LMFDB - Embedded newform 912.2.bb.f.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(31,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 5]))

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

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

chi := DirichletCharacter("912.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Root			$0.403374 - 1.68443i$ of defining polynomial
Character	$\chi$	$=$	912.31
Dual form			912.2.bb.f.559.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(-1.66044 - 2.87597i) q^{5} +2.71781i q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +(-1.66044 - 2.87597i) q^{5} +2.71781i q^{7} +(-0.500000 + 0.866025i) q^{9} +0.985762i q^{11} +(4.33502 + 2.50283i) q^{13} +(1.66044 - 2.87597i) q^{15} +(-2.51414 - 4.35461i) q^{17} +(0.193252 + 4.35461i) q^{19} +(-2.35369 + 1.35891i) q^{21} +(3.68872 + 2.12968i) q^{23} +(-3.01414 + 5.22064i) q^{25} -1.00000 q^{27} +(5.83502 + 3.36885i) q^{29} +2.32088 q^{31} +(-0.853695 + 0.492881i) q^{33} +(7.81635 - 4.51277i) q^{35} +8.27925i q^{37} +5.00565i q^{39} +(-9.96265 + 5.75194i) q^{41} +(9.48133 - 5.47405i) q^{43} +3.32088 q^{45} +(6.41478 + 3.70357i) q^{47} -0.386505 q^{49} +(2.51414 - 4.35461i) q^{51} +(5.14631 + 2.97122i) q^{53} +(2.83502 - 1.63680i) q^{55} +(-3.67458 + 2.34467i) q^{57} +(-1.66044 - 2.87597i) q^{59} +(3.62763 - 6.28324i) q^{61} +(-2.35369 - 1.35891i) q^{63} -16.6232i q^{65} +(-6.67458 + 11.5607i) q^{67} +4.25936i q^{69} +(2.19325 + 3.79882i) q^{71} +(-2.52827 - 4.37910i) q^{73} -6.02827 q^{75} -2.67912 q^{77} +(-5.48133 - 9.49394i) q^{79} +(-0.500000 - 0.866025i) q^{81} +8.70923i q^{83} +(-8.34916 + 14.4612i) q^{85} +6.73770i q^{87} +(-6.10896 - 3.52701i) q^{89} +(-6.80221 + 11.7818i) q^{91} +(1.16044 + 2.00994i) q^{93} +(12.2029 - 7.78637i) q^{95} +(-7.12763 + 4.11514i) q^{97} +(-0.853695 - 0.492881i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 2 q^{5} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 2 * q^5 - 3 * q^9	$ 6 q + 3 q^{3} - 2 q^{5} - 3 q^{9} - 3 q^{13} + 2 q^{15} - 2 q^{17} + 4 q^{19} - 9 q^{21} - 12 q^{23} - 5 q^{25} - 6 q^{27} + 6 q^{29} - 2 q^{31} - 6 q^{35} - 12 q^{41} + 33 q^{43} + 4 q^{45} + 18 q^{47} - 8 q^{49} + 2 q^{51} + 36 q^{53} - 12 q^{55} - q^{57} - 2 q^{59} + 3 q^{61} - 9 q^{63} - 19 q^{67} + 16 q^{71} + 11 q^{73} - 10 q^{75} - 32 q^{77} - 9 q^{79} - 3 q^{81} - 8 q^{85} + 6 q^{89} - q^{91} - q^{93} + 26 q^{95} - 24 q^{97}+O(q^{100}) $ 6 * q + 3 * q^3 - 2 * q^5 - 3 * q^9 - 3 * q^13 + 2 * q^15 - 2 * q^17 + 4 * q^19 - 9 * q^21 - 12 * q^23 - 5 * q^25 - 6 * q^27 + 6 * q^29 - 2 * q^31 - 6 * q^35 - 12 * q^41 + 33 * q^43 + 4 * q^45 + 18 * q^47 - 8 * q^49 + 2 * q^51 + 36 * q^53 - 12 * q^55 - q^57 - 2 * q^59 + 3 * q^61 - 9 * q^63 - 19 * q^67 + 16 * q^71 + 11 * q^73 - 10 * q^75 - 32 * q^77 - 9 * q^79 - 3 * q^81 - 8 * q^85 + 6 * q^89 - q^91 - q^93 + 26 * q^95 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$-1$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	−1.66044	−	2.87597i	−0.742572	−	1.28617i	−0.951320	−	0.308204i	$-0.900272\pi$
$5$	−1.66044	−	2.87597i	−0.742572	−	1.28617i	0.208748	−	0.977969i	$-0.433061\pi$
$6$		0			0
$7$			2.71781i			1.02724i	0.858019	+	0.513618i	$0.171695\pi$
$7$			2.71781i			1.02724i	−0.858019	+	0.513618i	$0.828305\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$			0.985762i			0.297218i	0.988896	+	0.148609i	$0.0474796\pi$
$11$			0.985762i			0.297218i	−0.988896	+	0.148609i	$0.952520\pi$
$12$		0			0
$13$	4.33502	+	2.50283i	1.20232	+	0.694159i	0.961070	−	0.276304i	$-0.0891098\pi$
$13$	4.33502	+	2.50283i	1.20232	+	0.694159i	0.241248	+	0.970463i	$0.422443\pi$
$14$		0			0
$15$	1.66044	−	2.87597i	0.428724	−	0.742572i
$16$		0			0
$17$	−2.51414	−	4.35461i	−0.609768	−	1.05615i	−0.991278	−	0.131784i	$-0.957929\pi$
$17$	−2.51414	−	4.35461i	−0.609768	−	1.05615i	0.381511	−	0.924364i	$-0.375404\pi$
$18$		0			0
$19$	0.193252	+	4.35461i	0.0443351	+	0.999017i
$19$	0.193252	+	4.35461i	0.0443351	+	0.999017i
$20$		0			0
$21$	−2.35369	+	1.35891i	−0.513618	+	0.296538i
$22$		0			0
$23$	3.68872	+	2.12968i	0.769150	+	0.444069i	0.832571	−	0.553918i	$-0.186868\pi$
$23$	3.68872	+	2.12968i	0.769150	+	0.444069i	−0.0634210	+	0.997987i	$0.520201\pi$
$24$		0			0
$25$	−3.01414	+	5.22064i	−0.602827	+	1.04413i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	5.83502	+	3.36885i	1.08354	+	0.625580i	0.931848	−	0.362848i	$-0.118196\pi$
$29$	5.83502	+	3.36885i	1.08354	+	0.625580i	0.151688	+	0.988428i	$0.451529\pi$
$30$		0			0
$31$	2.32088			0.416843			0.208422	−	0.978039i	$-0.433167\pi$
$31$	2.32088			0.416843			0.208422	+	0.978039i	$0.433167\pi$
$32$		0			0
$33$	−0.853695	+	0.492881i	−0.148609	+	0.0857995i
$34$		0			0
$35$	7.81635	−	4.51277i	1.32120	−	0.762797i
$36$		0			0
$37$			8.27925i			1.36110i	0.732701	+	0.680550i	$0.238259\pi$
$37$			8.27925i			1.36110i	−0.732701	+	0.680550i	$0.761741\pi$
$38$		0			0
$39$			5.00565i			0.801546i
$40$		0			0
$41$	−9.96265	+	5.75194i	−1.55591	+	0.898302i	−0.558263	+	0.829664i	$0.688532\pi$
$41$	−9.96265	+	5.75194i	−1.55591	+	0.898302i	−0.997642	+	0.0686385i	$0.978134\pi$
$42$		0			0
$43$	9.48133	−	5.47405i	1.44589	−	0.834784i	0.447656	−	0.894206i	$-0.352259\pi$
$43$	9.48133	−	5.47405i	1.44589	−	0.834784i	0.998233	+	0.0594217i	$0.0189257\pi$
$44$		0			0
$45$	3.32088			0.495048
$46$		0			0
$47$	6.41478	+	3.70357i	0.935692	+	0.540222i	0.888607	−	0.458669i	$-0.151674\pi$
$47$	6.41478	+	3.70357i	0.935692	+	0.540222i	0.0470845	+	0.998891i	$0.485007\pi$
$48$		0			0
$49$	−0.386505			−0.0552150
$50$		0			0
$51$	2.51414	−	4.35461i	0.352050	−	0.609768i
$52$		0			0
$53$	5.14631	+	2.97122i	0.706899	+	0.408129i	0.809912	−	0.586551i	$-0.199515\pi$
$53$	5.14631	+	2.97122i	0.706899	+	0.408129i	−0.103013	+	0.994680i	$0.532848\pi$
$54$		0			0
$55$	2.83502	−	1.63680i	0.382274	−	0.220706i
$56$		0			0
$57$	−3.67458	+	2.34467i	−0.486710	+	0.310559i
$58$		0			0
$59$	−1.66044	−	2.87597i	−0.216171	−	0.374419i	0.737463	−	0.675387i	$-0.236024\pi$
$59$	−1.66044	−	2.87597i	−0.216171	−	0.374419i	−0.953634	+	0.300968i	$0.902690\pi$
$60$		0			0
$61$	3.62763	−	6.28324i	0.464471	−	0.804487i	−0.534707	−	0.845038i	$-0.679578\pi$
$61$	3.62763	−	6.28324i	0.464471	−	0.804487i	0.999177	+	0.0405508i	$0.0129113\pi$
$62$		0			0
$63$	−2.35369	−	1.35891i	−0.296538	−	0.171206i
$64$		0			0
$65$		−	16.6232i		−	2.06185i
$66$		0			0
$67$	−6.67458	+	11.5607i	−0.815430	+	1.41237i	0.0935894	+	0.995611i	$0.470166\pi$
$67$	−6.67458	+	11.5607i	−0.815430	+	1.41237i	−0.909019	+	0.416755i	$0.863167\pi$
$68$		0			0
