LMFDB - Embedded newform 312.2.bf.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,2,Mod(49,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("312.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.bf (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:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	312.49
Dual form			312.2.bf.a.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{3} +1.73205i q^{5} +(2.36603 + 1.36603i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-2.36603 + 1.36603i) q^{11} +(-2.59808 - 2.50000i) q^{13} +(-1.50000 + 0.866025i) q^{15} +(-0.133975 + 0.232051i) q^{17} +(4.09808 + 2.36603i) q^{19} +2.73205i q^{21} +(4.09808 + 7.09808i) q^{23} +2.00000 q^{25} -1.00000 q^{27} +(-3.96410 - 6.86603i) q^{29} -1.46410i q^{31} +(-2.36603 - 1.36603i) q^{33} +(-2.36603 + 4.09808i) q^{35} +(-1.33013 + 0.767949i) q^{37} +(0.866025 - 3.50000i) q^{39} +(4.33013 - 2.50000i) q^{41} +(6.09808 - 10.5622i) q^{43} +(-1.50000 - 0.866025i) q^{45} +3.26795i q^{47} +(0.232051 + 0.401924i) q^{49} -0.267949 q^{51} -7.92820 q^{53} +(-2.36603 - 4.09808i) q^{55} +4.73205i q^{57} +(3.13397 - 5.42820i) q^{61} +(-2.36603 + 1.36603i) q^{63} +(4.33013 - 4.50000i) q^{65} +(7.56218 - 4.36603i) q^{67} +(-4.09808 + 7.09808i) q^{69} +(-1.90192 - 1.09808i) q^{71} -9.19615i q^{73} +(1.00000 + 1.73205i) q^{75} -7.46410 q^{77} -8.39230 q^{79} +(-0.500000 - 0.866025i) q^{81} -1.66025i q^{83} +(-0.401924 - 0.232051i) q^{85} +(3.96410 - 6.86603i) q^{87} +(8.19615 - 4.73205i) q^{89} +(-2.73205 - 9.46410i) q^{91} +(1.26795 - 0.732051i) q^{93} +(-4.09808 + 7.09808i) q^{95} +(8.66025 + 5.00000i) q^{97} -2.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 6 q^{7} - 2 q^{9} - 6 q^{11} - 6 q^{15} - 4 q^{17} + 6 q^{19} + 6 q^{23} + 8 q^{25} - 4 q^{27} - 2 q^{29} - 6 q^{33} - 6 q^{35} + 12 q^{37} + 14 q^{43} - 6 q^{45} - 6 q^{49} - 8 q^{51} - 4 q^{53}+ \cdots - 6 q^{95}+O(q^{100}) $ 4 * q + 2 * q^3 + 6 * q^7 - 2 * q^9 - 6 * q^11 - 6 * q^15 - 4 * q^17 + 6 * q^19 + 6 * q^23 + 8 * q^25 - 4 * q^27 - 2 * q^29 - 6 * q^33 - 6 * q^35 + 12 * q^37 + 14 * q^43 - 6 * q^45 - 6 * q^49 - 8 * q^51 - 4 * q^53 - 6 * q^55 + 16 * q^61 - 6 * q^63 + 6 * q^67 - 6 * q^69 - 18 * q^71 + 4 * q^75 - 16 * q^77 + 8 * q^79 - 2 * q^81 - 12 * q^85 + 2 * q^87 + 12 * q^89 - 4 * q^91 + 12 * q^93 - 6 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$5$			1.73205i			0.774597i	0.921954	+	0.387298i	$0.126592\pi$
$5$			1.73205i			0.774597i	−0.921954	+	0.387298i	$0.873408\pi$
$6$		0			0
$7$	2.36603	+	1.36603i	0.894274	+	0.516309i	0.875338	−	0.483512i	$-0.160639\pi$
$7$	2.36603	+	1.36603i	0.894274	+	0.516309i	0.0189356	+	0.999821i	$0.493972\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−2.36603	+	1.36603i	−0.713384	+	0.411872i	−0.812313	−	0.583222i	$-0.801792\pi$
$11$	−2.36603	+	1.36603i	−0.713384	+	0.411872i	0.0989291	+	0.995094i	$0.468458\pi$
$12$		0			0
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$14$		0			0
$15$	−1.50000	+	0.866025i	−0.387298	+	0.223607i
$16$		0			0
$17$	−0.133975	+	0.232051i	−0.0324936	+	0.0562806i	−0.881815	−	0.471596i	$-0.843678\pi$
$17$	−0.133975	+	0.232051i	−0.0324936	+	0.0562806i	0.849321	+	0.527876i	$0.177012\pi$
$18$		0			0
$19$	4.09808	+	2.36603i	0.940163	+	0.542803i	0.890011	−	0.455938i	$-0.150696\pi$
$19$	4.09808	+	2.36603i	0.940163	+	0.542803i	0.0501517	+	0.998742i	$0.484030\pi$
$20$		0			0
$21$			2.73205i			0.596182i
$22$		0			0
$23$	4.09808	+	7.09808i	0.854508	+	1.48005i	0.877101	+	0.480306i	$0.159475\pi$
$23$	4.09808	+	7.09808i	0.854508	+	1.48005i	−0.0225928	+	0.999745i	$0.507192\pi$
$24$		0			0
$25$	2.00000			0.400000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−3.96410	−	6.86603i	−0.736115	−	1.27499i	−0.954232	−	0.299066i	$-0.903325\pi$
$29$	−3.96410	−	6.86603i	−0.736115	−	1.27499i	0.218117	−	0.975923i	$-0.430009\pi$
$30$		0			0
$31$		−	1.46410i		−	0.262960i	−0.991319	−	0.131480i	$-0.958027\pi$
$31$		−	1.46410i		−	0.262960i	0.991319	−	0.131480i	$-0.0419730\pi$
$32$		0			0
$33$	−2.36603	−	1.36603i	−0.411872	−	0.237795i
$34$		0			0
$35$	−2.36603	+	4.09808i	−0.399931	+	0.692701i
$36$		0			0
$37$	−1.33013	+	0.767949i	−0.218672	+	0.126250i	−0.605335	−	0.795971i	$-0.706961\pi$
