$602$		0			0
$603$	31.2255	+	39.1556i	1.27160	+	1.59454i
$604$		0			0
$605$	−0.121951	−	0.534300i	−0.00495800	−	0.0217224i
$606$		0			0
$607$	16.4040	−	20.5699i	0.665817	−	0.834908i	−0.328146	−	0.944627i	$-0.606424\pi$
$607$	16.4040	−	20.5699i	0.665817	−	0.834908i	0.993963	+	0.109719i	$0.0349952\pi$
$608$		0			0
$609$	8.21418	+	4.18770i	0.332855	+	0.169694i
$610$		0			0
$611$	−28.6259	+	35.8957i	−1.15808	+	1.45219i
$612$		0			0
$613$	−4.99932	−	21.9034i	−0.201921	−	0.884672i	−0.969766	−	0.244037i	$-0.921528\pi$
$613$	−4.99932	−	21.9034i	−0.201921	−	0.884672i	0.767846	−	0.640635i	$-0.221329\pi$
$614$		0			0
$615$	−9.87316	−	12.3806i	−0.398124	−	0.499232i
$616$		0			0
$617$	−1.81423	−	0.873689i	−0.0730383	−	0.0351734i	0.397008	−	0.917815i	$-0.370049\pi$
$617$	−1.81423	−	0.873689i	−0.0730383	−	0.0351734i	−0.470046	+	0.882642i	$0.655763\pi$
$618$		0			0
$619$	2.72335	+	11.9318i	0.109461	+	0.479579i	0.999709	+	0.0241040i	$0.00767328\pi$
$619$	2.72335	+	11.9318i	0.109461	+	0.479579i	−0.890249	+	0.455475i	$0.849470\pi$
$620$		0			0
$621$	−4.33593			−0.173995
$622$		0			0
$623$	3.87879	+	4.86384i	0.155400	+	0.194866i
$624$		0			0
$625$	−17.6429	+	8.49638i	−0.705716	+	0.339855i
$626$		0			0
$627$	39.0309	−	18.7963i	1.55874	−	0.750652i
$628$		0			0
$629$	−17.3247	−	8.34316i	−0.690783	−	0.332663i
$630$		0			0
$631$	9.40605	−	41.2106i	0.374449	−	1.64057i	−0.339671	−	0.940544i	$-0.610316\pi$
$631$	9.40605	−	41.2106i	0.374449	−	1.64057i	0.714120	−	0.700023i	$-0.246827\pi$
$632$		0			0
$633$	15.7409	−	19.7384i	0.625643	−	0.784532i
$634$		0			0
$635$	−1.32943	+	5.82462i	−0.0527569	+	0.231143i
$636$		0			0
$637$	−36.3159			−1.43889
$638$		0			0
$639$	−1.53173			−0.0605942
$640$		0			0
$641$	2.99155	−	13.1068i	0.118159	−	0.517688i	−0.880859	−	0.473379i	$-0.843034\pi$
$641$	2.99155	−	13.1068i	0.118159	−	0.517688i	0.999018	−	0.0443094i	$-0.0141087\pi$
$642$		0			0
$643$	−3.02815	+	3.79719i	−0.119419	+	0.149746i	−0.837947	−	0.545751i	$-0.816244\pi$
$643$	−3.02815	+	3.79719i	−0.119419	+	0.149746i	0.718529	+	0.695497i	$0.244816\pi$
$644$		0			0
$645$	2.76936	−	12.1333i	0.109043	−	0.477750i
$646$		0			0
$647$	−11.8422	−	5.70291i	−0.465566	−	0.224205i	0.186369	−	0.982480i	$-0.440328\pi$
$647$	−11.8422	−	5.70291i	−0.465566	−	0.224205i	−0.651935	+	0.758275i	$0.726042\pi$
$648$		0			0
$649$	−3.21134	+	1.54650i	−0.126056	+	0.0607054i
$650$		0			0
$651$	3.04692	−	1.46732i	0.119418	−	0.0575088i
$652$		0			0
$653$	7.98269	+	10.0100i	0.312387	+	0.391721i	0.913094	−	0.407748i	$-0.133686\pi$
$653$	7.98269	+	10.0100i	0.312387	+	0.391721i	−0.600708	+	0.799469i	$0.705114\pi$
$654$		0			0
$655$	−1.26978			−0.0496144
$656$		0			0
$657$	−0.286002	−	1.25305i	−0.0111580	−	0.0488863i
$658$		0			0
$659$	5.61293	+	2.70304i	0.218649	+	0.105296i	0.540002	−	0.841664i	$-0.318423\pi$