$69$			4.25936i			0.512767i
$70$		0			0
$71$	2.19325	+	3.79882i	0.260291	+	0.450838i	0.966319	−	0.257346i	$-0.0828481\pi$
$71$	2.19325	+	3.79882i	0.260291	+	0.450838i	−0.706028	+	0.708184i	$0.749515\pi$
$72$		0			0
$73$	−2.52827	−	4.37910i	−0.295912	−	0.512535i	0.679285	−	0.733875i	$-0.262290\pi$
$73$	−2.52827	−	4.37910i	−0.295912	−	0.512535i	−0.975197	+	0.221340i	$0.928957\pi$
$74$		0			0
$75$	−6.02827			−0.696085
$76$		0			0
$77$	−2.67912			−0.305314
$78$		0			0
$79$	−5.48133	−	9.49394i	−0.616697	−	1.06815i	−0.990084	−	0.140476i	$-0.955137\pi$
$79$	−5.48133	−	9.49394i	−0.616697	−	1.06815i	0.373387	−	0.927676i	$-0.378196\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			8.70923i			0.955962i	0.878370	+	0.477981i	$0.158631\pi$
$83$			8.70923i			0.955962i	−0.878370	+	0.477981i	$0.841369\pi$
$84$		0			0
$85$	−8.34916	+	14.4612i	−0.905593	+	1.56853i
$86$		0			0
$87$			6.73770i			0.722358i
$88$		0			0
$89$	−6.10896	−	3.52701i	−0.647548	−	0.373862i	0.139968	−	0.990156i	$-0.455300\pi$
$89$	−6.10896	−	3.52701i	−0.647548	−	0.373862i	−0.787516	+	0.616294i	$0.788633\pi$
$90$		0			0
$91$	−6.80221	+	11.7818i	−0.713065	+	1.23507i
$92$		0			0
$93$	1.16044	+	2.00994i	0.120332	+	0.208422i
$94$		0			0
$95$	12.2029	−	7.78637i	1.25199	−	0.798865i
$96$		0			0
$97$	−7.12763	+	4.11514i	−0.723701	+	0.417829i	−0.816113	−	0.577892i	$-0.803876\pi$
$97$	−7.12763	+	4.11514i	−0.723701	+	0.417829i	0.0924121	+	0.995721i	$0.470542\pi$
$98$		0			0
$99$	−0.853695	−	0.492881i	−0.0857995	−	0.0495364i
$100$		0			0
$101$	2.83502	−	4.91040i	0.282095	−	0.488603i	−0.689805	−	0.723995i	$-0.742304\pi$
$101$	2.83502	−	4.91040i	0.282095	−	0.488603i	0.971901	+	0.235392i	$0.0756373\pi$
$102$		0			0
$103$	−10.1222			−0.997367			−0.498683	−	0.866784i	$-0.666183\pi$
$103$	−10.1222			−0.997367			−0.498683	+	0.866784i	$0.666183\pi$
$104$		0			0
$105$	7.81635	+	4.51277i	0.762797	+	0.440401i
$106$		0			0
$107$	0.971726			0.0939403			0.0469702	−	0.998896i	$-0.485043\pi$
$107$	0.971726			0.0939403			0.0469702	+	0.998896i	$0.485043\pi$
$108$		0			0
$109$	−0.579757	+	0.334723i	−0.0555307	+	0.0320607i	−0.527508	−	0.849550i	$-0.676874\pi$
$109$	−0.579757	+	0.334723i	−0.0555307	+	0.0320607i	0.471978	+	0.881611i	$0.343540\pi$
$110$		0			0
$111$	−7.17004	+	4.13963i	−0.680550	+	0.392916i
$112$		0			0
$113$		−	8.39291i		−	0.789539i	−0.918780	−	0.394769i	$-0.870825\pi$
$113$		−	8.39291i		−	0.789539i	0.918780	−	0.394769i	$-0.129175\pi$
$114$		0			0
$115$		−	14.1449i		−	1.31901i
$116$		0			0
$117$	−4.33502	+	2.50283i	−0.400773	+	0.231386i
$118$		0			0
$119$	11.8350	−	6.83295i	1.08491	−	0.626376i
$120$		0			0
$121$	10.0283			0.911661
$122$		0			0
$123$	−9.96265	−	5.75194i	−0.898302	−	0.518635i
$124$		0			0
$125$	3.41478			0.305427
$126$		0			0
$127$	3.70739	−	6.42139i	0.328978	−	0.569806i	−0.653332	−	0.757072i	$-0.726629\pi$
$127$	3.70739	−	6.42139i	0.328978	−	0.569806i	0.982309	+	0.187266i	$0.0599626\pi$
$128$		0			0
$129$	9.48133	+	5.47405i	0.834784	+	0.481963i
$130$		0			0
$131$	−16.5424	+	9.55077i	−1.44532	+	0.834454i	−0.998197	−	0.0600198i	$-0.980884\pi$
$131$	−16.5424	+	9.55077i	−1.44532	+	0.834454i	−0.447120	+	0.894474i	$0.647550\pi$
$132$		0			0
$133$	−11.8350	+	0.525224i	−1.02623	+	0.0455427i
$134$		0			0
$135$	1.66044	+	2.87597i	0.142908	+	0.247524i
$136$		0			0
$137$	10.5424	−	18.2600i	0.900699	−	1.56006i	0.0741101	−	0.997250i	$-0.476388\pi$
$137$	10.5424	−	18.2600i	0.900699	−	1.56006i	0.826589	−	0.562806i	$-0.190278\pi$
$138$		0			0
$139$	10.8588	+	6.26931i	0.921028	+	0.531756i	0.883963	−	0.467557i	$-0.154866\pi$
$139$	10.8588	+	6.26931i	0.921028	+	0.531756i	0.0370651	+	0.999313i	$0.488199\pi$
$140$		0			0
$141$			7.40715i			0.623794i
$142$		0			0
$143$	−2.46719	+	4.27330i	−0.206317	+	0.357351i
$144$		0			0
$145$		−	22.3751i		−	1.85815i
$146$		0			0
$147$	−0.193252	−	0.334723i	−0.0159392	−	0.0276075i
$148$		0			0
$149$	3.04695	+	5.27747i	0.249616	+	0.432347i	0.963419	−	0.267999i	$-0.0863624\pi$
$149$	3.04695	+	5.27747i	0.249616	+	0.432347i	−0.713804	+	0.700346i	$0.753029\pi$
$150$		0			0
$151$	−12.6983			−1.03337			−0.516687	−	0.856174i	$-0.672835\pi$
$151$	−12.6983			−1.03337			−0.516687	+	0.856174i	$0.672835\pi$
$152$		0			0
$153$	5.02827			0.406512
$154$		0			0
$155$	−3.85369	−	6.67479i	−0.309536	−	0.536132i
$156$		0			0
$157$	−8.43438	−	14.6088i	−0.673137	−	1.16591i	−0.977010	−	0.213195i	$-0.931613\pi$
$157$	−8.43438	−	14.6088i	−0.673137	−	1.16591i	0.303873	−	0.952713i	$-0.401720\pi$
$158$		0			0
$159$			5.94244i			0.471266i
$160$		0			0
$161$	−5.78807	+	10.0252i	−0.456164	+	0.790100i
$162$		0			0
$163$		−	16.1932i		−	1.26835i	−0.773189	−	0.634175i	$-0.781340\pi$
$163$		−	16.1932i		−	1.26835i	0.773189	−	0.634175i	$-0.218660\pi$
$164$		0			0
$165$	2.83502	+	1.63680i	0.220706	+	0.127425i
$166$		0			0
$167$	6.68872	−	11.5852i	0.517588	−	0.896489i	−0.482203	−	0.876060i	$-0.660163\pi$
$167$	6.68872	−	11.5852i	0.517588	−	0.896489i	0.999791	−	0.0204298i	$-0.00650347\pi$
$168$		0			0
$169$	6.02827	+	10.4413i	0.463713	+	0.803175i
$170$		0			0
$171$	−3.86783	−	2.00994i	−0.295780	−	0.153704i
$172$		0			0
$173$	10.9572	−	6.32614i	0.833060	−	0.480967i	−0.0218394	−	0.999761i	$-0.506952\pi$
$173$	10.9572	−	6.32614i	0.833060	−	0.480967i	0.854899	+	0.518794i	$0.173619\pi$
$174$		0			0
$175$	−14.1887	−	8.19186i	−1.07257	−	0.619246i
$176$		0			0
$177$	1.66044	−	2.87597i	0.124806	−	0.216171i
$178$		0			0
$179$	0.735663			0.0549861			0.0274930	−	0.999622i	$-0.491248\pi$
$179$	0.735663			0.0549861			0.0274930	+	0.999622i	$0.491248\pi$
$180$		0			0
$181$	5.42024	+	3.12938i	0.402883	+	0.232605i	0.687727	−	0.725969i	$-0.258608\pi$
$181$	5.42024	+	3.12938i	0.402883	+	0.232605i	−0.284844	+	0.958574i	$0.591942\pi$
$182$		0			0
$183$	7.25526			0.536325
$184$		0			0
$185$	23.8109	−	13.7472i	1.75061	−	1.01072i
$186$		0			0
$187$	4.29261	−	2.47834i	0.313907	−	0.181234i
$188$		0			0
$189$		−	2.71781i		−	0.197692i
$190$		0			0
$191$		−	1.84571i		−	0.133551i	−0.997768	−	0.0667754i	$-0.978729\pi$
$191$		−	1.84571i		−	0.133551i	0.997768	−	0.0667754i	$-0.0212711\pi$
$192$		0			0
$193$	−3.92024	+	2.26335i	−0.282185	+	0.162920i	−0.634412	−	0.772995i	$-0.718758\pi$
$193$	−3.92024	+	2.26335i	−0.282185	+	0.162920i	0.352227	+	0.935915i	$0.385424\pi$
$194$		0			0
$195$	14.3961	−	8.31160i	1.03093	−	0.595206i
$196$		0			0
$197$	−13.6892			−0.975318			−0.487659	−	0.873034i	$-0.662149\pi$
$197$	−13.6892			−0.975318			−0.487659	+	0.873034i	$0.662149\pi$
$198$		0			0
$199$	2.10389	+	1.21468i	0.149141	+	0.0861067i	0.572714	−	0.819756i	$-0.305891\pi$