$37$	−1.33013	+	0.767949i	−0.218672	+	0.126250i	0.386663	+	0.922221i	$0.373628\pi$
$38$		0			0
$39$	0.866025	−	3.50000i	0.138675	−	0.560449i
$40$		0			0
$41$	4.33013	−	2.50000i	0.676252	−	0.390434i	−0.122189	−	0.992507i	$-0.538991\pi$
$41$	4.33013	−	2.50000i	0.676252	−	0.390434i	0.798441	+	0.602072i	$0.205658\pi$
$42$		0			0
$43$	6.09808	−	10.5622i	0.929948	−	1.61072i	0.146544	−	0.989204i	$-0.453185\pi$
$43$	6.09808	−	10.5622i	0.929948	−	1.61072i	0.783404	−	0.621513i	$-0.213482\pi$
$44$		0			0
$45$	−1.50000	−	0.866025i	−0.223607	−	0.129099i
$46$		0			0
$47$			3.26795i			0.476679i	0.971182	+	0.238340i	$0.0766032\pi$
$47$			3.26795i			0.476679i	−0.971182	+	0.238340i	$0.923397\pi$
$48$		0			0
$49$	0.232051	+	0.401924i	0.0331501	+	0.0574177i
$50$		0			0
$51$	−0.267949			−0.0375204
$52$		0			0
$53$	−7.92820			−1.08902			−0.544511	−	0.838754i	$-0.683285\pi$
$53$	−7.92820			−1.08902			−0.544511	+	0.838754i	$0.683285\pi$
$54$		0			0
$55$	−2.36603	−	4.09808i	−0.319035	−	0.552584i
$56$		0			0
$57$			4.73205i			0.626775i
$58$		0			0
$59$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$59$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$60$		0			0
$61$	3.13397	−	5.42820i	0.401264	−	0.695010i	−0.592614	−	0.805486i	$-0.701904\pi$
$61$	3.13397	−	5.42820i	0.401264	−	0.695010i	0.993879	+	0.110476i	$0.0352375\pi$
$62$		0			0
$63$	−2.36603	+	1.36603i	−0.298091	+	0.172103i
$64$		0			0
$65$	4.33013	−	4.50000i	0.537086	−	0.558156i
$66$		0			0
$67$	7.56218	−	4.36603i	0.923867	−	0.533395i	0.0390004	−	0.999239i	$-0.487583\pi$
$67$	7.56218	−	4.36603i	0.923867	−	0.533395i	0.884867	+	0.465844i	$0.154249\pi$
$68$		0			0
$69$	−4.09808	+	7.09808i	−0.493350	+	0.854508i
$70$		0			0
$71$	−1.90192	−	1.09808i	−0.225717	−	0.130318i	0.382878	−	0.923799i	$-0.374933\pi$
$71$	−1.90192	−	1.09808i	−0.225717	−	0.130318i	−0.608595	+	0.793481i	$0.708266\pi$
$72$		0			0
$73$		−	9.19615i		−	1.07633i	−0.842840	−	0.538164i	$-0.819118\pi$
$73$		−	9.19615i		−	1.07633i	0.842840	−	0.538164i	$-0.180882\pi$
$74$		0			0
$75$	1.00000	+	1.73205i	0.115470	+	0.200000i
$76$		0			0
$77$	−7.46410			−0.850613
$78$		0			0
$79$	−8.39230			−0.944208			−0.472104	−	0.881543i	$-0.656505\pi$
$79$	−8.39230			−0.944208			−0.472104	+	0.881543i	$0.656505\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	1.66025i		−	0.182237i	−0.995840	−	0.0911183i	$-0.970956\pi$
$83$		−	1.66025i		−	0.182237i	0.995840	−	0.0911183i	$-0.0290441\pi$
$84$		0			0
$85$	−0.401924	−	0.232051i	−0.0435948	−	0.0251694i
$86$		0			0
$87$	3.96410	−	6.86603i	0.424996	−	0.736115i
$88$		0			0
$89$	8.19615	−	4.73205i	0.868790	−	0.501596i	0.00184433	−	0.999998i	$-0.499413\pi$
$89$	8.19615	−	4.73205i	0.868790	−	0.501596i	0.866946	+	0.498402i	$0.166080\pi$
$90$		0			0
$91$	−2.73205	−	9.46410i	−0.286397	−	0.992107i
$92$		0			0
$93$	1.26795	−	0.732051i	0.131480	−	0.0759101i
$94$		0			0
$95$	−4.09808	+	7.09808i	−0.420454	+	0.728247i
$96$		0			0
$97$	8.66025	+	5.00000i	0.879316	+	0.507673i	0.870433	−	0.492287i	$-0.163839\pi$
$97$	8.66025	+	5.00000i	0.879316	+	0.507673i	0.00888289	+	0.999961i	$0.497172\pi$
$98$		0			0
$99$		−	2.73205i		−	0.274581i
$100$		0			0
$101$	−3.76795	−	6.52628i	−0.374925	−	0.649389i	0.615391	−	0.788222i	$-0.288998\pi$
$101$	−3.76795	−	6.52628i	−0.374925	−	0.649389i	−0.990316	+	0.138833i	$0.955665\pi$
$102$		0			0
$103$	−0.732051			−0.0721311			−0.0360656	−	0.999349i	$-0.511483\pi$
$103$	−0.732051			−0.0721311			−0.0360656	+	0.999349i	$0.511483\pi$
$104$		0			0
$105$	−4.73205			−0.461801
$106$		0			0
$107$	−4.56218	−	7.90192i	−0.441042	−	0.763908i	0.556725	−	0.830697i	$-0.312058\pi$
$107$	−4.56218	−	7.90192i	−0.441042	−	0.763908i	−0.997767	+	0.0667892i	$0.978724\pi$
$108$		0			0
$109$			20.3923i			1.95323i	0.214999	+	0.976614i	$0.431025\pi$
$109$			20.3923i			1.95323i	−0.214999	+	0.976614i	$0.568975\pi$
$110$		0			0
$111$	−1.33013	−	0.767949i	−0.126250	−	0.0728905i
$112$		0			0
$113$	6.33013	−	10.9641i	0.595488	−	1.03142i	−0.397990	−	0.917390i	$-0.630292\pi$
$113$	6.33013	−	10.9641i	0.595488	−	1.03142i	0.993478	−	0.114026i	$-0.0363747\pi$
$114$		0			0
$115$	−12.2942	+	7.09808i	−1.14644	+	0.661899i
$116$		0			0
$117$	3.46410	−	1.00000i	0.320256	−	0.0924500i
$118$		0			0
$119$	−0.633975	+	0.366025i	−0.0581164	+	0.0335535i
