LMFDB - Embedded newform 912.2.bb.e.559.1

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			559.1
Root			$0.403374 + 1.68443i$ of defining polynomial
Character	$\chi$	$=$	912.559
Dual form			912.2.bb.e.31.1

$q$-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 $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

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

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	0.208748	+	0.977969i	$0.433061\pi$
$5$	−1.66044	+	2.87597i	−0.742572	+	1.28617i	−0.951320	+	0.308204i	$0.900272\pi$
$6$		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	0.241248	−	0.970463i	$-0.422443\pi$
$13$	4.33502	−	2.50283i	1.20232	−	0.694159i	0.961070	+	0.276304i	$0.0891098\pi$
$14$		0			0
$15$	−1.66044	−	2.87597i	−0.428724	−	0.742572i
$16$		0			0
$17$	−2.51414	+	4.35461i	−0.609768	+	1.05615i	0.381511	+	0.924364i	$0.375404\pi$
$17$	−2.51414	+	4.35461i	−0.609768	+	1.05615i	−0.991278	+	0.131784i	$0.957929\pi$
$18$		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	$-0.813132\pi$
$23$	−3.68872	+	2.12968i	−0.769150	+	0.444069i	0.0634210	+	0.997987i	$0.479799\pi$
$24$		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	0.151688	−	0.988428i	$-0.451529\pi$
$29$	5.83502	−	3.36885i	1.08354	−	0.625580i	0.931848	+	0.362848i	$0.118196\pi$
$30$		0			0
$31$	−2.32088			−0.416843			−0.208422	−	0.978039i	$-0.566833\pi$
$31$	−2.32088			−0.416843			−0.208422	+	0.978039i	$0.566833\pi$
$32$		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	$-0.761741\pi$
$37$		−	8.27925i		−	1.36110i	0.732701	−	0.680550i	$-0.238259\pi$
$38$		0			0
$39$			5.00565i			0.801546i
$40$		0			0
$41$	−9.96265	−	5.75194i	−1.55591	−	0.898302i	−0.997642	−	0.0686385i	$-0.978134\pi$
$41$	−9.96265	−	5.75194i	−1.55591	−	0.898302i	−0.558263	−	0.829664i	$-0.688532\pi$
$42$		0			0
$43$	−9.48133	−	5.47405i	−1.44589	−	0.834784i	−0.447656	−	0.894206i	$-0.647741\pi$
$43$	−9.48133	−	5.47405i	−1.44589	−	0.834784i	−0.998233	+	0.0594217i	$0.981074\pi$
$44$		0			0
$45$	3.32088			0.495048
$46$		0			0
$47$	−6.41478	+	3.70357i	−0.935692	+	0.540222i	−0.888607	−	0.458669i	$-0.848326\pi$
$47$	−6.41478	+	3.70357i	−0.935692	+	0.540222i	−0.0470845	+	0.998891i	$0.514993\pi$
$48$		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	−0.103013	−	0.994680i	$-0.532848\pi$
$53$	5.14631	−	2.97122i	0.706899	−	0.408129i	0.809912	+	0.586551i	$0.199515\pi$
$54$		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	$-0.763976\pi$
$59$	1.66044	−	2.87597i	0.216171	−	0.374419i	0.953634	+	0.300968i	$0.0973097\pi$
$60$		0			0
$61$	3.62763	+	6.28324i	0.464471	+	0.804487i	0.999177	−	0.0405508i	$-0.0129113\pi$
$61$	3.62763	+	6.28324i	0.464471	+	0.804487i	−0.534707	+	0.845038i	$0.679578\pi$
$62$		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	0.909019	+	0.416755i	$0.136833\pi$
$67$	6.67458	+	11.5607i	0.815430	+	1.41237i	−0.0935894	+	0.995611i	$0.529834\pi$
$68$		0			0
$69$		−	4.25936i		−	0.512767i
$70$		0			0
$71$	−2.19325	+	3.79882i	−0.260291	+	0.450838i	−0.966319	−	0.257346i	$-0.917152\pi$
$71$	−2.19325	+	3.79882i	−0.260291	+	0.450838i	0.706028	+	0.708184i	$0.250485\pi$
$72$		0			0
$73$	−2.52827	+	4.37910i	−0.295912	+	0.512535i	−0.975197	−	0.221340i	$-0.928957\pi$