$199$	2.10389	+	1.21468i	0.149141	+	0.0861067i	−0.423572	+	0.905862i	$0.639224\pi$
$200$		0			0
$201$	−13.3492			−0.941577
$202$		0			0
$203$	−9.15591	+	15.8585i	−0.642619	+	1.11305i
$204$		0			0
$205$	33.0848	+	19.1015i	2.31074	+	1.33411i
$206$		0			0
$207$	−3.68872	+	2.12968i	−0.256383	+	0.148023i
$208$		0			0
$209$	−4.29261	+	0.190501i	−0.296926	+	0.0131772i
$210$		0			0
$211$	6.77394	+	11.7328i	0.466337	+	0.807720i	0.999261	−	0.0384438i	$-0.0122401\pi$
$211$	6.77394	+	11.7328i	0.466337	+	0.807720i	−0.532924	+	0.846163i	$0.678907\pi$
$212$		0			0
$213$	−2.19325	+	3.79882i	−0.150279	+	0.260291i
$214$		0			0
$215$	−31.4864	−	18.1787i	−2.14735	−	1.23978i
$216$		0			0
$217$			6.30773i			0.428197i
$218$		0			0
$219$	2.52827	−	4.37910i	0.170845	−	0.295912i
$220$		0			0
$221$		−	25.1698i		−	1.69310i
$222$		0			0
$223$	7.80221	+	13.5138i	0.522475	+	0.904953i	0.999658	+	0.0261490i	$0.00832443\pi$
$223$	7.80221	+	13.5138i	0.522475	+	0.904953i	−0.477183	+	0.878804i	$0.658342\pi$
$224$		0			0
$225$	−3.01414	−	5.22064i	−0.200942	−	0.348043i
$226$		0			0
$227$	16.2926			1.08138			0.540689	−	0.841222i	$-0.318163\pi$
$227$	16.2926			1.08138			0.540689	+	0.841222i	$0.318163\pi$
$228$		0			0
$229$	11.3118			0.747506			0.373753	−	0.927528i	$-0.378071\pi$
$229$	11.3118			0.747506			0.373753	+	0.927528i	$0.378071\pi$
$230$		0			0
$231$	−1.33956	−	2.32018i	−0.0881364	−	0.152657i
$232$		0			0
$233$	−12.7977	−	22.1662i	−0.838404	−	1.45216i	−0.891229	−	0.453554i	$-0.850156\pi$
$233$	−12.7977	−	22.1662i	−0.838404	−	1.45216i	0.0528253	−	0.998604i	$-0.483177\pi$
$234$		0			0
$235$		−	24.5983i		−	1.60462i
$236$		0			0
$237$	5.48133	−	9.49394i	0.356050	−	0.616697i
$238$		0			0
$239$		−	2.47834i		−	0.160310i	−0.996782	−	0.0801552i	$-0.974458\pi$
$239$		−	2.47834i		−	0.160310i	0.996782	−	0.0801552i	$-0.0255416\pi$
$240$		0			0
$241$	−13.9148	−	8.03370i	−0.896330	−	0.517496i	−0.0203221	−	0.999793i	$-0.506469\pi$
$241$	−13.9148	−	8.03370i	−0.896330	−	0.517496i	−0.876008	+	0.482297i	$0.839803\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	0.641769	+	1.11158i	0.0410011	+	0.0710160i
$246$		0			0
$247$	−10.0611	+	19.3610i	−0.640171	+	1.23191i
$248$		0			0
$249$	−7.54241	+	4.35461i	−0.477981	+	0.275962i
$250$		0			0
$251$	−2.45213	−	1.41574i	−0.154777	−	0.0893604i	0.420611	−	0.907241i	$-0.361816\pi$
$251$	−2.45213	−	1.41574i	−0.154777	−	0.0893604i	−0.575388	+	0.817881i	$0.695149\pi$
$252$		0			0
$253$	−2.09936	+	3.63620i	−0.131986	+	0.228606i
$254$		0			0
$255$	−16.6983			−1.04569
$256$		0			0
$257$	−2.23113	−	1.28814i	−0.139174	−	0.0803521i	0.428796	−	0.903401i	$-0.358938\pi$
$257$	−2.23113	−	1.28814i	−0.139174	−	0.0803521i	−0.567970	+	0.823049i	$0.692271\pi$
$258$		0			0
$259$	−22.5015			−1.39817
$260$		0			0
$261$	−5.83502	+	3.36885i	−0.361179	+	0.208527i
$262$		0			0
$263$	−24.7977	+	14.3169i	−1.52909	+	0.882821i	−0.529690	+	0.848191i	$0.677692\pi$
$263$	−24.7977	+	14.3169i	−1.52909	+	0.882821i	−0.999400	+	0.0346292i	$0.988975\pi$
$264$		0			0
$265$		−	19.7342i		−	1.21226i
$266$		0			0
$267$		−	7.05402i		−	0.431699i
$268$		0			0
$269$	−19.2685	+	11.1247i	−1.17482	+	0.678282i	−0.954810	−	0.297215i	$-0.903942\pi$
$269$	−19.2685	+	11.1247i	−1.17482	+	0.678282i	−0.220009	+	0.975498i	$0.570609\pi$
$270$		0			0
$271$	−2.67004	+	1.54155i	−0.162194	+	0.0936425i	−0.578900	−	0.815399i	$-0.696518\pi$
$271$	−2.67004	+	1.54155i	−0.162194	+	0.0936425i	0.416706	+	0.909041i	$0.363184\pi$
$272$		0			0
$273$	−13.6044			−0.823377
$274$		0			0
$275$	−5.14631	−	2.97122i	−0.310334	−	0.179171i
$276$		0			0
$277$	4.25526			0.255674			0.127837	−	0.991795i	$-0.459197\pi$
$277$	4.25526			0.255674			0.127837	+	0.991795i	$0.459197\pi$
$278$		0			0
$279$	−1.16044	+	2.00994i	−0.0694739	+	0.120332i
$280$		0			0
$281$	13.2366	+	7.64215i	0.789629	+	0.455892i	0.839832	−	0.542847i	$-0.182654\pi$
$281$	13.2366	+	7.64215i	0.789629	+	0.455892i	−0.0502030	+	0.998739i	$0.515987\pi$
$282$		0			0
$283$	−24.3027	+	14.0312i	−1.44465	+	0.834068i	−0.998155	−	0.0607193i	$-0.980661\pi$
$283$	−24.3027	+	14.0312i	−1.44465	+	0.834068i	−0.446493	+	0.894787i	$0.647327\pi$
$284$		0			0
$285$	12.8446	+	6.67479i	0.760850	+	0.395381i
$286$		0			0
$287$	−15.6327	−	27.0766i	−0.922769	−	1.59828i
$288$		0			0
$289$	−4.14177	+	7.17375i	−0.243633	+	0.421986i
$290$		0			0
$291$	−7.12763	−	4.11514i	−0.417829	−	0.241234i
$292$		0			0
$293$			1.11158i			0.0649390i	0.999473	+	0.0324695i	$0.0103372\pi$
$293$			1.11158i			0.0649390i	−0.999473	+	0.0324695i	$0.989663\pi$
$294$		0			0
$295$	−5.51414	+	9.55077i	−0.321045	+	0.556067i
$296$		0			0
$297$		−	0.985762i		−	0.0571997i
$298$		0			0
$299$	10.6604	+	18.4644i	0.616509	+	1.06783i
$300$		0			0
$301$	14.8774	+	25.7685i	0.857521	+	1.48527i
$302$		0			0
$303$	5.67004			0.325735
$304$		0			0
$305$	−24.0939			−1.37961
$306$		0			0
$307$	−12.4485	−	21.5615i	−0.710474	−	1.23058i	−0.964679	−	0.263427i	$-0.915147\pi$
$307$	−12.4485	−	21.5615i	−0.710474	−	1.23058i	0.254205	−	0.967150i	$-0.418186\pi$
$308$		0			0
$309$	−5.06108	−	8.76605i	−0.287915	−	0.498683i
$310$		0			0
$311$		−	9.06236i		−	0.513879i	−0.966427	−	0.256940i	$-0.917286\pi$
$311$		−	9.06236i		−	0.513879i	0.966427	−	0.256940i	$-0.0827141\pi$
$312$		0			0
$313$	3.19325	−	5.53088i	0.180493	−	0.312624i	−0.761555	−	0.648100i	$-0.775564\pi$
$313$	3.19325	−	5.53088i	0.180493	−	0.312624i	0.942049	+	0.335476i	$0.108897\pi$
$314$		0			0
$315$			9.02554i			0.508532i
$316$		0			0
$317$	2.39611	+	1.38339i	0.134579	+	0.0776990i	0.565778	−	0.824558i	$-0.308576\pi$
$317$	2.39611	+	1.38339i	0.134579	+	0.0776990i	−0.431199	+	0.902257i	$0.641909\pi$
$318$		0			0
$319$	−3.32088	+	5.75194i	−0.185934	+	0.322047i
$320$		0			0
$321$	0.485863	+	0.841540i	0.0271182	+	0.0469702i
$322$		0			0
$323$	18.4768	−	11.7896i	1.02808	−	0.655993i
$324$		0			0
$325$	−26.1327	+	15.0877i	−1.44958	+	0.836916i
$326$		0			0
$327$	−0.579757	−	0.334723i	−0.0320607	−	0.0185102i
$328$		0			0
$329$	−10.0656	+	17.4342i	−0.554936	+	0.961177i
$330$		0			0
$331$	27.6610			1.52038			0.760192	−	0.649698i	$-0.225105\pi$
$331$	27.6610			1.52038			0.760192	+	0.649698i	$0.225105\pi$
$332$		0			0
$333$	−7.17004	−	4.13963i	−0.392916	−	0.226850i
$334$		0			0
$335$	44.3310			2.42206
$336$		0			0
$337$	15.9202	−	9.19156i	0.867231	−	0.500696i	0.000803838	−	1.00000i	$-0.499744\pi$
$337$	15.9202	−	9.19156i	0.867231	−	0.500696i	0.866427	+	0.499304i	$0.166411\pi$
$338$		0			0
$339$	7.26847	−	4.19646i	0.394769	−	0.227920i
$340$		0			0
$341$			2.28784i			0.123893i
$342$		0			0