$659$	5.61293	+	2.70304i	0.218649	+	0.105296i	−0.321353	+	0.946959i	$0.604138\pi$
$660$		0			0
$661$	24.1640	+	30.3007i	0.939872	+	1.17856i	0.983753	+	0.179526i	$0.0574563\pi$
$661$	24.1640	+	30.3007i	0.939872	+	1.17856i	−0.0438811	+	0.999037i	$0.513972\pi$
$662$		0			0
$663$	21.6549	+	94.8764i	0.841007	+	3.68469i
$664$		0			0
$665$	−1.26401	+	1.58502i	−0.0490163	+	0.0614645i
$666$		0			0
$667$	−5.31152	−	6.97929i	−0.205663	−	0.270239i
$668$		0			0
$669$	1.09198	−	1.36930i	0.0422183	−	0.0529400i
$670$		0			0
$671$	6.42009	+	28.1282i	0.247845	+	1.08588i
$672$		0			0
$673$	7.61156	+	9.54459i	0.293404	+	0.367917i	0.906583	−	0.422027i	$-0.138681\pi$
$673$	7.61156	+	9.54459i	0.293404	+	0.367917i	−0.613179	+	0.789944i	$0.710110\pi$
$674$		0			0
$675$	−11.1049	−	5.34782i	−0.427427	−	0.205838i
$676$		0			0
$677$	5.72363	+	25.0769i	0.219977	+	0.963782i	0.957494	+	0.288453i	$0.0931410\pi$
$677$	5.72363	+	25.0769i	0.219977	+	0.963782i	−0.737517	+	0.675328i	$0.764002\pi$
$678$		0			0
$679$	5.68538			0.218185
$680$		0			0
$681$	1.84536	+	2.31401i	0.0707143	+	0.0886729i
$682$		0			0
$683$	29.1088	−	14.0180i	1.11382	−	0.536386i	0.215840	−	0.976429i	$-0.430751\pi$
$683$	29.1088	−	14.0180i	1.11382	−	0.536386i	0.897977	+	0.440043i	$0.145037\pi$
$684$		0			0
$685$	−3.57475	+	1.72151i	−0.136584	+	0.0657755i
$686$		0			0
$687$	−11.9097	−	5.73542i	−0.454384	−	0.218820i
$688$		0			0
$689$	−9.50454	+	41.6421i	−0.362094	+	1.58644i
$690$		0			0
$691$	−18.2145	+	22.8403i	−0.692914	+	0.868886i	−0.996472	−	0.0839266i	$-0.973254\pi$
$691$	−18.2145	+	22.8403i	−0.692914	+	0.868886i	0.303558	+	0.952813i	$0.401825\pi$
$692$		0			0
$693$	−1.83239	+	8.02821i	−0.0696066	+	0.304966i
$694$		0			0
$695$	2.42179			0.0918637
$696$		0			0
$697$	−65.5074			−2.48127
$698$		0			0
$699$	2.20470	−	9.65940i	0.0833892	−	0.365352i
$700$		0			0
$701$	29.8358	−	37.4129i	1.12688	−	1.41306i	0.228668	−	0.973505i	$-0.426563\pi$
$701$	29.8358	−	37.4129i	1.12688	−	1.41306i	0.898213	−	0.439560i	$-0.144866\pi$
$702$		0			0
$703$	3.30719	−	14.4898i	0.124733	−	0.546492i
$704$		0			0
$705$	12.0753	+	5.81517i	0.454783	+	0.219012i
$706$		0			0
$707$	8.49035	−	4.08873i	0.319312	−	0.153773i
$708$		0			0
$709$	20.6001	−	9.92046i	0.773651	−	0.372571i	−0.00503262	−	0.999987i	$-0.501602\pi$
$709$	20.6001	−	9.92046i	0.773651	−	0.372571i	0.778684	+	0.627417i	$0.215888\pi$
$710$		0			0
$711$	42.9727	+	53.8861i	1.61160	+	2.02089i
$712$		0			0
$713$	−3.21695			−0.120476
$714$		0			0
$715$	−2.37455	−	10.4036i	−0.0888033	−	0.389073i
$716$		0			0
$717$	38.3712	+	18.4786i	1.43300	+	0.690096i
$718$		0			0
$719$	−16.6633	−	20.8951i	−0.621437	−	0.779257i	0.367109	−	0.930178i	$-0.380348\pi$
$719$	−16.6633	−	20.8951i	−0.621437	−	0.779257i	−0.988546	+	0.150921i	$0.951776\pi$