$73$	−2.52827	+	4.37910i	−0.295912	+	0.512535i	0.679285	+	0.733875i	$0.262290\pi$
$74$		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	−0.373387	−	0.927676i	$-0.621804\pi$
$79$	5.48133	−	9.49394i	0.616697	−	1.06815i	0.990084	−	0.140476i	$-0.0448631\pi$
$80$		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	−0.787516	−	0.616294i	$-0.788633\pi$
$89$	−6.10896	+	3.52701i	−0.647548	+	0.373862i	0.139968	+	0.990156i	$0.455300\pi$
$90$		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	0.0924121	−	0.995721i	$-0.470542\pi$
$97$	−7.12763	−	4.11514i	−0.723701	−	0.417829i	−0.816113	+	0.577892i	$0.803876\pi$
$98$		0			0
$99$	0.853695	−	0.492881i	0.0857995	−	0.0495364i
$100$		0			0
$101$	2.83502	+	4.91040i	0.282095	+	0.488603i	0.971901	−	0.235392i	$-0.0756373\pi$
$101$	2.83502	+	4.91040i	0.282095	+	0.488603i	−0.689805	+	0.723995i	$0.742304\pi$
$102$		0			0
$103$	10.1222			0.997367			0.498683	−	0.866784i	$-0.333817\pi$
$103$	10.1222			0.997367			0.498683	+	0.866784i	$0.333817\pi$
$104$		0			0
$105$	7.81635	−	4.51277i	0.762797	−	0.440401i
$106$		0			0
$107$	−0.971726			−0.0939403			−0.0469702	−	0.998896i	$-0.514957\pi$
$107$	−0.971726			−0.0939403			−0.0469702	+	0.998896i	$0.514957\pi$
$108$		0			0
$109$	−0.579757	−	0.334723i	−0.0555307	−	0.0320607i	0.471978	−	0.881611i	$-0.343540\pi$
$109$	−0.579757	−	0.334723i	−0.0555307	−	0.0320607i	−0.527508	+	0.849550i	$0.676874\pi$
$110$		0			0
$111$	7.17004	+	4.13963i	0.680550	+	0.392916i
$112$		0			0
$113$			8.39291i			0.789539i	0.918780	+	0.394769i	$0.129175\pi$
$113$			8.39291i			0.789539i	−0.918780	+	0.394769i	$0.870825\pi$
$114$		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	$-0.273371\pi$
$127$	−3.70739	−	6.42139i	−0.328978	−	0.569806i	−0.982309	+	0.187266i	$0.940037\pi$
$128$		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	$-0.0191164\pi$
$131$	16.5424	+	9.55077i	1.44532	+	0.834454i	0.447120	+	0.894474i	$0.352450\pi$
$132$		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	0.826589	+	0.562806i	$0.190278\pi$
$137$	10.5424	+	18.2600i	0.900699	+	1.56006i	0.0741101	+	0.997250i	$0.476388\pi$
$138$		0			0
$139$	−10.8588	+	6.26931i	−0.921028	+	0.531756i	−0.883963	−	0.467557i	$-0.845134\pi$
$139$	−10.8588	+	6.26931i	−0.921028	+	0.531756i	−0.0370651	+	0.999313i	$0.511801\pi$
$140$		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	−0.713804	−	0.700346i	$-0.753029\pi$
$149$	3.04695	−	5.27747i	0.249616	−	0.432347i	0.963419	+	0.267999i	$0.0863624\pi$
$150$		0			0
$151$	12.6983			1.03337			0.516687	−	0.856174i	$-0.327165\pi$
$151$	12.6983			1.03337			0.516687	+	0.856174i	$0.327165\pi$
$152$		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	0.303873	+	0.952713i	$0.401720\pi$
$157$	−8.43438	+	14.6088i	−0.673137	+	1.16591i	−0.977010	+	0.213195i	$0.931613\pi$
$158$		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	−0.999791	−	0.0204298i	$-0.993497\pi$
$167$	−6.68872	−	11.5852i	−0.517588	−	0.896489i	0.482203	−	0.876060i	$-0.339837\pi$
$168$		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	0.854899	−	0.518794i	$-0.173619\pi$
$173$	10.9572	+	6.32614i	0.833060	+	0.480967i	−0.0218394	+	0.999761i	$0.506952\pi$
$174$		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	$-0.508752\pi$