$343$			17.9742i			0.970518i
$344$		0			0
$345$	12.2498	−	7.07243i	0.659507	−	0.380767i
$346$		0			0
$347$	4.73153	−	2.73175i	0.254002	−	0.146648i	−0.367594	−	0.929987i	$-0.619818\pi$
$347$	4.73153	−	2.73175i	0.254002	−	0.146648i	0.621595	+	0.783339i	$0.286485\pi$
$348$		0			0
$349$	22.6700			1.21350			0.606750	−	0.794893i	$-0.292473\pi$
$349$	22.6700			1.21350			0.606750	+	0.794893i	$0.292473\pi$
$350$		0			0
$351$	−4.33502	−	2.50283i	−0.231386	−	0.133591i
$352$		0			0
$353$	2.03735			0.108437			0.0542185	−	0.998529i	$-0.482733\pi$
$353$	2.03735			0.108437			0.0542185	+	0.998529i	$0.482733\pi$
$354$		0			0
$355$	7.28354	−	12.6155i	0.386570	−	0.669559i
$356$		0			0
$357$	11.8350	+	6.83295i	0.626376	+	0.361638i
$358$		0			0
$359$	30.7175	−	17.7348i	1.62121	−	0.936005i	0.634611	−	0.772832i	$-0.281160\pi$
$359$	30.7175	−	17.7348i	1.62121	−	0.936005i	0.986597	−	0.163174i	$-0.0521731\pi$
$360$		0			0
$361$	−18.9253	+	1.68308i	−0.996069	+	0.0885831i
$362$		0			0
$363$	5.01414	+	8.68474i	0.263174	+	0.455831i
$364$		0			0
$365$	−8.39611	+	14.5425i	−0.439472	+	0.761188i
$366$		0			0
$367$	1.44398	+	0.833682i	0.0753752	+	0.0435179i	0.537214	−	0.843446i	$-0.319477\pi$
$367$	1.44398	+	0.833682i	0.0753752	+	0.0435179i	−0.461839	+	0.886964i	$0.652810\pi$
$368$		0			0
$369$		−	11.5039i		−	0.598868i
$370$		0			0
$371$	−8.07522	+	13.9867i	−0.419245	+	0.726153i
$372$		0			0
$373$		−	17.5110i		−	0.906686i	−0.891336	−	0.453343i	$-0.850231\pi$
$373$		−	17.5110i		−	0.906686i	0.891336	−	0.453343i	$-0.149769\pi$
$374$		0			0
$375$	1.70739	+	2.95729i	0.0881692	+	0.152714i
$376$		0			0
$377$	16.8633	+	29.2081i	0.868504	+	1.50429i
$378$		0			0
$379$	22.4905			1.15526			0.577630	−	0.816298i	$-0.303978\pi$
$379$	22.4905			1.15526			0.577630	+	0.816298i	$0.303978\pi$
$380$		0			0
$381$	7.41478			0.379871
$382$		0			0
$383$	10.1746	+	17.6229i	0.519897	+	0.900488i	0.999732	+	0.0231292i	$0.00736291\pi$
$383$	10.1746	+	17.6229i	0.519897	+	0.900488i	−0.479836	+	0.877358i	$0.659304\pi$
$384$		0			0
$385$	4.44852	+	7.70506i	0.226717	+	0.392686i
$386$		0			0
$387$			10.9481i			0.556523i
$388$		0			0
$389$	11.7881	−	20.4175i	0.597679	−	1.03521i	−0.395484	−	0.918473i	$-0.629423\pi$
$389$	11.7881	−	20.4175i	0.597679	−	1.03521i	0.993163	−	0.116738i	$-0.0372436\pi$
$390$		0			0
$391$		−	21.4172i		−	1.08312i
$392$		0			0
$393$	−16.5424	−	9.55077i	−0.834454	−	0.481772i
$394$		0			0
$395$	−18.2029	+	31.5283i	−0.915885	+	1.58636i
$396$		0			0
$397$	−16.3633	−	28.3421i	−0.821250	−	1.42245i	−0.904752	−	0.425939i	$-0.859944\pi$
$397$	−16.3633	−	28.3421i	−0.821250	−	1.42245i	0.0835014	−	0.996508i	$-0.473390\pi$
$398$		0			0
$399$	−6.37237	−	9.98682i	−0.319017	−	0.499966i
$400$		0			0
$401$	−16.3533	+	9.44158i	−0.816645	+	0.471490i	−0.849258	−	0.527978i	$-0.822950\pi$
$401$	−16.3533	+	9.44158i	−0.816645	+	0.471490i	0.0326134	+	0.999468i	$0.489617\pi$
$402$		0			0
$403$	10.0611	+	5.80877i	0.501178	+	0.289355i
$404$		0			0
$405$	−1.66044	+	2.87597i	−0.0825080	+	0.142908i
$406$		0			0
$407$	−8.16137			−0.404544
$408$		0			0
$409$	15.6646	+	9.04395i	0.774564	+	0.447194i	0.834500	−	0.551008i	$-0.185757\pi$
$409$	15.6646	+	9.04395i	0.774564	+	0.447194i	−0.0599366	+	0.998202i	$0.519090\pi$
$410$		0			0
$411$	21.0848			1.04004
$412$		0			0
$413$	7.81635	−	4.51277i	0.384617	−	0.222059i
$414$		0			0
$415$	25.0475	−	14.4612i	1.22953	−	0.709871i
$416$		0			0
$417$			12.5386i			0.614019i
$418$		0			0
$419$			0.353130i			0.0172515i	0.999963	+	0.00862577i	$0.00274570\pi$
$419$			0.353130i			0.0172515i	−0.999963	+	0.00862577i	$0.997254\pi$
$420$		0			0
$421$	24.7977	−	14.3169i	1.20856	−	0.697765i	0.246119	−	0.969240i	$-0.420845\pi$
$421$	24.7977	−	14.3169i	1.20856	−	0.697765i	0.962446	+	0.271474i	$0.0875112\pi$
$422$		0			0
$423$	−6.41478	+	3.70357i	−0.311897	+	0.180074i
$424$		0			0
$425$	30.3118			1.47034
$426$		0			0
$427$	17.0767	+	9.85922i	0.826398	+	0.477121i
$428$		0			0
$429$	−4.93438			−0.238234
$430$		0			0
$431$	−6.41478	+	11.1107i	−0.308989	+	0.535185i	−0.978141	−	0.207940i	$-0.933324\pi$
$431$	−6.41478	+	11.1107i	−0.308989	+	0.535185i	0.669152	+	0.743125i	$0.266657\pi$
$432$		0			0
$433$	−20.0525	−	11.5773i	−0.963664	−	0.556371i	−0.0663649	−	0.997795i	$-0.521140\pi$
$433$	−20.0525	−	11.5773i	−0.963664	−	0.556371i	−0.897299	+	0.441424i	$0.854473\pi$
$434$		0			0
$435$	19.3774	−	11.1876i	0.929077	−	0.536403i
$436$		0			0
$437$	−8.56108	+	16.4745i	−0.409532	+	0.788082i
$438$		0			0
$439$	13.0894	+	22.6714i	0.624721	+	1.08205i	0.988595	+	0.150600i	$0.0481206\pi$
$439$	13.0894	+	22.6714i	0.624721	+	1.08205i	−0.363874	+	0.931448i	$0.618546\pi$
$440$		0			0
$441$	0.193252	−	0.334723i	0.00920250	−	0.0159392i
$442$		0			0
$443$	−17.2871	−	9.98074i	−0.821337	−	0.474199i	0.0295402	−	0.999564i	$-0.490596\pi$
$443$	−17.2871	−	9.98074i	−0.821337	−	0.474199i	−0.850877	+	0.525364i	$0.823929\pi$
$444$		0			0
$445$			23.4256i			1.11048i
$446$		0			0
$447$	−3.04695	+	5.27747i	−0.144116	+	0.249616i
$448$		0			0
$449$			30.3224i			1.43100i	0.698613	+	0.715500i	$0.253801\pi$
$449$			30.3224i			1.43100i	−0.698613	+	0.715500i	$0.746199\pi$
$450$		0			0
$451$	−5.67004	−	9.82080i	−0.266992	−	0.462444i
$452$		0			0
$453$	−6.34916	−	10.9971i	−0.298309	−	0.516687i
$454$		0			0
$455$	45.1787			2.11801
$456$		0			0
$457$	−14.5569			−0.680945			−0.340473	−	0.940254i	$-0.610587\pi$
$457$	−14.5569			−0.680945			−0.340473	+	0.940254i	$0.610587\pi$
$458$		0			0
$459$	2.51414	+	4.35461i	0.117350	+	0.203256i
$460$		0			0
$461$	18.5147	+	32.0683i	0.862314	+	1.49357i	0.869690	+	0.493599i	$0.164319\pi$
$461$	18.5147	+	32.0683i	0.862314	+	1.49357i	−0.00737587	+	0.999973i	$0.502348\pi$
$462$		0			0
$463$			39.4283i			1.83239i	0.400735	+	0.916194i	$0.368755\pi$
$463$			39.4283i			1.83239i	−0.400735	+	0.916194i	$0.631245\pi$
$464$		0			0
$465$	3.85369	−	6.67479i	0.178711	−	0.309536i
$466$		0			0
$467$			6.16620i			0.285338i	0.989770	+	0.142669i	$0.0455684\pi$
$467$			6.16620i			0.285338i	−0.989770	+	0.142669i	$0.954432\pi$
$468$		0			0
$469$	−31.4198	−	18.1403i	−1.45083	−	0.837639i
$470$		0			0
$471$	8.43438	−	14.6088i	0.388636	−	0.673137i
$472$		0			0
$473$	5.39611	+	9.34633i	0.248113	+	0.429745i
$474$		0			0
$475$	−23.3163	−	12.1165i	−1.06983	−	0.555943i
$476$		0			0
$477$	−5.14631	+	2.97122i	−0.235633	+	0.136043i
$478$		0			0
$479$	−29.6382	−	17.1116i	−1.35420	−	0.781849i	−0.365367	−	0.930864i	$-0.619057\pi$
$479$	−29.6382	−	17.1116i	−1.35420	−	0.781849i	−0.988835	+	0.149015i	$0.952390\pi$
$480$		0			0
$481$	−20.7215	+	35.8907i	−0.944820	+	1.63648i