$720$		0			0
$721$	−1.41371	−	6.19385i	−0.0526492	−	0.230671i
$722$		0			0
$723$	36.5809	−	45.8710i	1.36046	−	1.70596i
$724$		0			0
$725$	−4.99540	−	24.4259i	−0.185525	−	0.907157i
$726$		0			0
$727$	4.87215	−	6.10949i	0.180698	−	0.226588i	−0.683230	−	0.730203i	$-0.739425\pi$
$727$	4.87215	−	6.10949i	0.180698	−	0.226588i	0.863928	+	0.503615i	$0.167997\pi$
$728$		0			0
$729$	9.13499	+	40.0230i	0.338333	+	1.48233i
$730$		0			0
$731$	−32.0997	−	40.2517i	−1.18725	−	1.48876i
$732$		0			0
$733$	−3.15887	−	1.52123i	−0.116675	−	0.0561879i	0.374636	−	0.927172i	$-0.377768\pi$
$733$	−3.15887	−	1.52123i	−0.116675	−	0.0561879i	−0.491311	+	0.870984i	$0.663482\pi$
$734$		0			0
$735$	2.35899	+	10.3354i	0.0870128	+	0.381228i
$736$		0			0
$737$	−39.7316			−1.46353
$738$		0			0
$739$	8.96361	+	11.2400i	0.329732	+	0.413470i	0.918869	−	0.394562i	$-0.129104\pi$
$739$	8.96361	+	11.2400i	0.329732	+	0.413470i	−0.589137	+	0.808033i	$0.700532\pi$
$740$		0			0
$741$	−67.7684	+	32.6355i	−2.48953	+	1.19890i
$742$		0			0
$743$	−29.1030	+	14.0152i	−1.06768	+	0.514169i	−0.883360	−	0.468696i	$-0.844724\pi$
$743$	−29.1030	+	14.0152i	−1.06768	+	0.514169i	−0.184324	+	0.982865i	$0.559010\pi$
$744$		0			0
$745$	6.04677	+	2.91197i	0.221536	+	0.106686i
$746$		0			0
$747$	−7.67180	+	33.6124i	−0.280697	+	1.22981i
$748$		0			0
$749$	0.436642	−	0.547532i	0.0159546	−	0.0200064i
$750$		0			0
$751$	−5.48785	+	24.0439i	−0.200255	+	0.877373i	0.770527	+	0.637408i	$0.219993\pi$
$751$	−5.48785	+	24.0439i	−0.200255	+	0.877373i	−0.970781	+	0.239965i	$0.922864\pi$
$752$		0			0
$753$	4.39538			0.160177
$754$		0			0
$755$	−4.96517			−0.180701
$756$		0			0
$757$	−10.3927	+	45.5332i	−0.377728	+	1.65493i	0.326678	+	0.945136i	$0.394071\pi$
$757$	−10.3927	+	45.5332i	−0.377728	+	1.65493i	−0.704406	+	0.709798i	$0.748786\pi$
$758$		0			0
$759$	8.54153	−	10.7107i	0.310038	−	0.388775i
$760$		0			0
$761$	−6.86687	+	30.0857i	−0.248924	+	1.09061i	0.683702	+	0.729762i	$0.260369\pi$
$761$	−6.86687	+	30.0857i	−0.248924	+	1.09061i	−0.932626	+	0.360845i	$0.882488\pi$
$762$		0			0
$763$	−2.64756	−	1.27500i	−0.0958482	−	0.0461580i
$764$		0			0
$765$	14.6348	−	7.04776i	0.529123	−	0.254812i
$766$		0			0
$767$	5.57576	−	2.68515i	0.201329	−	0.0969550i
$768$		0			0
$769$	−22.4543	−	28.1568i	−0.809723	−	1.01536i	−0.999438	−	0.0335214i	$-0.989328\pi$
$769$	−22.4543	−	28.1568i	−0.809723	−	1.01536i	0.189715	−	0.981839i	$-0.439244\pi$
$770$		0			0
$771$	−49.5018			−1.78276
$772$		0			0
$773$	7.37251	+	32.3011i	0.265171	+	1.16179i	0.915558	+	0.402186i	$0.131750\pi$
$773$	7.37251	+	32.3011i	0.265171	+	1.16179i	−0.650387	+	0.759603i	$0.725393\pi$
$774$		0			0
$775$	−8.23903	−	3.96771i	−0.295955	−	0.142524i
$776$		0			0
$777$	3.08058	+	3.86292i	0.110515	+	0.138582i
$778$		0			0