$179$	−0.735663			−0.0549861			−0.0274930	+	0.999622i	$0.508752\pi$
$180$		0			0
$181$	5.42024	−	3.12938i	0.402883	−	0.232605i	−0.284844	−	0.958574i	$-0.591942\pi$
$181$	5.42024	−	3.12938i	0.402883	−	0.232605i	0.687727	+	0.725969i	$0.258608\pi$
$182$		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	0.352227	−	0.935915i	$-0.385424\pi$
$193$	−3.92024	−	2.26335i	−0.282185	−	0.162920i	−0.634412	+	0.772995i	$0.718758\pi$
$194$		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	$-0.694109\pi$
$199$	−2.10389	+	1.21468i	−0.149141	+	0.0861067i	0.423572	+	0.905862i	$0.360776\pi$
$200$		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	$-0.987760\pi$
$211$	−6.77394	+	11.7328i	−0.466337	+	0.807720i	0.532924	+	0.846163i	$0.321093\pi$
$212$		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	0.477183	+	0.878804i	$0.341658\pi$
$223$	−7.80221	+	13.5138i	−0.522475	+	0.904953i	−0.999658	+	0.0261490i	$0.991676\pi$
$224$		0			0
$225$	−3.01414	+	5.22064i	−0.200942	+	0.348043i
$226$		0			0
$227$	−16.2926			−1.08138			−0.540689	−	0.841222i	$-0.681837\pi$
$227$	−16.2926			−1.08138			−0.540689	+	0.841222i	$0.681837\pi$
$228$		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	0.0528253	+	0.998604i	$0.483177\pi$
$233$	−12.7977	+	22.1662i	−0.838404	+	1.45216i	−0.891229	+	0.453554i	$0.850156\pi$
$234$		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	−0.876008	−	0.482297i	$-0.839803\pi$
$241$	−13.9148	+	8.03370i	−0.896330	+	0.517496i	−0.0203221	+	0.999793i	$0.506469\pi$
$242$		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	$-0.638184\pi$
$251$	2.45213	−	1.41574i	0.154777	−	0.0893604i	0.575388	+	0.817881i	$0.304851\pi$
$252$		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	−0.567970	−	0.823049i	$-0.692271\pi$
$257$	−2.23113	+	1.28814i	−0.139174	+	0.0803521i	0.428796	+	0.903401i	$0.358938\pi$
$258$		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	0.999400	+	0.0346292i	$0.0110250\pi$
$263$	24.7977	+	14.3169i	1.52909	+	0.882821i	0.529690	+	0.848191i	$0.322308\pi$
$264$		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	−0.220009	−	0.975498i	$-0.570609\pi$
$269$	−19.2685	−	11.1247i	−1.17482	−	0.678282i	−0.954810	+	0.297215i	$0.903942\pi$
$270$		0			0
$271$	2.67004	+	1.54155i	0.162194	+	0.0936425i	0.578900	−	0.815399i	$-0.303482\pi$
$271$	2.67004	+	1.54155i	0.162194	+	0.0936425i	−0.416706	+	0.909041i	$0.636816\pi$
$272$		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	−0.0502030	−	0.998739i	$-0.515987\pi$
$281$	13.2366	−	7.64215i	0.789629	−	0.455892i	0.839832	+	0.542847i	$0.182654\pi$
$282$		0			0
$283$	24.3027	+	14.0312i	1.44465	+	0.834068i	0.998155	−	0.0607193i	$-0.0193394\pi$
$283$	24.3027	+	14.0312i	1.44465	+	0.834068i	0.446493	+	0.894787i	$0.352673\pi$
$284$		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	$-0.989663\pi$
$293$		−	1.11158i		−	0.0649390i	0.999473	−	0.0324695i	$-0.0103372\pi$
$294$		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	−0.254205	−	0.967150i	$-0.581814\pi$
$307$	12.4485	−	21.5615i	0.710474	−	1.23058i	0.964679	−	0.263427i	$-0.0848529\pi$
$308$		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	0.942049	−	0.335476i	$-0.108897\pi$