$482$		0			0
$483$	−11.5761			−0.526733
$484$		0			0
$485$	23.6700	+	13.6659i	1.07480	+	0.620537i
$486$		0			0
$487$	18.0565			0.818220			0.409110	−	0.912485i	$-0.365839\pi$
$487$	18.0565			0.818220			0.409110	+	0.912485i	$0.365839\pi$
$488$		0			0
$489$	14.0237	−	8.09661i	0.634175	−	0.366141i
$490$		0			0
$491$	−14.2871	+	8.24869i	−0.644770	+	0.372258i	−0.786450	−	0.617654i	$-0.788083\pi$
$491$	−14.2871	+	8.24869i	−0.644770	+	0.372258i	0.141680	+	0.989913i	$0.454750\pi$
$492$		0			0
$493$		−	33.8790i		−	1.52583i
$494$		0			0
$495$			3.27360i			0.147137i
$496$		0			0
$497$	−10.3245	+	5.96085i	−0.463117	+	0.267381i
$498$		0			0
$499$	29.0237	−	16.7569i	1.29928	−	0.750140i	0.319001	−	0.947754i	$-0.396653\pi$
$499$	29.0237	−	16.7569i	1.29928	−	0.750140i	0.980280	+	0.197614i	$0.0633193\pi$
$500$		0			0
$501$	13.3774			0.597660
$502$		0			0
$503$	−4.62723	−	2.67153i	−0.206318	−	0.119118i	0.393281	−	0.919418i	$-0.371340\pi$
$503$	−4.62723	−	2.67153i	−0.206318	−	0.119118i	−0.599599	+	0.800301i	$0.704673\pi$
$504$		0			0
$505$	−18.8296			−0.837904
$506$		0			0
$507$	−6.02827	+	10.4413i	−0.267725	+	0.463713i
$508$		0			0
$509$	22.7074	+	13.1101i	1.00649	+	0.581096i	0.910161	−	0.414254i	$-0.135958\pi$
$509$	22.7074	+	13.1101i	1.00649	+	0.581096i	0.0963261	+	0.995350i	$0.469291\pi$
$510$		0			0
$511$	11.9016	−	6.87137i	0.526494	−	0.303972i
$512$		0			0
$513$	−0.193252	−	4.35461i	−0.00853230	−	0.192261i
$514$		0			0
$515$	16.8073	+	29.1111i	0.740617	+	1.28279i
$516$		0			0
$517$	−3.65084	+	6.32344i	−0.160564	+	0.278105i
$518$		0			0
$519$	10.9572	+	6.32614i	0.480967	+	0.277687i
$520$		0			0
$521$		−	29.6197i		−	1.29766i	−0.760933	−	0.648830i	$-0.775259\pi$
$521$		−	29.6197i		−	1.29766i	0.760933	−	0.648830i	$-0.224741\pi$
$522$		0			0
$523$	3.70285	−	6.41353i	0.161914	−	0.280444i	−0.773641	−	0.633624i	$-0.781566\pi$
$523$	3.70285	−	6.41353i	0.161914	−	0.280444i	0.935555	+	0.353180i	$0.114900\pi$
$524$		0			0
$525$		−	16.3837i		−	0.715044i
$526$		0			0
$527$	−5.83502	−	10.1066i	−0.254178	−	0.440248i
$528$		0			0
$529$	−2.42892	−	4.20701i	−0.105605	−	0.182913i
$530$		0			0
$531$	3.32088			0.144114
$532$		0			0
$533$	−57.5844			−2.49426
$534$		0			0
$535$	−1.61350	−	2.79466i	−0.0697575	−	0.120823i
$536$		0			0
$537$	0.367832	+	0.637103i	0.0158731	+	0.0274930i
$538$		0			0
$539$		−	0.381002i		−	0.0164109i
$540$		0			0
$541$	7.30128	−	12.6462i	0.313907	−	0.543702i	−0.665298	−	0.746578i	$-0.731695\pi$
$541$	7.30128	−	12.6462i	0.313907	−	0.543702i	0.979204	+	0.202876i	$0.0650288\pi$
$542$		0			0
$543$			6.25876i			0.268589i
$544$		0			0
$545$	1.92531	+	1.11158i	0.0824711	+	0.0476147i
$546$		0			0
$547$	−20.8022	+	36.0305i	−0.889438	+	1.54055i	−0.0488977	+	0.998804i	$0.515571\pi$
$547$	−20.8022	+	36.0305i	−0.889438	+	1.54055i	−0.840541	+	0.541749i	$0.817762\pi$
$548$		0			0
$549$	3.62763	+	6.28324i	0.154824	+	0.268162i
$550$		0			0
$551$	−13.5424	+	26.0603i	−0.576926	+	1.11021i
$552$		0			0
$553$	25.8027	−	14.8972i	1.09724	−	0.633494i
$554$		0			0
$555$	23.8109	+	13.7472i	1.01072	+	0.583537i
$556$		0			0
$557$	−22.2125	+	38.4731i	−0.941172	+	1.63016i	−0.177931	+	0.984043i	$0.556941\pi$
$557$	−22.2125	+	38.4731i	−0.941172	+	1.63016i	−0.763240	+	0.646115i	$0.776393\pi$
$558$		0			0
$559$	54.8023			2.31789
$560$		0			0
$561$	4.29261	+	2.47834i	0.181234	+	0.104636i
$562$		0			0
$563$	−39.2545			−1.65438			−0.827189	−	0.561923i	$-0.810062\pi$
$563$	−39.2545			−1.65438			−0.827189	+	0.561923i	$0.810062\pi$
$564$		0			0
$565$	−24.1378	+	13.9359i	−1.01548	+	0.586290i
$566$		0			0
$567$	2.35369	−	1.35891i	0.0988459	−	0.0570687i
$568$		0			0
$569$			27.2761i			1.14347i	0.820438	+	0.571736i	$0.193730\pi$
$569$			27.2761i			1.14347i	−0.820438	+	0.571736i	$0.806270\pi$
$570$		0			0
$571$			1.07155i			0.0448429i	0.999749	+	0.0224214i	$0.00713757\pi$
$571$			1.07155i			0.0448429i	−0.999749	+	0.0224214i	$0.992862\pi$
$572$		0			0
$573$	1.59843	−	0.922854i	0.0667754	−	0.0385528i
$574$		0			0
$575$	−22.2366	+	12.8383i	−0.927330	+	0.535394i
$576$		0			0
$577$	17.6135			0.733259			0.366630	−	0.930367i	$-0.380512\pi$
$577$	17.6135			0.733259			0.366630	+	0.930367i	$0.380512\pi$
$578$		0			0
$579$	−3.92024	−	2.26335i	−0.162920	−	0.0940617i
$580$		0			0
$581$	−23.6700			−0.981999
$582$		0			0
$583$	−2.92892	+	5.07303i	−0.121303	+	0.210103i
$584$		0			0
$585$	14.3961	+	8.31160i	0.595206	+	0.343642i
$586$		0			0
$587$	−19.2366	+	11.1063i	−0.793979	+	0.458404i	−0.841361	−	0.540473i	$-0.818245\pi$
$587$	−19.2366	+	11.1063i	−0.793979	+	0.458404i	0.0473824	+	0.998877i	$0.484912\pi$
$588$		0			0
$589$	0.448517	+	10.1066i	0.0184808	+	0.416433i
$590$		0			0
$591$	−6.84462	−	11.8552i	−0.281550	−	0.487659i
$592$		0			0
$593$	−6.10896	+	10.5810i	−0.250865	+	0.434511i	−0.963764	−	0.266756i	$-0.914048\pi$
$593$	−6.10896	+	10.5810i	−0.250865	+	0.434511i	0.712899	+	0.701266i	$0.247382\pi$
$594$		0			0
$595$	−39.3027	−	22.6914i	−1.61126	−	0.930259i
$596$		0			0
$597$			2.42937i			0.0994274i
$598$		0			0
$599$	13.4955	−	23.3748i	0.551410	−	0.955070i	−0.446763	−	0.894652i	$-0.647423\pi$
$599$	13.4955	−	23.3748i	0.551410	−	0.955070i	0.998173	−	0.0604175i	$-0.0192432\pi$
$600$		0			0
$601$		−	24.4514i		−	0.997392i	−0.866777	−	0.498696i	$-0.833812\pi$
$601$		−	24.4514i		−	0.997392i	0.866777	−	0.498696i	$-0.166188\pi$
$602$		0			0
$603$	−6.67458	−	11.5607i	−0.271810	−	0.470789i
$604$		0			0
$605$	−16.6514	−	28.8410i	−0.676974	−	1.17255i
$606$		0			0
$607$	−13.7175			−0.556777			−0.278388	−	0.960469i	$-0.589800\pi$
$607$	−13.7175			−0.556777			−0.278388	+	0.960469i	$0.589800\pi$
$608$		0			0
$609$	−18.3118			−0.742032
$610$		0			0
$611$	18.5388	+	32.1101i	0.750000	+	1.29904i
$612$		0			0
$613$	−20.6646	−	35.7921i	−0.834634	−	1.44563i	−0.894328	−	0.447413i	$-0.852346\pi$
$613$	−20.6646	−	35.7921i	−0.834634	−	1.44563i	0.0596932	−	0.998217i	$-0.480988\pi$
$614$		0			0
$615$			38.2031i			1.54050i
$616$		0			0
$617$	12.9157	−	22.3707i	0.519967	−	0.900609i	−0.479764	−	0.877398i	$-0.659278\pi$
$617$	12.9157	−	22.3707i	0.519967	−	0.900609i	0.999731	−	0.0232112i	$-0.00738901\pi$
$618$		0			0
$619$		−	38.1873i		−	1.53488i	−0.641121	−	0.767440i	$-0.721530\pi$
$619$		−	38.1873i		−	1.53488i	0.641121	−	0.767440i	$-0.278470\pi$
$620$		0			0
$621$	−3.68872	−	2.12968i	−0.148023	−	0.0854612i
$622$		0			0
$623$	9.58575	−	16.6030i	0.384045	−	0.665185i
$624$		0			0
$625$	9.40064	+	16.2824i	0.376026	+	0.651296i
$626$		0			0
$627$	−2.31128	−	3.62226i	−0.0923038	−	0.144659i
$628$		0			0
$629$	36.0529	−	20.8152i	1.43752	−	0.829955i