$120$		0			0
$121$	−1.76795	+	3.06218i	−0.160723	+	0.278380i
$122$		0			0
$123$	4.33013	+	2.50000i	0.390434	+	0.225417i
$124$		0			0
$125$			12.1244i			1.08444i
$126$		0			0
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	0.941014	−	0.338368i	$-0.109875\pi$
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	−0.763542	+	0.645758i	$0.776542\pi$
$128$		0			0
$129$	12.1962			1.07381
$130$		0			0
$131$	−15.3205			−1.33856			−0.669280	−	0.743011i	$-0.733397\pi$
$131$	−15.3205			−1.33856			−0.669280	+	0.743011i	$0.733397\pi$
$132$		0			0
$133$	6.46410	+	11.1962i	0.560509	+	0.970830i
$134$		0			0
$135$		−	1.73205i		−	0.149071i
$136$		0			0
$137$	4.79423	+	2.76795i	0.409599	+	0.236482i	0.690617	−	0.723220i	$-0.257339\pi$
$137$	4.79423	+	2.76795i	0.409599	+	0.236482i	−0.281019	+	0.959702i	$0.590672\pi$
$138$		0			0
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	0.0346338	+	0.999400i	$0.488974\pi$
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	−0.882823	+	0.469706i	$0.844360\pi$
$140$		0			0
$141$	−2.83013	+	1.63397i	−0.238340	+	0.137605i
$142$		0			0
$143$	9.56218	+	2.36603i	0.799629	+	0.197857i
$144$		0			0
$145$	11.8923	−	6.86603i	0.987602	−	0.570192i
$146$		0			0
$147$	−0.232051	+	0.401924i	−0.0191392	+	0.0331501i
$148$		0			0
$149$	18.6962	+	10.7942i	1.53165	+	0.884298i	0.999286	+	0.0377811i	$0.0120290\pi$
$149$	18.6962	+	10.7942i	1.53165	+	0.884298i	0.532362	+	0.846517i	$0.321304\pi$
$150$		0			0
$151$		−	17.2679i		−	1.40525i	−0.711562	−	0.702623i	$-0.752012\pi$
$151$		−	17.2679i		−	1.40525i	0.711562	−	0.702623i	$-0.247988\pi$
$152$		0			0
$153$	−0.133975	−	0.232051i	−0.0108312	−	0.0187602i
$154$		0			0
$155$	2.53590			0.203688
$156$		0			0
$157$	−23.0526			−1.83979			−0.919897	−	0.392159i	$-0.871728\pi$
$157$	−23.0526			−1.83979			−0.919897	+	0.392159i	$0.871728\pi$
$158$		0			0
$159$	−3.96410	−	6.86603i	−0.314374	−	0.544511i
$160$		0			0
$161$			22.3923i			1.76476i
$162$		0			0
$163$	11.6603	+	6.73205i	0.913302	+	0.527295i	0.881492	−	0.472199i	$-0.156540\pi$
$163$	11.6603	+	6.73205i	0.913302	+	0.527295i	0.0318096	+	0.999494i	$0.489873\pi$
$164$		0			0
$165$	2.36603	−	4.09808i	0.184195	−	0.319035i
$166$		0			0
$167$	−1.26795	+	0.732051i	−0.0981169	+	0.0566478i	−0.548256	−	0.836311i	$-0.684708\pi$
$167$	−1.26795	+	0.732051i	−0.0981169	+	0.0566478i	0.450139	+	0.892959i	$0.351375\pi$
$168$		0			0
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$		0			0
$171$	−4.09808	+	2.36603i	−0.313388	+	0.180934i
$172$		0			0
$173$	8.73205	−	15.1244i	0.663886	−	1.14988i	−0.315701	−	0.948859i	$-0.602240\pi$
$173$	8.73205	−	15.1244i	0.663886	−	1.14988i	0.979586	−	0.201025i	$-0.0644271\pi$
$174$		0			0
$175$	4.73205	+	2.73205i	0.357709	+	0.206524i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	10.3660	+	17.9545i	0.774793	+	1.34198i	0.934911	+	0.354883i	$0.115479\pi$
$179$	10.3660	+	17.9545i	0.774793	+	1.34198i	−0.160118	+	0.987098i	$0.551187\pi$
$180$		0			0
$181$	−19.1962			−1.42684			−0.713419	−	0.700737i	$-0.752855\pi$
$181$	−19.1962			−1.42684			−0.713419	+	0.700737i	$0.752855\pi$
$182$		0			0
$183$	6.26795			0.463340
$184$		0			0
$185$	−1.33013	−	2.30385i	−0.0977929	−	0.169382i
$186$		0			0
$187$		−	0.732051i		−	0.0535329i
$188$		0			0
$189$	−2.36603	−	1.36603i	−0.172103	−	0.0993637i
$190$		0			0
$191$	7.46410	−	12.9282i	0.540083	−	0.935452i	−0.458815	−	0.888532i	$-0.651726\pi$
$191$	7.46410	−	12.9282i	0.540083	−	0.935452i	0.998899	−	0.0469202i	$-0.0149407\pi$
$192$		0			0
$193$	−10.1603	+	5.86603i	−0.731351	+	0.422246i	−0.818916	−	0.573913i	$-0.805425\pi$
$193$	−10.1603	+	5.86603i	−0.731351	+	0.422246i	0.0875652	+	0.996159i	$0.472091\pi$
$194$		0			0
$195$	6.06218	+	1.50000i	0.434122	+	0.107417i
$196$		0			0
$197$	−0.928203	+	0.535898i	−0.0661317	+	0.0381812i	−0.532701	−	0.846303i	$-0.678823\pi$
$197$	−0.928203	+	0.535898i	−0.0661317	+	0.0381812i	0.466570	+	0.884485i	$0.345490\pi$
$198$		0			0
$199$	−0.169873	+	0.294229i	−0.0120420	+	0.0208573i	−0.871984	−	0.489535i	$-0.837167\pi$
$199$	−0.169873	+	0.294229i	−0.0120420	+	0.0208573i	0.859942	+	0.510392i	$0.170500\pi$
$200$		0			0
$201$	7.56218	+	4.36603i	0.533395	+	0.307956i
$202$		0			0
$203$		−	21.6603i		−	1.52025i
$204$		0			0