$779$	−11.2666	−	49.3622i	−0.403668	−	1.76858i
$780$		0			0
$781$	0.757647	−	0.950059i	0.0271107	−	0.0339958i
$782$		0			0
$783$	9.19064	−	11.0035i	0.328447	−	0.393232i
$784$		0			0
$785$	−6.93693	+	8.69864i	−0.247590	+	0.310468i
$786$		0			0
$787$	−2.24673	−	9.84358i	−0.0800874	−	0.350886i	0.918968	−	0.394331i	$-0.129024\pi$
$787$	−2.24673	−	9.84358i	−0.0800874	−	0.350886i	−0.999056	+	0.0434453i	$0.986167\pi$
$788$		0			0
$789$	−18.4282	−	23.1082i	−0.656060	−	0.822674i
$790$		0			0
$791$	−0.764063	−	0.367953i	−0.0271670	−	0.0130829i
$792$		0			0
$793$	−11.1470	−	48.8383i	−0.395843	−	1.73430i
$794$		0			0
$795$	12.4687			0.442217
$796$		0			0
$797$	17.8407	+	22.3716i	0.631952	+	0.792442i	0.989971	−	0.141272i	$-0.0451192\pi$
$797$	17.8407	+	22.3716i	0.631952	+	0.792442i	−0.358019	+	0.933714i	$0.616548\pi$
$798$		0			0
$799$	49.9531	−	24.0561i	1.76721	−	0.851044i
$800$		0			0
$801$	34.7107	−	16.7158i	1.22644	−	0.590623i
$802$		0			0
$803$	0.918678	+	0.442412i	0.0324194	+	0.0156124i
$804$		0			0
$805$	−0.142659	+	0.625032i	−0.00502808	+	0.0220295i
$806$		0			0
$807$	−25.8849	+	32.4587i	−0.911193	+	1.14260i
$808$		0			0
$809$	1.03868	−	4.55073i	0.0365179	−	0.159995i	−0.953381	−	0.301768i	$-0.902423\pi$
$809$	1.03868	−	4.55073i	0.0365179	−	0.159995i	0.989899	+	0.141773i	$0.0452803\pi$
$810$		0			0
$811$	37.5173			1.31741			0.658706	−	0.752400i	$-0.271104\pi$
$811$	37.5173			1.31741			0.658706	+	0.752400i	$0.271104\pi$
$812$		0			0
$813$	−43.4788			−1.52487
$814$		0			0
$815$	2.62829	−	11.5153i	0.0920651	−	0.403364i
$816$		0			0
$817$	24.8103	−	31.1111i	0.868003	−	1.08844i
$818$		0			0
$819$	3.18152	−	13.9392i	0.111171	−	0.487074i
$820$		0			0
$821$	−22.9446	−	11.0496i	−0.800773	−	0.385632i	−0.0117002	−	0.999932i	$-0.503724\pi$
$821$	−22.9446	−	11.0496i	−0.800773	−	0.385632i	−0.789073	+	0.614300i	$0.789439\pi$
$822$		0			0
$823$	−23.3418	+	11.2408i	−0.813644	+	0.391830i	−0.793956	−	0.607976i	$-0.791982\pi$
$823$	−23.3418	+	11.2408i	−0.813644	+	0.391830i	−0.0196886	+	0.999806i	$0.506267\pi$
$824$		0			0
$825$	35.0863	−	16.8967i	1.22155	−	0.588267i
$826$		0			0
$827$	−8.88368	−	11.1398i	−0.308916	−	0.387368i	0.603003	−	0.797739i	$-0.293971\pi$
$827$	−8.88368	−	11.1398i	−0.308916	−	0.387368i	−0.911919	+	0.410371i	$0.865399\pi$
$828$		0			0
$829$	−37.1504			−1.29029			−0.645143	−	0.764062i	$-0.723202\pi$
$829$	−37.1504			−1.29029			−0.645143	+	0.764062i	$0.723202\pi$
$830$		0			0
$831$	−1.30761	−	5.72903i	−0.0453606	−	0.198738i
$832$		0			0
$833$	39.5120	+	19.0280i	1.36901	+	0.659281i
$834$		0			0
$835$	−9.07068	−	11.3743i	−0.313904	−	0.393623i
$836$		0			0
$837$	−1.17015	−	5.12676i	−0.0404462	−	0.177207i
$838$		0			0
$839$	17.3506	−	21.7570i	0.599010	−	0.751135i	−0.386213	−	0.922410i	$-0.626217\pi$