$313$	3.19325	+	5.53088i	0.180493	+	0.312624i	−0.761555	+	0.648100i	$0.775564\pi$
$314$		0			0
$315$			9.02554i			0.508532i
$316$		0			0
$317$	2.39611	−	1.38339i	0.134579	−	0.0776990i	−0.431199	−	0.902257i	$-0.641909\pi$
$317$	2.39611	−	1.38339i	0.134579	−	0.0776990i	0.565778	+	0.824558i	$0.308576\pi$
$318$		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	$-0.774895\pi$
$331$	−27.6610			−1.52038			−0.760192	+	0.649698i	$0.774895\pi$
$332$		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	0.866427	−	0.499304i	$-0.166411\pi$
$337$	15.9202	+	9.19156i	0.867231	+	0.500696i	0.000803838		1.00000i	$0.499744\pi$
$338$		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	$-0.380182\pi$
$347$	−4.73153	−	2.73175i	−0.254002	−	0.146648i	−0.621595	+	0.783339i	$0.713515\pi$
$348$		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	−0.986597	−	0.163174i	$-0.947827\pi$
$359$	−30.7175	−	17.7348i	−1.62121	−	0.936005i	−0.634611	−	0.772832i	$-0.718840\pi$
$360$		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	$-0.680523\pi$
$367$	−1.44398	+	0.833682i	−0.0753752	+	0.0435179i	0.461839	+	0.886964i	$0.347190\pi$
$368$		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	$0.149769\pi$
$373$			17.5110i			0.906686i	−0.891336	+	0.453343i	$0.850231\pi$
$374$		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	$-0.696022\pi$
$379$	−22.4905			−1.15526			−0.577630	+	0.816298i	$0.696022\pi$
$380$		0			0
$381$	7.41478			0.379871
$382$		0			0
$383$	−10.1746	+	17.6229i	−0.519897	+	0.900488i	0.479836	+	0.877358i	$0.340696\pi$
$383$	−10.1746	+	17.6229i	−0.519897	+	0.900488i	−0.999732	+	0.0231292i	$0.992637\pi$
$384$		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	0.993163	+	0.116738i	$0.0372436\pi$
$389$	11.7881	+	20.4175i	0.597679	+	1.03521i	−0.395484	+	0.918473i	$0.629423\pi$
$390$		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	0.0835014	+	0.996508i	$0.473390\pi$
$397$	−16.3633	+	28.3421i	−0.821250	+	1.42245i	−0.904752	+	0.425939i	$0.859944\pi$
$398$		0			0
$399$	6.37237	−	9.98682i	0.319017	−	0.499966i
$400$		0			0
$401$	−16.3533	−	9.44158i	−0.816645	−	0.471490i	0.0326134	−	0.999468i	$-0.489617\pi$
$401$	−16.3533	−	9.44158i	−0.816645	−	0.471490i	−0.849258	+	0.527978i	$0.822950\pi$
$402$		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	−0.0599366	−	0.998202i	$-0.519090\pi$
$409$	15.6646	−	9.04395i	0.774564	−	0.447194i	0.834500	+	0.551008i	$0.185757\pi$
$410$		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	0.962446	−	0.271474i	$-0.0875112\pi$
$421$	24.7977	+	14.3169i	1.20856	+	0.697765i	0.246119	+	0.969240i	$0.420845\pi$
$422$		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	$-0.0666760\pi$
$431$	6.41478	+	11.1107i	0.308989	+	0.535185i	−0.669152	+	0.743125i	$0.733343\pi$
$432$		0			0
$433$	−20.0525	+	11.5773i	−0.963664	+	0.556371i	−0.897299	−	0.441424i	$-0.854473\pi$
$433$	−20.0525	+	11.5773i	−0.963664	+	0.556371i	−0.0663649	+	0.997795i	$0.521140\pi$
$434$		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	0.363874	+	0.931448i	$0.381454\pi$
$439$	−13.0894	+	22.6714i	−0.624721	+	1.08205i	−0.988595	+	0.150600i	$0.951879\pi$
$440$		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	$-0.509404\pi$