$205$	4.33013	+	7.50000i	0.302429	+	0.523823i
$206$		0			0
$207$	−8.19615			−0.569672
$208$		0			0
$209$	−12.9282			−0.894263
$210$		0			0
$211$	5.66025	+	9.80385i	0.389668	+	0.674925i	0.992405	−	0.123015i	$-0.0392564\pi$
$211$	5.66025	+	9.80385i	0.389668	+	0.674925i	−0.602737	+	0.797940i	$0.705923\pi$
$212$		0			0
$213$		−	2.19615i		−	0.150478i
$214$		0			0
$215$	18.2942	+	10.5622i	1.24766	+	0.720335i
$216$		0			0
$217$	2.00000	−	3.46410i	0.135769	−	0.235159i
$218$		0			0
$219$	7.96410	−	4.59808i	0.538164	−	0.310709i
$220$		0			0
$221$	0.928203	−	0.267949i	0.0624377	−	0.0180242i
$222$		0			0
$223$	−14.5359	+	8.39230i	−0.973396	+	0.561990i	−0.900270	−	0.435332i	$-0.856631\pi$
$223$	−14.5359	+	8.39230i	−0.973396	+	0.561990i	−0.0731260	+	0.997323i	$0.523298\pi$
$224$		0			0
$225$	−1.00000	+	1.73205i	−0.0666667	+	0.115470i
$226$		0			0
$227$	−19.0981	−	11.0263i	−1.26758	−	0.731840i	−0.293054	−	0.956096i	$-0.594671\pi$
$227$	−19.0981	−	11.0263i	−1.26758	−	0.731840i	−0.974530	+	0.224256i	$0.928005\pi$
$228$		0			0
$229$		−	0.143594i		−	0.00948893i	−0.999989	−	0.00474446i	$-0.998490\pi$
$229$		−	0.143594i		−	0.00948893i	0.999989	−	0.00474446i	$-0.00151022\pi$
$230$		0			0
$231$	−3.73205	−	6.46410i	−0.245551	−	0.425307i
$232$		0			0
$233$	2.00000			0.131024			0.0655122	−	0.997852i	$-0.479132\pi$
$233$	2.00000			0.131024			0.0655122	+	0.997852i	$0.479132\pi$
$234$		0			0
$235$	−5.66025			−0.369234
$236$		0			0
$237$	−4.19615	−	7.26795i	−0.272569	−	0.472104i
$238$		0			0
$239$			23.2679i			1.50508i	0.658547	+	0.752539i	$0.271171\pi$
$239$			23.2679i			1.50508i	−0.658547	+	0.752539i	$0.728829\pi$
$240$		0			0
$241$	4.62436	+	2.66987i	0.297881	+	0.171982i	0.641491	−	0.767131i	$-0.278316\pi$
$241$	4.62436	+	2.66987i	0.297881	+	0.171982i	−0.343610	+	0.939113i	$0.611650\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−0.696152	+	0.401924i	−0.0444755	+	0.0256780i
$246$		0			0
$247$	−4.73205	−	16.3923i	−0.301093	−	1.04302i
$248$		0			0
$249$	1.43782	−	0.830127i	0.0911183	−	0.0526072i
$250$		0			0
$251$	−1.26795	+	2.19615i	−0.0800322	+	0.138620i	−0.903264	−	0.429086i	$-0.858836\pi$
$251$	−1.26795	+	2.19615i	−0.0800322	+	0.138620i	0.823231	+	0.567706i	$0.192169\pi$
$252$		0			0
$253$	−19.3923	−	11.1962i	−1.21918	−	0.703896i
$254$		0			0
$255$		−	0.464102i		−	0.0290632i
$256$		0			0
$257$	−7.13397	−	12.3564i	−0.445005	−	0.770771i	0.553047	−	0.833150i	$-0.313465\pi$
$257$	−7.13397	−	12.3564i	−0.445005	−	0.770771i	−0.998053	+	0.0623783i	$0.980131\pi$
$258$		0			0
$259$	−4.19615			−0.260736
$260$		0			0
$261$	7.92820			0.490743
$262$		0			0
$263$	−14.8301	−	25.6865i	−0.914465	−	1.58390i	−0.807683	−	0.589617i	$-0.799279\pi$
$263$	−14.8301	−	25.6865i	−0.914465	−	1.58390i	−0.106782	−	0.994282i	$-0.534055\pi$
$264$		0			0
$265$		−	13.7321i		−	0.843553i
$266$		0			0
$267$	8.19615	+	4.73205i	0.501596	+	0.289597i
$268$		0			0
$269$	−1.26795	+	2.19615i	−0.0773082	+	0.133902i	−0.902088	−	0.431553i	$-0.857966\pi$
$269$	−1.26795	+	2.19615i	−0.0773082	+	0.133902i	0.824779	+	0.565455i	$0.191299\pi$
$270$		0			0
$271$	−13.8564	+	8.00000i	−0.841717	+	0.485965i	−0.857847	−	0.513905i	$-0.828199\pi$
$271$	−13.8564	+	8.00000i	−0.841717	+	0.485965i	0.0161307	+	0.999870i	$0.494865\pi$
$272$		0			0
$273$	6.83013	−	7.09808i	0.413378	−	0.429595i
$274$		0			0
$275$	−4.73205	+	2.73205i	−0.285353	+	0.164749i
$276$		0			0
$277$	8.06218	−	13.9641i	0.484409	−	0.839022i	−0.515430	−	0.856932i	$-0.672368\pi$
$277$	8.06218	−	13.9641i	0.484409	−	0.839022i	0.999840	+	0.0179100i	$0.00570122\pi$
$278$		0			0
$279$	1.26795	+	0.732051i	0.0759101	+	0.0438267i
$280$		0			0
$281$		−	30.7128i		−	1.83217i	−0.400981	−	0.916086i	$-0.631331\pi$
$281$		−	30.7128i		−	1.83217i	0.400981	−	0.916086i	$-0.368669\pi$
$282$		0			0
$283$	11.7583	+	20.3660i	0.698960	+	1.21063i	0.968827	+	0.247737i	$0.0796869\pi$
$283$	11.7583	+	20.3660i	0.698960	+	1.21063i	−0.269867	+	0.962898i	$0.586980\pi$
$284$		0			0
$285$	−8.19615			−0.485498
$286$		0			0
$287$	13.6603			0.806339
$288$		0			0
$289$	8.46410	+	14.6603i	0.497888	+	0.862368i
$290$		0			0
$291$			10.0000i			0.586210i
$292$		0			0
$293$	−19.1603	−	11.0622i	−1.11935	−	0.646259i	−0.178118	−	0.984009i	$-0.557001\pi$