$839$	17.3506	−	21.7570i	0.599010	−	0.751135i	0.985223	+	0.171274i	$0.0547884\pi$
$840$		0			0
$841$	28.9702	+	1.31435i	0.998972	+	0.0453225i
$842$		0			0
$843$	−8.31726	+	10.4295i	−0.286462	+	0.359212i
$844$		0			0
$845$	2.36248	+	10.3507i	0.0812718	+	0.356075i
$846$		0			0
$847$	0.363205	+	0.455444i	0.0124799	+	0.0156493i
$848$		0			0
$849$	29.3578	+	14.1380i	1.00756	+	0.485214i
$850$		0			0
$851$	−1.04584	−	4.58214i	−0.0358511	−	0.157074i
$852$		0			0
$853$	11.2969			0.386800			0.193400	−	0.981120i	$-0.438049\pi$
$853$	11.2969			0.386800			0.193400	+	0.981120i	$0.438049\pi$
$854$		0			0
$855$	7.82778	+	9.81572i	0.267704	+	0.335691i
$856$		0			0
$857$	5.81994	−	2.80274i	0.198805	−	0.0957397i	−0.331832	−	0.943338i	$-0.607667\pi$
$857$	5.81994	−	2.80274i	0.198805	−	0.0957397i	0.530638	+	0.847599i	$0.321952\pi$
$858$		0			0
$859$	15.2289	−	7.33383i	0.519602	−	0.250227i	−0.155653	−	0.987812i	$-0.549748\pi$
$859$	15.2289	−	7.33383i	0.519602	−	0.250227i	0.675254	+	0.737585i	$0.264034\pi$
$860$		0			0
$861$	15.1651	+	7.30314i	0.516826	+	0.248890i
$862$		0			0
$863$	−11.2652	+	49.3560i	−0.383471	+	1.68010i	0.303039	+	0.952978i	$0.401999\pi$
$863$	−11.2652	+	49.3560i	−0.383471	+	1.68010i	−0.686511	+	0.727120i	$0.740859\pi$
$864$		0			0
$865$	−0.391155	+	0.490493i	−0.0132997	+	0.0166773i
$866$		0			0
$867$	16.1378	−	70.7042i	0.548067	−	2.40124i
$868$		0			0
$869$	−54.6789			−1.85485
$870$		0			0
$871$	68.9850			2.33747
$872$		0			0
$873$	7.83462	−	34.3257i	0.265162	−	1.16175i
$874$		0			0
$875$	−2.36343	+	2.96364i	−0.0798984	+	0.100189i
$876$		0			0
$877$	8.66815	−	37.9777i	0.292703	−	1.28241i	−0.588045	−	0.808828i	$-0.700102\pi$
$877$	8.66815	−	37.9777i	0.292703	−	1.28241i	0.880747	−	0.473586i	$-0.157041\pi$
$878$		0			0
$879$	53.1500	+	25.5957i	1.79271	+	0.863321i
$880$		0			0
$881$	4.20644	−	2.02572i	0.141719	−	0.0682481i	−0.361680	−	0.932302i	$-0.617797\pi$
$881$	4.20644	−	2.02572i	0.141719	−	0.0682481i	0.503399	+	0.864054i	$0.332083\pi$
$882$		0			0
$883$	−19.1275	+	9.21133i	−0.643692	+	0.309986i	−0.727102	−	0.686529i	$-0.759133\pi$
$883$	−19.1275	+	9.21133i	−0.643692	+	0.309986i	0.0834097	+	0.996515i	$0.473419\pi$
$884$		0			0
$885$	−1.12638	−	1.41243i	−0.0378627	−	0.0474783i
$886$		0			0
$887$	−18.2793			−0.613760			−0.306880	−	0.951748i	$-0.599285\pi$
$887$	−18.2793			−0.613760			−0.306880	+	0.951748i	$0.599285\pi$
$888$		0			0
$889$	−1.41311	−	6.19123i	−0.0473941	−	0.207647i
$890$		0			0
$891$	−14.2327	−	6.85409i	−0.476813	−	0.229621i
$892$		0			0
$893$	26.7186	+	33.5040i	0.894103	+	1.12117i
$894$		0			0
$895$	2.34819	+	10.2881i	0.0784915	+	0.343894i
$896$		0			0
$897$	−14.8304	+	18.5968i	−0.495174	+	0.620929i
$898$		0			0
$899$	6.81880	−	8.16380i	0.227420	−	0.272278i
$900$		0			0
$901$	32.1597	−	40.3270i	1.07140	−	1.34349i
$902$		0			0