$443$	17.2871	−	9.98074i	0.821337	−	0.474199i	0.850877	+	0.525364i	$0.176071\pi$
$444$		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	$-0.746199\pi$
$449$		−	30.3224i		−	1.43100i	0.698613	−	0.715500i	$-0.253801\pi$
$450$		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	−0.00737587	−	0.999973i	$-0.502348\pi$
$461$	18.5147	−	32.0683i	0.862314	−	1.49357i	0.869690	−	0.493599i	$-0.164319\pi$
$462$		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	$-0.380943\pi$
$479$	29.6382	−	17.1116i	1.35420	−	0.781849i	0.988835	+	0.149015i	$0.0476101\pi$
$480$		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	$-0.634161\pi$
$487$	−18.0565			−0.818220			−0.409110	+	0.912485i	$0.634161\pi$
$488$		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	$-0.211917\pi$
$491$	14.2871	+	8.24869i	0.644770	+	0.372258i	−0.141680	+	0.989913i	$0.545250\pi$
$492$		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	$-0.603347\pi$
$499$	−29.0237	−	16.7569i	−1.29928	−	0.750140i	−0.980280	+	0.197614i	$0.936681\pi$
$500$		0			0
$501$	13.3774			0.597660
$502$		0			0
$503$	4.62723	−	2.67153i	0.206318	−	0.119118i	−0.393281	−	0.919418i	$-0.628660\pi$
$503$	4.62723	−	2.67153i	0.206318	−	0.119118i	0.599599	+	0.800301i	$0.295327\pi$
$504$		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	0.0963261	−	0.995350i	$-0.469291\pi$
$509$	22.7074	−	13.1101i	1.00649	−	0.581096i	0.910161	+	0.414254i	$0.135958\pi$
$510$		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	$0.224741\pi$
$521$			29.6197i			1.29766i	−0.760933	+	0.648830i	$0.775259\pi$
$522$		0			0
$523$	−3.70285	−	6.41353i	−0.161914	−	0.280444i	0.773641	−	0.633624i	$-0.218434\pi$
$523$	−3.70285	−	6.41353i	−0.161914	−	0.280444i	−0.935555	+	0.353180i	$0.885100\pi$
$524$		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	0.979204	−	0.202876i	$-0.0650288\pi$
$541$	7.30128	+	12.6462i	0.313907	+	0.543702i	−0.665298	+	0.746578i	$0.731695\pi$
$542$		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	0.840541	+	0.541749i	$0.182238\pi$
$547$	20.8022	+	36.0305i	0.889438	+	1.54055i	0.0488977	+	0.998804i	$0.484429\pi$
$548$		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	−0.763240	−	0.646115i	$-0.776393\pi$
$557$	−22.2125	−	38.4731i	−0.941172	−	1.63016i	−0.177931	−	0.984043i	$-0.556941\pi$
$558$		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	$-0.189938\pi$
$563$	39.2545			1.65438			0.827189	+	0.561923i	$0.189938\pi$
$564$		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	$-0.806270\pi$
$569$		−	27.2761i		−	1.14347i	0.820438	−	0.571736i	$-0.193730\pi$
$570$		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	$-0.181755\pi$
$587$	19.2366	+	11.1063i	0.793979	+	0.458404i	−0.0473824	+	0.998877i	$0.515088\pi$
$588$		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	0.712899	−	0.701266i	$-0.247382\pi$
$593$	−6.10896	−	10.5810i	−0.250865	−	0.434511i	−0.963764	+	0.266756i	$0.914048\pi$
$594$		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	−0.998173	−	0.0604175i	$-0.980757\pi$
$599$	−13.4955	−	23.3748i	−0.551410	−	0.955070i	0.446763	−	0.894652i	$-0.352577\pi$
$600$		0			0
$601$			24.4514i			0.997392i	0.866777	+	0.498696i	$0.166188\pi$
$601$			24.4514i			0.997392i	−0.866777	+	0.498696i	$0.833812\pi$