$293$	−19.1603	−	11.0622i	−1.11935	−	0.646259i	−0.941236	+	0.337750i	$0.890334\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2.36603	−	1.36603i	0.137291	−	0.0792648i
$298$		0			0
$299$	7.09808	−	28.6865i	0.410492	−	1.65899i
$300$		0			0
$301$	28.8564	−	16.6603i	1.66326	−	0.960281i
$302$		0			0
$303$	3.76795	−	6.52628i	0.216463	−	0.374925i
$304$		0			0
$305$	9.40192	+	5.42820i	0.538353	+	0.310818i
$306$		0			0
$307$			7.26795i			0.414804i	0.978256	+	0.207402i	$0.0665008\pi$
$307$			7.26795i			0.414804i	−0.978256	+	0.207402i	$0.933499\pi$
$308$		0			0
$309$	−0.366025	−	0.633975i	−0.0208225	−	0.0360656i
$310$		0			0
$311$	21.6603			1.22824			0.614120	−	0.789213i	$-0.289511\pi$
$311$	21.6603			1.22824			0.614120	+	0.789213i	$0.289511\pi$
$312$		0			0
$313$	−31.3205			−1.77034			−0.885170	−	0.465268i	$-0.845958\pi$
$313$	−31.3205			−1.77034			−0.885170	+	0.465268i	$0.845958\pi$
$314$		0			0
$315$	−2.36603	−	4.09808i	−0.133310	−	0.230900i
$316$		0			0
$317$			0.803848i			0.0451486i	0.999745	+	0.0225743i	$0.00718623\pi$
$317$			0.803848i			0.0451486i	−0.999745	+	0.0225743i	$0.992814\pi$
$318$		0			0
$319$	18.7583	+	10.8301i	1.05026	+	0.606371i
$320$		0			0
$321$	4.56218	−	7.90192i	0.254636	−	0.441042i
$322$		0			0
$323$	−1.09808	+	0.633975i	−0.0610986	+	0.0352753i
$324$		0			0
$325$	−5.19615	−	5.00000i	−0.288231	−	0.277350i
$326$		0			0
$327$	−17.6603	+	10.1962i	−0.976614	+	0.563849i
$328$		0			0
$329$	−4.46410	+	7.73205i	−0.246114	+	0.426282i
$330$		0			0
$331$	−10.3923	−	6.00000i	−0.571213	−	0.329790i	0.186421	−	0.982470i	$-0.440311\pi$
$331$	−10.3923	−	6.00000i	−0.571213	−	0.329790i	−0.757634	+	0.652680i	$0.773645\pi$
$332$		0			0
$333$		−	1.53590i		−	0.0841667i
$334$		0			0
$335$	7.56218	+	13.0981i	0.413166	+	0.715624i
$336$		0			0
$337$	4.07180			0.221805			0.110902	−	0.993831i	$-0.464626\pi$
$337$	4.07180			0.221805			0.110902	+	0.993831i	$0.464626\pi$
$338$		0			0
$339$	12.6603			0.687611
$340$		0			0
$341$	2.00000	+	3.46410i	0.108306	+	0.187592i
$342$		0			0
$343$		−	17.8564i		−	0.964155i
$344$		0			0
$345$	−12.2942	−	7.09808i	−0.661899	−	0.382148i
$346$		0			0
$347$	8.75833	−	15.1699i	0.470172	−	0.814361i	−0.529246	−	0.848468i	$-0.677525\pi$
$347$	8.75833	−	15.1699i	0.470172	−	0.814361i	0.999418	+	0.0341067i	$0.0108586\pi$
$348$		0			0
$349$	−10.7321	+	6.19615i	−0.574474	+	0.331672i	−0.758934	−	0.651167i	$-0.774280\pi$
$349$	−10.7321	+	6.19615i	−0.574474	+	0.331672i	0.184461	+	0.982840i	$0.440946\pi$
$350$		0			0
$351$	2.59808	+	2.50000i	0.138675	+	0.133440i
$352$		0			0
$353$	−15.1865	+	8.76795i	−0.808298	+	0.466671i	−0.846364	−	0.532604i	$-0.821213\pi$
$353$	−15.1865	+	8.76795i	−0.808298	+	0.466671i	0.0380667	+	0.999275i	$0.487880\pi$
$354$		0			0
$355$	1.90192	−	3.29423i	0.100944	−	0.174840i
$356$		0			0
$357$	−0.633975	−	0.366025i	−0.0335535	−	0.0193721i
$358$		0			0
$359$			25.5167i			1.34672i	0.739316	+	0.673359i	$0.235149\pi$
$359$			25.5167i			1.34672i	−0.739316	+	0.673359i	$0.764851\pi$
$360$		0			0
$361$	1.69615	+	2.93782i	0.0892712	+	0.154622i
$362$		0			0
$363$	−3.53590			−0.185587
$364$		0			0
$365$	15.9282			0.833720
$366$		0			0
$367$	0.562178	+	0.973721i	0.0293454	+	0.0508278i	0.880325	−	0.474371i	$-0.157324\pi$
$367$	0.562178	+	0.973721i	0.0293454	+	0.0508278i	−0.850980	+	0.525199i	$0.823991\pi$
$368$		0			0
$369$			5.00000i			0.260290i
$370$		0			0
$371$	−18.7583	−	10.8301i	−0.973884	−	0.562272i
$372$		0			0
$373$	16.3301	−	28.2846i	0.845542	−	1.46452i	−0.0396078	−	0.999215i	$-0.512611\pi$
$373$	16.3301	−	28.2846i	0.845542	−	1.46452i	0.885150	−	0.465306i	$-0.154056\pi$
$374$		0			0
$375$	−10.5000	+	6.06218i	−0.542218	+	0.313050i
$376$		0			0
$377$	−6.86603	+	27.7487i	−0.353618	+	1.42913i
$378$		0			0
$379$	13.5167	−	7.80385i	0.694304	−	0.400857i	−0.110918	−	0.993830i	$-0.535379\pi$
$379$	13.5167	−	7.80385i	0.694304	−	0.400857i	0.805222	+	0.592973i	$0.202046\pi$
$380$		0			0
$381$	−2.00000	+	3.46410i	−0.102463	+	0.177471i
$382$		0			0
$383$	0.588457	+	0.339746i	0.0300688	+	0.0173602i	0.514959	−	0.857215i	$-0.327807\pi$
$383$	0.588457	+	0.339746i	0.0300688	+	0.0173602i	−0.484890	+	0.874575i	$0.661140\pi$
$384$		0			0
$385$		−	12.9282i		−	0.658882i
$386$		0			0
$387$	6.09808	+	10.5622i	0.309983	+	0.536906i
$388$		0			0