$903$	2.94366	+	12.8970i	0.0979590	+	0.429186i
$904$		0			0
$905$	−1.28658	−	1.61332i	−0.0427674	−	0.0536287i
$906$		0			0
$907$	15.3852	+	7.40912i	0.510857	+	0.246016i	0.671511	−	0.740995i	$-0.265646\pi$
$907$	15.3852	+	7.40912i	0.510857	+	0.246016i	−0.160653	+	0.987011i	$0.551360\pi$
$908$		0			0
$909$	−12.9859	−	56.8951i	−0.430717	−	1.88709i
$910$		0			0
$911$	−33.9161			−1.12369			−0.561846	−	0.827242i	$-0.689909\pi$
$911$	−33.9161			−1.12369			−0.561846	+	0.827242i	$0.689909\pi$
$912$		0			0
$913$	−17.0534	−	21.3843i	−0.564386	−	0.707718i
$914$		0			0
$915$	−13.1752	+	6.34484i	−0.435559	+	0.209754i
$916$		0			0
$917$	1.21604	−	0.585614i	0.0401571	−	0.0193387i
$918$		0			0
$919$	−1.48458	−	0.714935i	−0.0489717	−	0.0235835i	0.409238	−	0.912428i	$-0.365795\pi$
$919$	−1.48458	−	0.714935i	−0.0489717	−	0.0235835i	−0.458209	+	0.888844i	$0.651509\pi$
$920$		0			0
$921$	7.73321	−	33.8814i	0.254818	−	1.11643i
$922$		0			0
$923$	−1.31548	+	1.64956i	−0.0432997	+	0.0542960i
$924$		0			0
$925$	2.97296	−	13.0254i	0.0977502	−	0.428272i
$926$		0			0
$927$	−39.3437			−1.29222
$928$		0			0
$929$	4.05397			0.133006			0.0665032	−	0.997786i	$-0.478816\pi$
$929$	4.05397			0.133006			0.0665032	+	0.997786i	$0.478816\pi$
$930$		0			0
$931$	−7.54261	+	33.0464i	−0.247199	+	1.08305i
$932$		0			0
$933$	−49.1602	+	61.6449i	−1.60943	+	2.01817i
$934$		0			0
$935$	−2.86751	+	12.5634i	−0.0937775	+	0.410866i
$936$		0			0
$937$	16.5794	+	7.98424i	0.541627	+	0.260834i	0.684633	−	0.728888i	$-0.259963\pi$
$937$	16.5794	+	7.98424i	0.541627	+	0.260834i	−0.143006	+	0.989722i	$0.545677\pi$
$938$		0			0
$939$	−63.8230	+	30.7356i	−2.08279	+	1.00302i
$940$		0			0
$941$	38.0680	−	18.3326i	1.24098	−	0.597625i	0.305901	−	0.952063i	$-0.401042\pi$
$941$	38.0680	−	18.3326i	1.24098	−	0.597625i	0.935079	+	0.354439i	$0.115328\pi$
$942$		0			0
$943$	−9.98294	−	12.5182i	−0.325089	−	0.407649i
$944$		0			0
$945$	−1.04799			−0.0340910
$946$		0			0
$947$	−8.32199	−	36.4610i	−0.270428	−	1.18482i	−0.909509	−	0.415684i	$-0.863542\pi$
$947$	−8.32199	−	36.4610i	−0.270428	−	1.18482i	0.639081	−	0.769140i	$-0.279315\pi$
$948$		0			0
$949$	−1.59508	−	0.768149i	−0.0517784	−	0.0249352i
$950$		0			0
$951$	−50.2917	−	63.0638i	−1.63082	−	2.04498i
$952$		0			0
$953$	0.775737	+	3.39873i	0.0251286	+	0.110096i	0.985937	−	0.167118i	$-0.0534461\pi$
$953$	0.775737	+	3.39873i	0.0251286	+	0.110096i	−0.960808	+	0.277214i	$0.910589\pi$
$954$		0			0
$955$	−6.73259	+	8.44241i	−0.217862	+	0.273190i
$956$		0			0
$957$	9.07610	+	44.3792i	0.293389	+	1.43458i
$958$		0			0
$959$	2.62951	−	3.29730i	0.0849113	−	0.106475i
$960$		0			0
$961$	6.02998	+	26.4191i	0.194516	+	0.852228i
$962$		0			0
$963$	−2.70404	−	3.39076i	−0.0871364	−	0.109266i
$964$		0			0
$965$	2.57607	+	1.24057i	0.0829265	+	0.0399353i