$602$		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	$-0.410200\pi$
$607$	13.7175			0.556777			0.278388	+	0.960469i	$0.410200\pi$
$608$		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	0.0596932	+	0.998217i	$0.480988\pi$
$613$	−20.6646	+	35.7921i	−0.834634	+	1.44563i	−0.894328	+	0.447413i	$0.852346\pi$
$614$		0			0
$615$			38.2031i			1.54050i
$616$		0			0
$617$	12.9157	+	22.3707i	0.519967	+	0.900609i	0.999731	+	0.0232112i	$0.00738901\pi$
$617$	12.9157	+	22.3707i	0.519967	+	0.900609i	−0.479764	+	0.877398i	$0.659278\pi$
$618$		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	$-0.492732\pi$
$631$	22.6090	−	13.0533i	0.900048	−	0.519643i	0.877216	+	0.480096i	$0.159398\pi$
$632$		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	0.257104	−	0.966384i	$-0.417232\pi$
$641$	−11.4249	−	6.59617i	−0.451257	−	0.260533i	−0.708361	+	0.705851i	$0.750565\pi$
$642$		0			0
$643$	−28.2790	−	16.3269i	−1.11521	−	0.643870i	−0.175040	−	0.984561i	$-0.556005\pi$
$643$	−28.2790	−	16.3269i	−1.11521	−	0.643870i	−0.940175	+	0.340692i	$0.889339\pi$
$644$		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	$-0.260981\pi$
$659$	−7.49546	−	12.9825i	−0.291982	−	0.505727i	−0.974278	+	0.225348i	$0.927648\pi$
$660$		0			0
$661$	−19.5953	+	11.3134i	−0.762171	+	0.440040i	−0.830075	−	0.557652i	$-0.811702\pi$
$661$	−19.5953	+	11.3134i	−0.762171	+	0.440040i	0.0679038	+	0.997692i	$0.478369\pi$
$662$		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	$-0.831932\pi$
$673$		−	26.1398i		−	1.00762i	0.863815	−	0.503808i	$-0.168068\pi$
$674$		0			0
$675$	−3.01414	−	5.22064i	−0.116014	−	0.200942i
$676$		0			0
$677$			4.42199i			0.169951i	0.996383	+	0.0849755i	$0.0270812\pi$
$677$			4.42199i			0.169951i	−0.996383	+	0.0849755i	$0.972919\pi$
$678$		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	$-0.613442\pi$
$683$	−18.2361			−0.697784			−0.348892	+	0.937163i	$0.613442\pi$
$684$		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	−0.994003	−	0.109356i	$-0.965121\pi$
$701$	−10.6514	+	18.4487i	−0.402297	+	0.696798i	0.591706	+	0.806154i	$0.298455\pi$
$702$		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	0.815136	−	0.579270i	$-0.196662\pi$
$709$	−2.50546	−	4.33959i	−0.0940947	−	0.162977i	−0.909230	+	0.416293i	$0.863329\pi$
$710$		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	$-0.125315\pi$
$719$	28.2366	+	16.3024i	1.05305	+	0.607977i	0.129546	+	0.991573i	$0.458648\pi$
$720$		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	$-0.223393\pi$
$727$	15.8113	+	9.12865i	0.586408	+	0.338563i	−0.177268	+	0.984163i	$0.556726\pi$
$728$		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	$-0.515993\pi$
$739$	−25.5607	−	14.7575i	−0.940265	−	0.542862i	−0.890043	+	0.455876i	$0.849326\pi$
$740$		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	$-0.748442\pi$
$743$	7.18365	−	12.4424i	0.263543	−	0.456469i	0.967181	+	0.254089i	$0.0817757\pi$
$744$		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	$-0.109425\pi$
$751$	4.90157	+	8.48977i	0.178861	+	0.309796i	−0.762630	+	0.646835i	$0.776092\pi$
$752$		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	−0.542203	−	0.840247i	$-0.682410\pi$
$757$	12.5620	−	21.7580i	0.456574	−	0.790810i	0.998777	+	0.0494379i	$0.0157430\pi$