$389$	−17.5359			−0.889105			−0.444553	−	0.895753i	$-0.646637\pi$
$389$	−17.5359			−0.889105			−0.444553	+	0.895753i	$0.646637\pi$
$390$		0			0
$391$	−2.19615			−0.111064
$392$		0			0
$393$	−7.66025	−	13.2679i	−0.386409	−	0.669280i
$394$		0			0
$395$		−	14.5359i		−	0.731380i
$396$		0			0
$397$	15.1244	+	8.73205i	0.759070	+	0.438249i	0.828962	−	0.559305i	$-0.188932\pi$
$397$	15.1244	+	8.73205i	0.759070	+	0.438249i	−0.0698920	+	0.997555i	$0.522265\pi$
$398$		0			0
$399$	−6.46410	+	11.1962i	−0.323610	+	0.560509i
$400$		0			0
$401$	−19.4545	+	11.2321i	−0.971511	+	0.560902i	−0.899696	−	0.436516i	$-0.856212\pi$
$401$	−19.4545	+	11.2321i	−0.971511	+	0.560902i	−0.0718141	+	0.997418i	$0.522879\pi$
$402$		0			0
$403$	−3.66025	+	3.80385i	−0.182330	+	0.189483i
$404$		0			0
$405$	1.50000	−	0.866025i	0.0745356	−	0.0430331i
$406$		0			0
$407$	2.09808	−	3.63397i	0.103998	−	0.180129i
$408$		0			0
$409$	−28.7487	−	16.5981i	−1.42153	−	0.820722i	−0.425102	−	0.905145i	$-0.639762\pi$
$409$	−28.7487	−	16.5981i	−1.42153	−	0.820722i	−0.996430	+	0.0844233i	$0.973095\pi$
$410$		0			0
$411$			5.53590i			0.273066i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	2.87564			0.141160
$416$		0			0
$417$	−20.0000			−0.979404
$418$		0			0
$419$	5.80385	+	10.0526i	0.283537	+	0.491100i	0.972253	−	0.233931i	$-0.0751590\pi$
$419$	5.80385	+	10.0526i	0.283537	+	0.491100i	−0.688717	+	0.725031i	$0.741826\pi$
$420$		0			0
$421$		−	5.00000i		−	0.243685i	−0.992549	−	0.121843i	$-0.961120\pi$
$421$		−	5.00000i		−	0.243685i	0.992549	−	0.121843i	$-0.0388803\pi$
$422$		0			0
$423$	−2.83013	−	1.63397i	−0.137605	−	0.0794466i
$424$		0			0
$425$	−0.267949	+	0.464102i	−0.0129974	+	0.0225122i
$426$		0			0
$427$	14.8301	−	8.56218i	0.717680	−	0.414353i
$428$		0			0
$429$	2.73205	+	9.46410i	0.131905	+	0.456931i
$430$		0			0
$431$	−24.2942	+	14.0263i	−1.17021	+	0.675622i	−0.953730	−	0.300665i	$-0.902792\pi$
$431$	−24.2942	+	14.0263i	−1.17021	+	0.675622i	−0.216482	+	0.976287i	$0.569458\pi$
$432$		0			0
$433$	−1.57180	+	2.72243i	−0.0755357	+	0.130832i	−0.901319	−	0.433156i	$-0.857400\pi$
$433$	−1.57180	+	2.72243i	−0.0755357	+	0.130832i	0.825783	+	0.563987i	$0.190733\pi$
$434$		0			0
$435$	11.8923	+	6.86603i	0.570192	+	0.329201i
$436$		0			0
$437$			38.7846i			1.85532i
$438$		0			0
$439$	4.90192	+	8.49038i	0.233956	+	0.405224i	0.958969	−	0.283512i	$-0.0914995\pi$
$439$	4.90192	+	8.49038i	0.233956	+	0.405224i	−0.725013	+	0.688735i	$0.758166\pi$
$440$		0			0
$441$	−0.464102			−0.0221001
$442$		0			0
$443$	19.3205			0.917945			0.458973	−	0.888450i	$-0.348218\pi$
$443$	19.3205			0.917945			0.458973	+	0.888450i	$0.348218\pi$
$444$		0			0
$445$	8.19615	+	14.1962i	0.388535	+	0.672962i
$446$		0			0
$447$			21.5885i			1.02110i
$448$		0			0
$449$	2.87564	+	1.66025i	0.135710	+	0.0783522i	0.566318	−	0.824187i	$-0.308367\pi$
$449$	2.87564	+	1.66025i	0.135710	+	0.0783522i	−0.430608	+	0.902539i	$0.641701\pi$
$450$		0			0
$451$	−6.83013	+	11.8301i	−0.321618	+	0.557059i
$452$		0			0
$453$	14.9545	−	8.63397i	0.702623	−	0.405660i
$454$		0			0
$455$	16.3923	−	4.73205i	0.768483	−	0.221842i
$456$		0			0
$457$	34.1603	−	19.7224i	1.59795	−	0.922576i	0.606067	−	0.795413i	$-0.292746\pi$
$457$	34.1603	−	19.7224i	1.59795	−	0.922576i	0.991882	−	0.127163i	$-0.0405872\pi$
$458$		0			0
$459$	0.133975	−	0.232051i	0.00625340	−	0.0108312i
$460$		0			0
$461$	29.0885	+	16.7942i	1.35478	+	0.782185i	0.988915	−	0.148481i	$-0.0474384\pi$
$461$	29.0885	+	16.7942i	1.35478	+	0.782185i	0.365869	+	0.930666i	$0.380772\pi$
$462$		0			0
$463$			6.33975i			0.294633i	0.989089	+	0.147316i	$0.0470636\pi$
$463$			6.33975i			0.294633i	−0.989089	+	0.147316i	$0.952936\pi$
$464$		0			0
$465$	1.26795	+	2.19615i	0.0587997	+	0.101844i
$466$		0			0
$467$	−11.6603			−0.539572			−0.269786	−	0.962920i	$-0.586953\pi$
$467$	−11.6603			−0.539572			−0.269786	+	0.962920i	$0.586953\pi$
$468$		0			0
$469$	23.8564			1.10159
$470$		0			0
$471$	−11.5263	−	19.9641i	−0.531103	−	0.919897i
$472$		0			0
$473$			33.3205i			1.53208i
$474$		0			0
$475$	8.19615	+	4.73205i	0.376065	+	0.217121i
$476$		0			0
$477$	3.96410	−	6.86603i	0.181504	−	0.314374i
$478$		0			0
$479$	1.26795	−	0.732051i	0.0579341	−	0.0334483i	−0.470753	−	0.882265i	$-0.656018\pi$