$966$		0			0
$967$	−1.25765	−	5.51014i	−0.0404434	−	0.177194i	0.950672	−	0.310197i	$-0.100395\pi$
$967$	−1.25765	−	5.51014i	−0.0404434	−	0.177194i	−0.991116	+	0.133003i	$0.957538\pi$
$968$		0			0
$969$	90.8322			2.91795
$970$		0			0
$971$	21.3905	+	26.8229i	0.686455	+	0.860787i	0.995931	−	0.0901202i	$-0.0287251\pi$
$971$	21.3905	+	26.8229i	0.686455	+	0.860787i	−0.309476	+	0.950907i	$0.600154\pi$
$972$		0			0
$973$	−2.31929	+	1.11691i	−0.0743531	+	0.0358066i
$974$		0			0
$975$	−60.9195	+	29.3373i	−1.95098	+	0.939544i
$976$		0			0
$977$	−29.2767	−	14.0989i	−0.936644	−	0.451064i	−0.0976602	−	0.995220i	$-0.531136\pi$
$977$	−29.2767	−	14.0989i	−0.936644	−	0.451064i	−0.838984	+	0.544156i	$0.816850\pi$
$978$		0			0
$979$	−6.80112	+	29.7976i	−0.217365	+	0.952337i
$980$		0			0
$981$	−11.3463	+	14.2278i	−0.362258	+	0.454257i
$982$		0			0
$983$	−2.58321	+	11.3178i	−0.0823917	+	0.360982i	−0.999271	−	0.0381835i	$-0.987843\pi$
$983$	−2.58321	+	11.3178i	−0.0823917	+	0.360982i	0.916879	+	0.399165i	$0.130700\pi$
$984$		0			0
$985$	8.93473			0.284684
$986$		0			0
$987$	−14.2462			−0.453461
$988$		0			0
$989$	2.80015	−	12.2683i	0.0890396	−	0.390108i
$990$		0			0
$991$	−11.6945	+	14.6644i	−0.371488	+	0.465831i	−0.932075	−	0.362264i	$-0.882004\pi$
$991$	−11.6945	+	14.6644i	−0.371488	+	0.465831i	0.560588	+	0.828095i	$0.310575\pi$
$992$		0			0
$993$	−5.22845	+	22.9073i	−0.165920	+	0.726942i
$994$		0			0
$995$	7.38135	+	3.55467i	0.234005	+	0.112691i
$996$		0			0
$997$	−5.13512	+	2.47294i	−0.162631	+	0.0783189i	−0.513428	−	0.858132i	$-0.671625\pi$
$997$	−5.13512	+	2.47294i	−0.162631	+	0.0783189i	0.350798	+	0.936451i	$0.385911\pi$
$998$		0			0
$999$	6.92200	−	3.33346i	0.219002	−	0.105466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	116.2.g.b.81.2	yes	12
3.2	odd	2		1044.2.u.c.1009.2		12
4.3	odd	2		464.2.u.g.81.1		12
29.11	odd	28		3364.2.c.j.1681.11		12
29.13	even	14		3364.2.a.p.1.5		6
29.16	even	7		3364.2.a.m.1.2		6
29.18	odd	28		3364.2.c.j.1681.2		12
29.24	even	7	inner	116.2.g.b.53.2	✓	12
87.53	odd	14		1044.2.u.c.865.2		12
116.111	odd	14		464.2.u.g.401.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
116.2.g.b.53.2	✓	12	29.24	even	7	inner
116.2.g.b.81.2	yes	12	1.1	even	1	trivial
464.2.u.g.81.1		12	4.3	odd	2
464.2.u.g.401.1		12	116.111	odd	14
1044.2.u.c.865.2		12	87.53	odd	14
1044.2.u.c.1009.2		12	3.2	odd	2
3364.2.a.m.1.2		6	29.16	even	7
3364.2.a.p.1.5		6	29.13	even	14
3364.2.c.j.1681.2		12	29.18	odd	28
3364.2.c.j.1681.11		12	29.11	odd	28