$630$		0			0
$631$	−22.6090	−	13.0533i	−0.900048	−	0.519643i	−0.0228325	−	0.999739i	$-0.507268\pi$
$631$	−22.6090	−	13.0533i	−0.900048	−	0.519643i	−0.877216	+	0.480096i	$0.840602\pi$
$632$		0			0
$633$	−6.77394	+	11.7328i	−0.269240	+	0.466337i
$634$		0			0
$635$	−24.6236			−0.977159
$636$		0			0
$637$	−1.67551	−	0.967354i	−0.0663860	−	0.0383280i
$638$		0			0
$639$	−4.38650			−0.173527
$640$		0			0
$641$	−11.4249	+	6.59617i	−0.451257	+	0.260533i	−0.708361	−	0.705851i	$-0.750565\pi$
$641$	−11.4249	+	6.59617i	−0.451257	+	0.260533i	0.257104	+	0.966384i	$0.417232\pi$
$642$		0			0
$643$	28.2790	−	16.3269i	1.11521	−	0.643870i	0.175040	−	0.984561i	$-0.443995\pi$
$643$	28.2790	−	16.3269i	1.11521	−	0.643870i	0.940175	+	0.340692i	$0.110661\pi$
$644$		0			0
$645$		−	36.3574i		−	1.43157i
$646$		0			0
$647$		−	23.5235i		−	0.924805i	−0.886670	−	0.462403i	$-0.846988\pi$
$647$		−	23.5235i		−	0.924805i	0.886670	−	0.462403i	$-0.153012\pi$
$648$		0			0
$649$	2.83502	−	1.63680i	0.111284	−	0.0642500i
$650$		0			0
$651$	−5.46265	+	3.15386i	−0.214098	+	0.123610i
$652$		0			0
$653$	49.5953			1.94082			0.970408	−	0.241471i	$-0.0776299\pi$
$653$	49.5953			1.94082			0.970408	+	0.241471i	$0.0776299\pi$
$654$		0			0
$655$	54.9354	+	31.7170i	2.14651	+	1.23929i
$656$		0			0
$657$	5.05655			0.197275
$658$		0			0
$659$	7.49546	−	12.9825i	0.291982	−	0.505727i	−0.682296	−	0.731076i	$-0.739019\pi$
$659$	7.49546	−	12.9825i	0.291982	−	0.505727i	0.974278	+	0.225348i	$0.0723520\pi$
$660$		0			0
$661$	−19.5953	−	11.3134i	−0.762171	−	0.440040i	0.0679038	−	0.997692i	$-0.478369\pi$
$661$	−19.5953	−	11.3134i	−0.762171	−	0.440040i	−0.830075	+	0.557652i	$0.811702\pi$
$662$		0			0
$663$	21.7977	−	12.5849i	0.846552	−	0.488757i
$664$		0			0
$665$	21.1619	+	33.1651i	0.820623	+	1.28609i
$666$		0			0
$667$	14.3492	+	24.8535i	0.555602	+	0.962330i
$668$		0			0
$669$	−7.80221	+	13.5138i	−0.301651	+	0.522475i
$670$		0			0
$671$	6.19378	+	3.57598i	0.239108	+	0.138049i
$672$		0			0
$673$			26.1398i			1.00762i	0.863815	+	0.503808i	$0.168068\pi$
$673$			26.1398i			1.00762i	−0.863815	+	0.503808i	$0.831932\pi$
$674$		0			0
$675$	3.01414	−	5.22064i	0.116014	−	0.200942i
$676$		0			0
$677$		−	4.42199i		−	0.169951i	−0.996383	−	0.0849755i	$-0.972919\pi$
$677$		−	4.42199i		−	0.169951i	0.996383	−	0.0849755i	$-0.0270812\pi$
$678$		0			0
$679$	−11.1842	−	19.3716i	−0.429209	−	0.743413i
$680$		0			0
$681$	8.14631	+	14.1098i	0.312167	+	0.540689i
$682$		0			0
$683$	18.2361			0.697784			0.348892	−	0.937163i	$-0.386558\pi$
$683$	18.2361			0.697784			0.348892	+	0.937163i	$0.386558\pi$
$684$		0			0
$685$	−70.0203			−2.67534
$686$		0			0
$687$	5.65591	+	9.79632i	0.215786	+	0.373753i
$688$		0			0
$689$	14.8729	+	25.7606i	0.566612	+	0.981401i
$690$		0			0
$691$			9.05341i			0.344408i	0.985061	+	0.172204i	$0.0550888\pi$
$691$			9.05341i			0.344408i	−0.985061	+	0.172204i	$0.944911\pi$
$692$		0			0
$693$	1.33956	−	2.32018i	0.0508856	−	0.0881364i
$694$		0			0
$695$		−	41.6393i		−	1.57947i
$696$		0			0
$697$	50.0950	+	28.9223i	1.89748	+	1.09551i
$698$		0			0
$699$	12.7977	−	22.1662i	0.484053	−	0.838404i
$700$		0			0
$701$	−10.6514	−	18.4487i	−0.402297	−	0.696798i	0.591706	−	0.806154i	$-0.298455\pi$
$701$	−10.6514	−	18.4487i	−0.402297	−	0.696798i	−0.994003	+	0.109356i	$0.965121\pi$
$702$		0			0
$703$	−36.0529	+	1.59999i	−1.35976	+	0.0603446i
$704$		0			0
$705$	21.3027	−	12.2991i	0.802308	−	0.463212i
$706$		0			0
$707$	13.3455	+	7.70506i	0.501911	+	0.289778i
$708$		0			0
$709$	−2.50546	+	4.33959i	−0.0940947	+	0.162977i	−0.909230	−	0.416293i	$-0.863329\pi$
$709$	−2.50546	+	4.33959i	−0.0940947	+	0.162977i	0.815136	+	0.579270i	$0.196662\pi$
$710$		0			0
$711$	10.9627			0.411132
$712$		0			0
$713$	8.56108	+	4.94274i	0.320615	+	0.185107i
$714$		0			0
$715$	16.3865			0.612821
$716$		0			0
$717$	2.14631	−	1.23917i	0.0801552	−	0.0462776i
$718$		0			0
$719$	−28.2366	+	16.3024i	−1.05305	+	0.607977i	−0.923501	−	0.383596i	$-0.874685\pi$
$719$	−28.2366	+	16.3024i	−1.05305	+	0.607977i	−0.129546	+	0.991573i	$0.541352\pi$
$720$		0			0
$721$		−	27.5102i		−	1.02453i
$722$		0			0
$723$		−	16.0674i		−	0.597553i
$724$		0			0
$725$	−35.1751	+	20.3084i	−1.30637	+	0.754233i
$726$		0			0
$727$	−15.8113	+	9.12865i	−0.586408	+	0.338563i	−0.763676	−	0.645600i	$-0.776607\pi$
$727$	−15.8113	+	9.12865i	−0.586408	+	0.338563i	0.177268	+	0.984163i	$0.443274\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−47.6747	−	27.5250i	−1.76331	−	1.01805i
$732$		0			0
$733$	46.0275			1.70006			0.850032	−	0.526731i	$-0.176583\pi$
$733$	46.0275			1.70006			0.850032	+	0.526731i	$0.176583\pi$
$734$		0			0
$735$	−0.641769	+	1.11158i	−0.0236720	+	0.0410011i
$736$		0			0
$737$	−11.3961	−	6.57954i	−0.419781	−	0.242361i
$738$		0			0
$739$	25.5607	−	14.7575i	0.940265	−	0.542862i	0.0502216	−	0.998738i	$-0.484007\pi$
$739$	25.5607	−	14.7575i	0.940265	−	0.542862i	0.890043	+	0.455876i	$0.150674\pi$
$740$		0			0
$741$	−21.7977	+	0.967354i	−0.800758	+	0.0355366i
$742$		0			0
$743$	−7.18365	−	12.4424i	−0.263543	−	0.456469i	0.703638	−	0.710558i	$-0.251558\pi$
$743$	−7.18365	−	12.4424i	−0.263543	−	0.456469i	−0.967181	+	0.254089i	$0.918224\pi$
$744$		0			0
$745$	10.1186	−	17.5259i	0.370715	−	0.642098i
$746$		0			0
$747$	−7.54241	−	4.35461i	−0.275962	−	0.159327i
$748$		0			0
$749$			2.64097i			0.0964989i
$750$		0			0
$751$	−4.90157	+	8.48977i	−0.178861	+	0.309796i	−0.941491	−	0.337039i	$-0.890575\pi$
$751$	−4.90157	+	8.48977i	−0.178861	+	0.309796i	0.762630	+	0.646835i	$0.223908\pi$
$752$		0			0
$753$		−	2.83147i		−	0.103185i
$754$		0			0
$755$	21.0848	+	36.5200i	0.767355	+	1.32910i
$756$		0			0
$757$	12.5620	+	21.7580i	0.456574	+	0.790810i	0.998777	−	0.0494379i	$-0.0157430\pi$
$757$	12.5620	+	21.7580i	0.456574	+	0.790810i	−0.542203	+	0.840247i	$0.682410\pi$
$758$		0			0
$759$	−4.19872			−0.152404
$760$		0			0
$761$	−24.8778			−0.901821			−0.450910	−	0.892569i	$-0.648901\pi$
$761$	−24.8778			−0.901821			−0.450910	+	0.892569i	$0.648901\pi$
$762$		0			0
$763$	−0.909714	−	1.57567i	−0.0329339	−	0.0570431i
$764$		0			0
$765$	−8.34916	−	14.4612i	−0.301864	−	0.522845i
$766$		0			0
$767$		−	16.6232i		−	0.600229i
$768$		0			0
$769$	9.36876	−	16.2272i	0.337846	−	0.585167i	−0.646181	−	0.763184i	$-0.723635\pi$
$769$	9.36876	−	16.2272i	0.337846	−	0.585167i	0.984027	+	0.178017i	$0.0569683\pi$
$770$		0			0
$771$		−	2.57628i		−	0.0927826i
$772$		0			0
$773$	−18.9627	−	10.9481i	−0.682039	−	0.393776i	0.118584	−	0.992944i	$-0.462165\pi$
$773$	−18.9627	−	10.9481i	−0.682039	−	0.393776i	−0.800623	+	0.599169i	$0.795498\pi$