$479$	1.26795	−	0.732051i	0.0579341	−	0.0334483i	0.528687	+	0.848817i	$0.322684\pi$
$480$		0			0
$481$	5.37564	+	1.33013i	0.245108	+	0.0606486i
$482$		0			0
$483$	−19.3923	+	11.1962i	−0.882380	+	0.509443i
$484$		0			0
$485$	−8.66025	+	15.0000i	−0.393242	+	0.681115i
$486$		0			0
$487$	0.509619	+	0.294229i	0.0230930	+	0.0133328i	0.511502	−	0.859282i	$-0.329089\pi$
$487$	0.509619	+	0.294229i	0.0230930	+	0.0133328i	−0.488409	+	0.872615i	$0.662423\pi$
$488$		0			0
$489$			13.4641i			0.608868i
$490$		0			0
$491$	−12.9545	−	22.4378i	−0.584628	−	1.01260i	−0.994922	−	0.100651i	$-0.967907\pi$
$491$	−12.9545	−	22.4378i	−0.584628	−	1.01260i	0.410294	−	0.911953i	$-0.365426\pi$
$492$		0			0
$493$	2.12436			0.0956762
$494$		0			0
$495$	4.73205			0.212690
$496$		0			0
$497$	−3.00000	−	5.19615i	−0.134568	−	0.233079i
$498$		0			0
$499$			13.8564i			0.620298i	0.950688	+	0.310149i	$0.100379\pi$
$499$			13.8564i			0.620298i	−0.950688	+	0.310149i	$0.899621\pi$
$500$		0			0
$501$	−1.26795	−	0.732051i	−0.0566478	−	0.0327056i
$502$		0			0
$503$	−4.63397	+	8.02628i	−0.206619	+	0.357874i	−0.950647	−	0.310274i	$-0.899579\pi$
$503$	−4.63397	+	8.02628i	−0.206619	+	0.357874i	0.744029	+	0.668148i	$0.232913\pi$
$504$		0			0
$505$	11.3038	−	6.52628i	0.503015	−	0.290416i
$506$		0			0
$507$	−11.0000	+	6.92820i	−0.488527	+	0.307692i
$508$		0			0
$509$	25.6244	−	14.7942i	1.13578	−	0.655743i	0.190398	−	0.981707i	$-0.439022\pi$
$509$	25.6244	−	14.7942i	1.13578	−	0.655743i	0.945382	+	0.325964i	$0.105689\pi$
$510$		0			0
$511$	12.5622	−	21.7583i	0.555718	−	0.962532i
$512$		0			0
$513$	−4.09808	−	2.36603i	−0.180934	−	0.104463i
$514$		0			0
$515$		−	1.26795i		−	0.0558725i
$516$		0			0
$517$	−4.46410	−	7.73205i	−0.196331	−	0.340055i
$518$		0			0
$519$	17.4641			0.766589
$520$		0			0
$521$	19.9808			0.875373			0.437687	−	0.899128i	$-0.355798\pi$
$521$	19.9808			0.875373			0.437687	+	0.899128i	$0.355798\pi$
$522$		0			0
$523$	4.29423	+	7.43782i	0.187774	+	0.325233i	0.944508	−	0.328490i	$-0.106540\pi$
$523$	4.29423	+	7.43782i	0.187774	+	0.325233i	−0.756734	+	0.653723i	$0.773206\pi$
$524$		0			0
$525$			5.46410i			0.238473i
$526$		0			0
$527$	0.339746	+	0.196152i	0.0147996	+	0.00854453i
$528$		0			0
$529$	−22.0885	+	38.2583i	−0.960368	+	1.66341i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−17.5000	−	4.33013i	−0.758009	−	0.187559i
$534$		0			0
$535$	13.6865	−	7.90192i	0.591720	−	0.341630i
$536$		0			0
$537$	−10.3660	+	17.9545i	−0.447327	+	0.774793i
$538$		0			0
$539$	−1.09808	−	0.633975i	−0.0472975	−	0.0273072i
$540$		0			0
$541$			17.3923i			0.747754i	0.927478	+	0.373877i	$0.121972\pi$
$541$			17.3923i			0.747754i	−0.927478	+	0.373877i	$0.878028\pi$
$542$		0			0
$543$	−9.59808	−	16.6244i	−0.411893	−	0.713419i
$544$		0			0
$545$	−35.3205			−1.51296
$546$		0			0
$547$	−2.05256			−0.0877611			−0.0438805	−	0.999037i	$-0.513972\pi$
$547$	−2.05256			−0.0877611			−0.0438805	+	0.999037i	$0.513972\pi$
$548$		0			0
$549$	3.13397	+	5.42820i	0.133755	+	0.231670i
$550$		0			0
$551$		−	37.5167i		−	1.59826i
$552$		0			0
$553$	−19.8564	−	11.4641i	−0.844380	−	0.487503i
$554$		0			0
$555$	1.33013	−	2.30385i	0.0564607	−	0.0977929i
$556$		0			0
$557$	0.356406	−	0.205771i	0.0151014	−	0.00871881i	−0.492430	−	0.870352i	$-0.663891\pi$
$557$	0.356406	−	0.205771i	0.0151014	−	0.00871881i	0.507532	+	0.861633i	$0.330558\pi$
$558$		0			0
$559$	−42.2487	+	12.1962i	−1.78693	+	0.515842i
$560$		0			0
$561$	0.633975	−	0.366025i	0.0267664	−	0.0154536i
$562$		0			0
$563$	−9.46410	+	16.3923i	−0.398864	+	0.690853i	−0.993586	−	0.113078i	$-0.963929\pi$
$563$	−9.46410	+	16.3923i	−0.398864	+	0.690853i	0.594722	+	0.803932i	$0.297262\pi$
$564$		0			0
$565$	18.9904	+	10.9641i	0.798931	+	0.461263i
$566$		0			0
$567$		−	2.73205i		−	0.114735i
$568$		0			0
$569$	−8.00000	−	13.8564i	−0.335377	−	0.580891i	0.648180	−	0.761487i	$-0.275531\pi$
$569$	−8.00000	−	13.8564i	−0.335377	−	0.580891i	−0.983557	+	0.180597i	$0.942197\pi$
$570$		0			0
$571$	13.6603			0.571664			0.285832	−	0.958280i	$-0.407730\pi$
$571$	13.6603			0.571664			0.285832	+	0.958280i	$0.407730\pi$
$572$		0			0
$573$	14.9282			0.623635
$574$		0			0
$575$	8.19615	+	14.1962i	0.341803	+	0.592020i
$576$		0			0
$577$		−	25.5885i		−	1.06526i	−0.846348	−	0.532631i	$-0.821203\pi$