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:	\( N \)	\(=\)	\( 116 = 2^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	116.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.588980 - 2.58049i) q^{3} +(-0.379425 + 0.475783i) q^{5} +(0.143938 - 0.630635i) q^{7} +(-3.60913 - 1.73806i) q^{9} +O(q^{10})\)	\(q+(0.588980 - 2.58049i) q^{3} +(-0.379425 + 0.475783i) q^{5} +(0.143938 - 0.630635i) q^{7} +(-3.60913 - 1.73806i) q^{9} +(2.86324 - 1.37887i) q^{11} +(-4.97137 + 2.39409i) q^{13} +(1.00428 + 1.25933i) q^{15} +6.66330 q^{17} +(1.14602 + 5.02104i) q^{19} +(-1.54257 - 0.742863i) q^{21} +(1.01545 + 1.27333i) q^{23} +(1.03020 + 4.51359i) q^{25} +(-1.65990 + 2.08145i) q^{27} +(-5.38378 - 0.122066i) q^{29} +(-1.23153 + 1.54429i) q^{31} +(-1.87176 - 8.20070i) q^{33} +(0.245432 + 0.307762i) q^{35} +(-2.60003 - 1.25211i) q^{37} +(3.24988 + 14.2387i) q^{39} -9.83108 q^{41} +(-4.81739 - 6.04081i) q^{43} +(2.19633 - 1.05770i) q^{45} +(7.49675 - 3.61024i) q^{47} +(5.92980 + 2.85564i) q^{49} +(3.92455 - 17.1946i) q^{51} +(4.82640 - 6.05211i) q^{53} +(-0.430344 + 1.88546i) q^{55} +13.6317 q^{57} -1.12157 q^{59} +(-2.02019 + 8.85104i) q^{61} +(-1.61557 + 2.02587i) q^{63} +(0.747195 - 3.27367i) q^{65} +(-11.2641 - 5.42452i) q^{67} +(3.88390 - 1.87039i) q^{69} +(0.344508 - 0.165906i) q^{71} +(0.200048 + 0.250852i) q^{73} +12.2540 q^{75} +(-0.457430 - 2.00413i) q^{77} +(-15.5018 - 7.46526i) q^{79} +(-3.09926 - 3.88635i) q^{81} +(-1.91516 - 8.39086i) q^{83} +(-2.52822 + 3.17029i) q^{85} +(-3.48593 + 13.8209i) q^{87} +(-5.99640 + 7.51924i) q^{89} +(0.794224 + 3.47972i) q^{91} +(3.25968 + 4.08751i) q^{93} +(-2.82375 - 1.35985i) q^{95} +(1.95580 + 8.56894i) q^{97} -12.7304 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - q^{5} - 7 q^{7} + q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - q^5 - 7 * q^7 + q^9	\( 12 q - 3 q^{3} - q^{5} - 7 q^{7} + q^{9} + 3 q^{11} - 21 q^{13} + 29 q^{15} - 10 q^{17} + 17 q^{19} + 3 q^{21} - 19 q^{23} - 3 q^{25} + 9 q^{27} - 5 q^{29} - 27 q^{31} - 47 q^{33} + 27 q^{35} - 3 q^{37} - 37 q^{39} - 2 q^{41} - 9 q^{43} + 22 q^{45} + 19 q^{47} + 17 q^{49} + 2 q^{51} + 22 q^{53} + 49 q^{55} + 30 q^{57} + 36 q^{59} - 33 q^{61} + 9 q^{63} + 38 q^{65} - 3 q^{67} + 47 q^{69} - 35 q^{71} + 34 q^{73} - 44 q^{75} - 27 q^{77} - 19 q^{79} - 39 q^{81} - q^{83} - 34 q^{85} - 25 q^{87} - 11 q^{89} - 23 q^{91} + 7 q^{93} - 105 q^{95} + 38 q^{97} - 16 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - q^5 - 7 * q^7 + q^9 + 3 * q^11 - 21 * q^13 + 29 * q^15 - 10 * q^17 + 17 * q^19 + 3 * q^21 - 19 * q^23 - 3 * q^25 + 9 * q^27 - 5 * q^29 - 27 * q^31 - 47 * q^33 + 27 * q^35 - 3 * q^37 - 37 * q^39 - 2 * q^41 - 9 * q^43 + 22 * q^45 + 19 * q^47 + 17 * q^49 + 2 * q^51 + 22 * q^53 + 49 * q^55 + 30 * q^57 + 36 * q^59 - 33 * q^61 + 9 * q^63 + 38 * q^65 - 3 * q^67 + 47 * q^69 - 35 * q^71 + 34 * q^73 - 44 * q^75 - 27 * q^77 - 19 * q^79 - 39 * q^81 - q^83 - 34 * q^85 - 25 * q^87 - 11 * q^89 - 23 * q^91 + 7 * q^93 - 105 * q^95 + 38 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more