$758$		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	0.984027	−	0.178017i	$-0.0569683\pi$
$769$	9.36876	+	16.2272i	0.337846	+	0.585167i	−0.646181	+	0.763184i	$0.723635\pi$
$770$		0			0
$771$		−	2.57628i		−	0.0927826i
$772$		0			0
$773$	−18.9627	+	10.9481i	−0.682039	+	0.393776i	−0.800623	−	0.599169i	$-0.795498\pi$
$773$	−18.9627	+	10.9481i	−0.682039	+	0.393776i	0.118584	+	0.992944i	$0.462165\pi$
$774$		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	$-0.222636\pi$
$787$	42.9336			1.53042			0.765208	+	0.643783i	$0.222636\pi$
$788$		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	$-0.992659\pi$
$797$		−	1.30208i		−	0.0461219i	0.999734	−	0.0230610i	$-0.00734119\pi$
$798$		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	$-0.167084\pi$
$811$	−0.0373465	−	0.0646860i	−0.00131141	−	0.00227143i	−0.866680	+	0.498864i	$0.833751\pi$
$812$		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	0.582176	−	0.813063i	$-0.302201\pi$
$821$	−11.8350	−	20.4989i	−0.413045	−	0.715415i	−0.995221	+	0.0976477i	$0.968868\pi$
$822$		0			0
$823$	29.2070	−	16.8627i	1.01809	−	0.587795i	0.104541	−	0.994521i	$-0.466663\pi$
$823$	29.2070	−	16.8627i	1.01809	−	0.587795i	0.913551	+	0.406725i	$0.133329\pi$
$824$		0			0
$825$			5.94244i			0.206889i
$826$		0			0
$827$	−11.5990	−	20.0900i	−0.403335	−	0.698597i	0.590791	−	0.806825i	$-0.298816\pi$
$827$	−11.5990	−	20.0900i	−0.403335	−	0.698597i	−0.994126	+	0.108228i	$0.965483\pi$
$828$		0			0
$829$			13.6537i			0.474214i	0.971484	+	0.237107i	$0.0761992\pi$
$829$			13.6537i			0.474214i	−0.971484	+	0.237107i	$0.923801\pi$
$830$		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	$-0.750119\pi$
$839$	7.48639	−	12.9668i	0.258459	−	0.447664i	0.965829	+	0.259179i	$0.0834520\pi$
$840$		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	−0.992901	−	0.118944i	$-0.962049\pi$
$853$	−11.4909	+	19.9029i	−0.393442	+	0.681461i	0.599459	+	0.800405i	$0.295382\pi$
$854$		0			0
$855$	−0.641769	+	14.4612i	−0.0219480	+	0.494561i
$856$		0			0
$857$	2.45213	+	1.41574i	0.0837630	+	0.0483606i	0.541296	−	0.840832i	$-0.317934\pi$
$857$	2.45213	+	1.41574i	0.0837630	+	0.0483606i	−0.457533	+	0.889192i	$0.651267\pi$
$858$		0			0
$859$	−6.42839	+	3.71143i	−0.219334	+	0.126632i	−0.605642	−	0.795737i	$-0.707084\pi$
$859$	−6.42839	+	3.71143i	−0.219334	+	0.126632i	0.386308	+	0.922370i	$0.373750\pi$
$860$		0			0
$861$	15.6327	+	27.0766i	0.532761	+	0.922769i
$862$		0			0
$863$	2.96080			0.100787			0.0503934	−	0.998729i	$-0.483952\pi$
$863$	2.96080			0.100787			0.0503934	+	0.998729i	$0.483952\pi$
$864$		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	0.983655	+	0.180065i	$0.0576309\pi$
$877$	48.3133	+	27.8937i	1.63142	+	0.941903i	0.647768	+	0.761837i	$0.275702\pi$
$878$		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	$-0.649734\pi$
$883$	2.73659	−	1.57997i	0.0920936	−	0.0531703i	0.545340	+	0.838215i	$0.316401\pi$
$884$		0			0
$885$	−11.0283			−0.370711
$886$		0			0
$887$	−16.7453	−	29.0036i	−0.562251	−	0.973847i	−0.997300	−	0.0734403i	$-0.976602\pi$
$887$	−16.7453	−	29.0036i	−0.562251	−	0.973847i	0.435049	−	0.900407i	$-0.356731\pi$
$888$		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	$-0.934122\pi$