$774$		0			0
$775$	−6.99546	+	12.1165i	−0.251284	+	0.435237i
$776$		0			0
$777$	−11.2507	−	19.4868i	−0.403618	−	0.699086i
$778$		0			0
$779$	−26.9728	−	42.2719i	−0.966400	−	1.51455i
$780$		0			0
$781$	−3.74474	+	2.16202i	−0.133997	+	0.0773633i
$782$		0			0
$783$	−5.83502	−	3.36885i	−0.208527	−	0.120393i
$784$		0			0
$785$	−28.0096	+	48.5141i	−0.999706	+	1.73154i
$786$		0			0
$787$	−42.9336			−1.53042			−0.765208	−	0.643783i	$-0.777364\pi$
$787$	−42.9336			−1.53042			−0.765208	+	0.643783i	$0.777364\pi$
$788$		0			0
$789$	−24.7977	−	14.3169i	−0.882821	−	0.509697i
$790$		0			0
$791$	22.8104			0.811043
$792$		0			0
$793$	31.4517	−	18.1587i	1.11688	−	0.644833i
$794$		0			0
$795$	17.0903	−	9.86708i	0.606130	−	0.349949i
$796$		0			0
$797$			1.30208i			0.0461219i	0.999734	+	0.0230610i	$0.00734119\pi$
$797$			1.30208i			0.0461219i	−0.999734	+	0.0230610i	$0.992659\pi$
$798$		0			0
$799$		−	37.2452i		−	1.31764i
$800$		0			0
$801$	6.10896	−	3.52701i	0.215849	−	0.124621i
$802$		0			0
$803$	4.31675	−	2.49228i	0.152335	−	0.0879505i
$804$		0			0
$805$	38.4431			1.35494
$806$		0			0
$807$	−19.2685	−	11.1247i	−0.678282	−	0.391607i
$808$		0			0
$809$	31.3593			1.10253			0.551267	−	0.834329i	$-0.314145\pi$
$809$	31.3593			1.10253			0.551267	+	0.834329i	$0.314145\pi$
$810$		0			0
$811$	0.0373465	−	0.0646860i	0.00131141	−	0.00227143i	−0.865369	−	0.501135i	$-0.832916\pi$
$811$	0.0373465	−	0.0646860i	0.00131141	−	0.00227143i	0.866680	+	0.498864i	$0.166249\pi$
$812$		0			0
$813$	−2.67004	−	1.54155i	−0.0936425	−	0.0540645i
$814$		0			0
$815$	−46.5712	+	26.8879i	−1.63132	+	0.941842i
$816$		0			0
$817$	25.6696	+	40.2296i	0.898067	+	1.40746i
$818$		0			0
$819$	−6.80221	−	11.7818i	−0.237688	−	0.411689i
$820$		0			0
$821$	−11.8350	+	20.4989i	−0.413045	+	0.715415i	−0.995221	−	0.0976477i	$-0.968868\pi$
$821$	−11.8350	+	20.4989i	−0.413045	+	0.715415i	0.582176	+	0.813063i	$0.302201\pi$
$822$		0			0
$823$	−29.2070	−	16.8627i	−1.01809	−	0.587795i	−0.104541	−	0.994521i	$-0.533337\pi$
$823$	−29.2070	−	16.8627i	−1.01809	−	0.587795i	−0.913551	+	0.406725i	$0.866671\pi$
$824$		0			0
$825$		−	5.94244i		−	0.206889i
$826$		0			0
$827$	11.5990	−	20.0900i	0.403335	−	0.698597i	−0.590791	−	0.806825i	$-0.701184\pi$
$827$	11.5990	−	20.0900i	0.403335	−	0.698597i	0.994126	+	0.108228i	$0.0345175\pi$
$828$		0			0
$829$		−	13.6537i		−	0.474214i	−0.971484	−	0.237107i	$-0.923801\pi$
$829$		−	13.6537i		−	0.474214i	0.971484	−	0.237107i	$-0.0761992\pi$
$830$		0			0
$831$	2.12763	+	3.68517i	0.0738067	+	0.127837i
$832$		0			0
$833$	0.971726	+	1.68308i	0.0336683	+	0.0583152i
$834$		0			0
$835$	−44.4249			−1.53739
$836$		0			0
$837$	−2.32088			−0.0802215
$838$		0			0
$839$	−7.48639	−	12.9668i	−0.258459	−	0.447664i	0.707370	−	0.706843i	$-0.249881\pi$
$839$	−7.48639	−	12.9668i	−0.258459	−	0.447664i	−0.965829	+	0.259179i	$0.916548\pi$
$840$		0			0
$841$	8.19832	+	14.1999i	0.282701	+	0.489652i
$842$		0			0
$843$			15.2843i			0.526419i
$844$		0			0
$845$	20.0192	−	34.6743i	0.688681	−	1.19283i
$846$		0			0
$847$			27.2550i			0.936492i
$848$		0			0
$849$	−24.3027	−	14.0312i	−0.834068	−	0.481549i
$850$		0			0
$851$	−17.6322	+	30.5398i	−0.604423	+	1.04689i
$852$		0			0
$853$	−11.4909	−	19.9029i	−0.393442	−	0.681461i	0.599459	−	0.800405i	$-0.295382\pi$
$853$	−11.4909	−	19.9029i	−0.393442	−	0.681461i	−0.992901	+	0.118944i	$0.962049\pi$
$854$		0			0
$855$	0.641769	+	14.4612i	0.0219480	+	0.494561i
$856$		0			0
$857$	2.45213	−	1.41574i	0.0837630	−	0.0483606i	−0.457533	−	0.889192i	$-0.651267\pi$
$857$	2.45213	−	1.41574i	0.0837630	−	0.0483606i	0.541296	+	0.840832i	$0.317934\pi$
$858$		0			0
$859$	6.42839	+	3.71143i	0.219334	+	0.126632i	0.605642	−	0.795737i	$-0.292916\pi$
$859$	6.42839	+	3.71143i	0.219334	+	0.126632i	−0.386308	+	0.922370i	$0.626250\pi$
$860$		0			0
$861$	15.6327	−	27.0766i	0.532761	−	0.922769i
$862$		0			0
$863$	−2.96080			−0.100787			−0.0503934	−	0.998729i	$-0.516048\pi$
$863$	−2.96080			−0.100787			−0.0503934	+	0.998729i	$0.516048\pi$
$864$		0			0
$865$	−36.3876	−	21.0084i	−1.23721	−	0.714306i
$866$		0			0
$867$	−8.28354			−0.281324
$868$		0			0
$869$	9.35876	−	5.40328i	0.317474	−	0.183294i
$870$		0			0
$871$	−57.8689	+	33.4106i	−1.96081	+	1.13208i
$872$		0			0
$873$		−	8.23028i		−	0.278553i
$874$		0			0
$875$			9.28073i			0.313746i
$876$		0			0
$877$	48.3133	−	27.8937i	1.63142	−	0.941903i	0.647768	−	0.761837i	$-0.275702\pi$
$877$	48.3133	−	27.8937i	1.63142	−	0.941903i	0.983655	−	0.180065i	$-0.0576309\pi$
$878$		0			0
$879$	−0.962653	+	0.555788i	−0.0324695	+	0.0187463i
$880$		0			0
$881$	45.9627			1.54852			0.774261	−	0.632867i	$-0.218122\pi$
$881$	45.9627			1.54852			0.774261	+	0.632867i	$0.218122\pi$
$882$		0			0
$883$	−2.73659	−	1.57997i	−0.0920936	−	0.0531703i	0.453246	−	0.891386i	$-0.350266\pi$
$883$	−2.73659	−	1.57997i	−0.0920936	−	0.0531703i	−0.545340	+	0.838215i	$0.683599\pi$
$884$		0			0
$885$	−11.0283			−0.370711
$886$		0			0
$887$	16.7453	−	29.0036i	0.562251	−	0.973847i	−0.435049	−	0.900407i	$-0.643269\pi$
$887$	16.7453	−	29.0036i	0.562251	−	0.973847i	0.997300	−	0.0734403i	$-0.0233978\pi$
$888$		0			0
$889$	17.4521	+	10.0760i	0.585325	+	0.337938i
$890$		0			0
$891$	0.853695	−	0.492881i	0.0285998	−	0.0165121i
$892$		0			0
$893$	−14.8880	+	28.6496i	−0.498207	+	0.958722i
$894$		0			0
$895$	−1.22153	−	2.11575i	−0.0408311	−	0.0707216i
$896$		0			0
$897$	−10.6604	+	18.4644i	−0.355942	+	0.616509i
$898$		0			0
$899$	13.5424	+	7.81871i	0.451665	+	0.260769i
$900$		0			0
$901$		−	29.8802i		−	0.995455i
$902$		0			0
$903$	−14.8774	+	25.7685i	−0.495090	+	0.857521i
$904$		0			0
$905$		−	20.7846i		−	0.690904i
$906$		0			0
$907$	9.37743	+	16.2422i	0.311373	+	0.539313i	0.978660	−	0.205487i	$-0.0658780\pi$
$907$	9.37743	+	16.2422i	0.311373	+	0.539313i	−0.667287	+	0.744800i	$0.732545\pi$
$908$		0			0
$909$	2.83502	+	4.91040i	0.0940317	+	0.162868i
$910$		0			0
$911$	30.4540			1.00899			0.504493	−	0.863416i	$-0.331680\pi$
$911$	30.4540			1.00899			0.504493	+	0.863416i	$0.331680\pi$
$912$		0			0
$913$	−8.58522			−0.284129
$914$		0			0
$915$	−12.0469	−	20.8659i	−0.398260	−	0.689806i
$916$		0			0
$917$	−25.9572	−	44.9592i	−0.857182	−	1.48468i
$918$		0			0
$919$			23.8834i			0.787841i	0.919144	+	0.393921i	$0.128882\pi$
$919$			23.8834i			0.787841i	−0.919144	+	0.393921i	$0.871118\pi$
$920$		0			0
$921$	12.4485	−	21.5615i	0.410193	−	0.710474i
$922$		0			0
$923$			21.9573i			0.722734i
$924$		0			0
$925$	−43.2230	−	24.9548i	−1.42116	−	0.820509i
$926$		0			0
$927$	5.06108	−	8.76605i	0.166228	−	0.287915i