$907$	−9.37743	+	16.2422i	−0.311373	+	0.539313i	0.667287	+	0.744800i	$0.267455\pi$
$908$		0			0
$909$	2.83502	−	4.91040i	0.0940317	−	0.162868i
$910$		0			0
$911$	−30.4540			−1.00899			−0.504493	−	0.863416i	$-0.668320\pi$
$911$	−30.4540			−1.00899			−0.504493	+	0.863416i	$0.668320\pi$
$912$		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	−0.983705	−	0.179791i	$-0.942458\pi$
$929$	−10.2457	+	17.7460i	−0.336149	+	0.582228i	0.647556	+	0.762018i	$0.275791\pi$
$930$		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	0.943810	−	0.330488i	$-0.107213\pi$
$937$	5.68418	+	9.84529i	0.185694	+	0.321632i	−0.758116	+	0.652120i	$0.773880\pi$
$938$		0			0
$939$	−6.38650			−0.208416
$940$		0			0
$941$	−4.51053	+	2.60415i	−0.147039	+	0.0848930i	−0.571715	−	0.820453i	$-0.693722\pi$
$941$	−4.51053	+	2.60415i	−0.147039	+	0.0848930i	0.424676	+	0.905346i	$0.360388\pi$
$942$		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	0.964632	+	0.263600i	$0.0849099\pi$
$947$	51.5525	+	29.7639i	1.67523	+	0.967196i	0.710600	+	0.703596i	$0.248423\pi$
$948$		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	0.925216	−	0.379440i	$-0.123883\pi$
$953$	32.6988	+	18.8787i	1.05922	+	0.611541i	0.134003	+	0.990981i	$0.457217\pi$
$954$		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	$-0.564262\pi$
$967$	−35.7366	−	20.6325i	−1.14921	−	0.663497i	−0.948695	+	0.316193i	$0.897595\pi$
$968$		0			0
$969$	19.4485	−	10.1066i	0.624776	−	0.324669i
$970$		0			0
$971$	30.3209	−	52.5173i	0.973043	−	1.68536i	0.286797	−	0.957991i	$-0.407409\pi$
$971$	30.3209	−	52.5173i	0.973043	−	1.68536i	0.686246	−	0.727370i	$-0.259257\pi$
$972$		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	$0.106358\pi$
$977$			20.5016i			0.655903i	−0.944695	+	0.327951i	$0.893642\pi$
$978$		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	$-0.788900\pi$
$983$	4.36237	−	7.55584i	0.139138	−	0.240994i	0.927171	+	0.374640i	$0.122234\pi$
$984$		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	−0.326767	−	0.945105i	$-0.605959\pi$
$991$	20.6227	−	35.7196i	0.655102	−	1.13467i	0.981868	−	0.189564i	$-0.0607075\pi$
$992$		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	0.841934	−	0.539580i	$-0.181417\pi$
$997$	−1.46265	−	2.53339i	−0.0463227	−	0.0802333i	−0.888257	+	0.459347i	$0.848084\pi$
$998$		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.e.559.1	yes	6
3.2	odd	2		2736.2.bm.n.559.3		6
4.3	odd	2		912.2.bb.f.559.1	yes	6
12.11	even	2		2736.2.bm.o.559.3		6
19.12	odd	6		912.2.bb.f.31.1	yes	6
57.50	even	6		2736.2.bm.o.1855.3		6
76.31	even	6	inner	912.2.bb.e.31.1	✓	6
228.107	odd	6		2736.2.bm.n.1855.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.bb.e.31.1	✓	6	76.31	even	6	inner
912.2.bb.e.559.1	yes	6	1.1	even	1	trivial
912.2.bb.f.31.1	yes	6	19.12	odd	6
912.2.bb.f.559.1	yes	6	4.3	odd	2
2736.2.bm.n.559.3		6	3.2	odd	2
2736.2.bm.n.1855.3		6	228.107	odd	6
2736.2.bm.o.559.3		6	12.11	even	2
2736.2.bm.o.1855.3		6	57.50	even	6

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

Varieties

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Representations

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Database

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