$928$		0			0
$929$	−10.2457	−	17.7460i	−0.336149	−	0.582228i	0.647556	−	0.762018i	$-0.275791\pi$
$929$	−10.2457	−	17.7460i	−0.336149	−	0.582228i	−0.983705	+	0.179791i	$0.942458\pi$
$930$		0			0
$931$	−0.0746930	−	1.68308i	−0.00244796	−	0.0551607i
$932$		0			0
$933$	7.84823	−	4.53118i	0.256940	−	0.148344i
$934$		0			0
$935$	−14.2553	−	8.23028i	−0.466197	−	0.269159i
$936$		0			0
$937$	5.68418	−	9.84529i	0.185694	−	0.321632i	−0.758116	−	0.652120i	$-0.773880\pi$
$937$	5.68418	−	9.84529i	0.185694	−	0.321632i	0.943810	+	0.330488i	$0.107213\pi$
$938$		0			0
$939$	6.38650			0.208416
$940$		0			0
$941$	−4.51053	−	2.60415i	−0.147039	−	0.0848930i	0.424676	−	0.905346i	$-0.360388\pi$
$941$	−4.51053	−	2.60415i	−0.147039	−	0.0848930i	−0.571715	+	0.820453i	$0.693722\pi$
$942$		0			0
$943$	−48.9992			−1.59563
$944$		0			0
$945$	−7.81635	+	4.51277i	−0.254266	+	0.146800i
$946$		0			0
$947$	−51.5525	+	29.7639i	−1.67523	+	0.967196i	−0.710600	+	0.703596i	$0.751577\pi$
$947$	−51.5525	+	29.7639i	−1.67523	+	0.967196i	−0.964632	+	0.263600i	$0.915090\pi$
$948$		0			0
$949$		−	25.3113i		−	0.821640i
$950$		0			0
$951$			2.76678i			0.0897191i
$952$		0			0
$953$	32.6988	−	18.8787i	1.05922	−	0.611541i	0.134003	−	0.990981i	$-0.457217\pi$
$953$	32.6988	−	18.8787i	1.05922	−	0.611541i	0.925216	+	0.379440i	$0.123883\pi$
$954$		0			0
$955$	−5.30820	+	3.06469i	−0.171769	+	0.0991711i
$956$		0			0
$957$	−6.64177			−0.214698
$958$		0			0
$959$	49.6272	+	28.6523i	1.60255	+	0.925231i
$960$		0			0
$961$	−25.6135			−0.826242
$962$		0			0
$963$	−0.485863	+	0.841540i	−0.0156567	+	0.0271182i
$964$		0			0
$965$	13.0187	+	7.51633i	0.419086	+	0.241959i
$966$		0			0
$967$	35.7366	−	20.6325i	1.14921	−	0.663497i	0.200516	−	0.979690i	$-0.435738\pi$
$967$	35.7366	−	20.6325i	1.14921	−	0.663497i	0.948695	+	0.316193i	$0.102405\pi$
$968$		0			0
$969$	19.4485	+	10.1066i	0.624776	+	0.324669i
$970$		0			0
$971$	−30.3209	−	52.5173i	−0.973043	−	1.68536i	−0.686246	−	0.727370i	$-0.740743\pi$
$971$	−30.3209	−	52.5173i	−0.973043	−	1.68536i	−0.286797	−	0.957991i	$-0.592591\pi$
$972$		0			0
$973$	−17.0388	+	29.5121i	−0.546239	+	0.946114i
$974$		0			0
$975$	−26.1327	−	15.0877i	−0.836916	−	0.483194i
$976$		0			0
$977$		−	20.5016i		−	0.655903i	−0.944695	−	0.327951i	$-0.893642\pi$
$977$		−	20.5016i		−	0.655903i	0.944695	−	0.327951i	$-0.106358\pi$
$978$		0			0
$979$	3.47679	−	6.02198i	0.111119	−	0.192463i
$980$		0			0
$981$		−	0.669446i		−	0.0213738i
$982$		0			0
$983$	−4.36237	−	7.55584i	−0.139138	−	0.240994i	0.788033	−	0.615633i	$-0.211100\pi$
$983$	−4.36237	−	7.55584i	−0.139138	−	0.240994i	−0.927171	+	0.374640i	$0.877766\pi$
$984$		0			0
$985$	22.7302	+	39.3699i	0.724244	+	1.25443i
$986$		0			0
$987$	−20.1312			−0.640784
$988$		0			0
$989$	46.6319			1.48281
$990$		0			0
$991$	−20.6227	−	35.7196i	−0.655102	−	1.13467i	−0.981868	−	0.189564i	$-0.939293\pi$
$991$	−20.6227	−	35.7196i	−0.655102	−	1.13467i	0.326767	−	0.945105i	$-0.394041\pi$
$992$		0			0
$993$	13.8305	+	23.9551i	0.438897	+	0.760192i
$994$		0			0
$995$		−	8.06765i		−	0.255762i
$996$		0			0
$997$	−1.46265	+	2.53339i	−0.0463227	+	0.0802333i	−0.888257	−	0.459347i	$-0.848084\pi$
$997$	−1.46265	+	2.53339i	−0.0463227	+	0.0802333i	0.841934	+	0.539580i	$0.181417\pi$
$998$		0			0
$999$		−	8.27925i		−	0.261944i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bb.f.31.1	yes	6
3.2	odd	2		2736.2.bm.o.1855.3		6
4.3	odd	2		912.2.bb.e.31.1	✓	6
12.11	even	2		2736.2.bm.n.1855.3		6
19.8	odd	6		912.2.bb.e.559.1	yes	6
57.8	even	6		2736.2.bm.n.559.3		6
76.27	even	6	inner	912.2.bb.f.559.1	yes	6
228.179	odd	6		2736.2.bm.o.559.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.bb.e.31.1	✓	6	4.3	odd	2
912.2.bb.e.559.1	yes	6	19.8	odd	6
912.2.bb.f.31.1	yes	6	1.1	even	1	trivial
912.2.bb.f.559.1	yes	6	76.27	even	6	inner
2736.2.bm.n.559.3		6	57.8	even	6
2736.2.bm.n.1855.3		6	12.11	even	2
2736.2.bm.o.559.3		6	228.179	odd	6
2736.2.bm.o.1855.3		6	3.2	odd	2

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-1.66044 - 2.87597i) q^{5} +2.71781i q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(-1.66044 - 2.87597i) q^{5} +2.71781i q^{7} +(-0.500000 + 0.866025i) q^{9} +0.985762i q^{11} +(4.33502 + 2.50283i) q^{13} +(1.66044 - 2.87597i) q^{15} +(-2.51414 - 4.35461i) q^{17} +(0.193252 + 4.35461i) q^{19} +(-2.35369 + 1.35891i) q^{21} +(3.68872 + 2.12968i) q^{23} +(-3.01414 + 5.22064i) q^{25} -1.00000 q^{27} +(5.83502 + 3.36885i) q^{29} +2.32088 q^{31} +(-0.853695 + 0.492881i) q^{33} +(7.81635 - 4.51277i) q^{35} +8.27925i q^{37} +5.00565i q^{39} +(-9.96265 + 5.75194i) q^{41} +(9.48133 - 5.47405i) q^{43} +3.32088 q^{45} +(6.41478 + 3.70357i) q^{47} -0.386505 q^{49} +(2.51414 - 4.35461i) q^{51} +(5.14631 + 2.97122i) q^{53} +(2.83502 - 1.63680i) q^{55} +(-3.67458 + 2.34467i) q^{57} +(-1.66044 - 2.87597i) q^{59} +(3.62763 - 6.28324i) q^{61} +(-2.35369 - 1.35891i) q^{63} -16.6232i q^{65} +(-6.67458 + 11.5607i) q^{67} +4.25936i q^{69} +(2.19325 + 3.79882i) q^{71} +(-2.52827 - 4.37910i) q^{73} -6.02827 q^{75} -2.67912 q^{77} +(-5.48133 - 9.49394i) q^{79} +(-0.500000 - 0.866025i) q^{81} +8.70923i q^{83} +(-8.34916 + 14.4612i) q^{85} +6.73770i q^{87} +(-6.10896 - 3.52701i) q^{89} +(-6.80221 + 11.7818i) q^{91} +(1.16044 + 2.00994i) q^{93} +(12.2029 - 7.78637i) q^{95} +(-7.12763 + 4.11514i) q^{97} +(-0.853695 - 0.492881i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 2 q^{5} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 2 * q^5 - 3 * q^9	\( 6 q + 3 q^{3} - 2 q^{5} - 3 q^{9} - 3 q^{13} + 2 q^{15} - 2 q^{17} + 4 q^{19} - 9 q^{21} - 12 q^{23} - 5 q^{25} - 6 q^{27} + 6 q^{29} - 2 q^{31} - 6 q^{35} - 12 q^{41} + 33 q^{43} + 4 q^{45} + 18 q^{47} - 8 q^{49} + 2 q^{51} + 36 q^{53} - 12 q^{55} - q^{57} - 2 q^{59} + 3 q^{61} - 9 q^{63} - 19 q^{67} + 16 q^{71} + 11 q^{73} - 10 q^{75} - 32 q^{77} - 9 q^{79} - 3 q^{81} - 8 q^{85} + 6 q^{89} - q^{91} - q^{93} + 26 q^{95} - 24 q^{97}+O(q^{100}) \) 6 * q + 3 * q^3 - 2 * q^5 - 3 * q^9 - 3 * q^13 + 2 * q^15 - 2 * q^17 + 4 * q^19 - 9 * q^21 - 12 * q^23 - 5 * q^25 - 6 * q^27 + 6 * q^29 - 2 * q^31 - 6 * q^35 - 12 * q^41 + 33 * q^43 + 4 * q^45 + 18 * q^47 - 8 * q^49 + 2 * q^51 + 36 * q^53 - 12 * q^55 - q^57 - 2 * q^59 + 3 * q^61 - 9 * q^63 - 19 * q^67 + 16 * q^71 + 11 * q^73 - 10 * q^75 - 32 * q^77 - 9 * q^79 - 3 * q^81 - 8 * q^85 + 6 * q^89 - q^91 - q^93 + 26 * q^95 - 24 * q^97

Introduction

L-functions

Modular forms

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Database

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