$577$		−	25.5885i		−	1.06526i	0.846348	−	0.532631i	$-0.178797\pi$
$578$		0			0
$579$	−10.1603	−	5.86603i	−0.422246	−	0.243784i
$580$		0			0
$581$	2.26795	−	3.92820i	0.0940904	−	0.162969i
$582$		0			0
$583$	18.7583	−	10.8301i	0.776891	−	0.448538i
$584$		0			0
$585$	1.73205	+	6.00000i	0.0716115	+	0.248069i
$586$		0			0
$587$	−25.8564	+	14.9282i	−1.06721	+	0.616153i	−0.927417	−	0.374028i	$-0.877976\pi$
$587$	−25.8564	+	14.9282i	−1.06721	+	0.616153i	−0.139791	+	0.990181i	$0.544643\pi$
$588$		0			0
$589$	3.46410	−	6.00000i	0.142736	−	0.247226i
$590$		0			0
$591$	−0.928203	−	0.535898i	−0.0381812	−	0.0220439i
$592$		0			0
$593$		−	28.1769i		−	1.15709i	−0.815651	−	0.578544i	$-0.803621\pi$
$593$		−	28.1769i		−	1.15709i	0.815651	−	0.578544i	$-0.196379\pi$
$594$		0			0
$595$	−0.633975	−	1.09808i	−0.0259904	−	0.0450167i
$596$		0			0
$597$	−0.339746			−0.0139049
$598$		0			0
$599$	−26.5359			−1.08423			−0.542114	−	0.840305i	$-0.682376\pi$
$599$	−26.5359			−1.08423			−0.542114	+	0.840305i	$0.682376\pi$
$600$		0			0
$601$	20.8205	+	36.0622i	0.849286	+	1.47101i	0.881846	+	0.471537i	$0.156301\pi$
$601$	20.8205	+	36.0622i	0.849286	+	1.47101i	−0.0325600	+	0.999470i	$0.510366\pi$
$602$		0			0
$603$			8.73205i			0.355597i
$604$		0			0
$605$	−5.30385	−	3.06218i	−0.215632	−	0.124495i
$606$		0			0
$607$	−0.392305	+	0.679492i	−0.0159232	+	0.0275797i	−0.873877	−	0.486147i	$-0.838402\pi$
$607$	−0.392305	+	0.679492i	−0.0159232	+	0.0275797i	0.857954	+	0.513726i	$0.171735\pi$
$608$		0			0
$609$	18.7583	−	10.8301i	0.760126	−	0.438859i
$610$		0			0
$611$	8.16987	−	8.49038i	0.330518	−	0.343484i
$612$		0			0
$613$	31.4545	−	18.1603i	1.27043	−	0.733486i	0.295365	−	0.955385i	$-0.404559\pi$
$613$	31.4545	−	18.1603i	1.27043	−	0.733486i	0.975070	+	0.221899i	$0.0712255\pi$
$614$		0			0
$615$	−4.33013	+	7.50000i	−0.174608	+	0.302429i
$616$		0			0
$617$	32.7224	+	18.8923i	1.31736	+	0.760576i	0.983302	−	0.181979i	$-0.0582502\pi$
$617$	32.7224	+	18.8923i	1.31736	+	0.760576i	0.334053	+	0.942554i	$0.391584\pi$
$618$		0			0
$619$		−	44.3923i		−	1.78428i	−0.451762	−	0.892139i	$-0.649204\pi$
$619$		−	44.3923i		−	1.78428i	0.451762	−	0.892139i	$-0.350796\pi$
$620$		0			0
$621$	−4.09808	−	7.09808i	−0.164450	−	0.284836i
$622$		0			0
$623$	25.8564			1.03592
$624$		0			0
$625$	−11.0000			−0.440000
$626$		0			0
$627$	−6.46410	−	11.1962i	−0.258151	−	0.447131i
$628$		0			0
$629$		−	0.411543i		−	0.0164093i
$630$		0			0
$631$	−29.3205	−	16.9282i	−1.16723	−	0.673901i	−0.214205	−	0.976789i	$-0.568716\pi$
$631$	−29.3205	−	16.9282i	−1.16723	−	0.673901i	−0.953026	+	0.302888i	$0.902049\pi$
$632$		0			0
$633$	−5.66025	+	9.80385i	−0.224975	+	0.389668i
$634$		0			0
$635$	−6.00000	+	3.46410i	−0.238103	+	0.137469i
$636$		0			0
$637$	0.401924	−	1.62436i	0.0159248	−	0.0643593i
$638$		0			0
$639$	1.90192	−	1.09808i	0.0752389	−	0.0434392i
$640$		0			0
$641$	−6.25833	+	10.8397i	−0.247189	+	0.428144i	−0.962745	−	0.270412i	$-0.912840\pi$
$641$	−6.25833	+	10.8397i	−0.247189	+	0.428144i	0.715556	+	0.698556i	$0.246174\pi$
$642$		0			0
$643$	−24.0000	−	13.8564i	−0.946468	−	0.546443i	−0.0544858	−	0.998515i	$-0.517352\pi$
$643$	−24.0000	−	13.8564i	−0.946468	−	0.546443i	−0.891982	+	0.452071i	$0.850685\pi$
$644$		0			0
$645$			21.1244i			0.831771i
$646$		0			0
$647$	−7.12436	−	12.3397i	−0.280087	−	0.485125i	0.691319	−	0.722550i	$-0.257030\pi$
$647$	−7.12436	−	12.3397i	−0.280087	−	0.485125i	−0.971406	+	0.237425i	$0.923697\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	4.00000			0.156772
$652$		0			0
$653$	−16.7321	−	28.9808i	−0.654776	−	1.13410i	−0.981950	−	0.189141i	$-0.939430\pi$
$653$	−16.7321	−	28.9808i	−0.654776	−	1.13410i	0.327174	−	0.944964i	$-0.393904\pi$
$654$		0			0
$655$		−	26.5359i		−	1.03684i
$656$		0			0
$657$	7.96410	+	4.59808i	0.310709	+	0.179388i
$658$		0			0
$659$	4.33975	−	7.51666i	0.169053	−	0.292808i	−0.769034	−	0.639207i	$-0.779263\pi$
$659$	4.33975	−	7.51666i	0.169053	−	0.292808i	0.938087	+	0.346400i	$0.112596\pi$
$660$		0			0
$661$	−4.66987	+	2.69615i	−0.181637	+	0.104868i	−0.588062	−	0.808816i	$-0.700109\pi$
$661$	−4.66987	+	2.69615i	−0.181637	+	0.104868i	0.406425	+	0.913684i	$0.366775\pi$
$662$		0			0
$663$	0.696152	+	0.669873i	0.0270363	+	0.0260157i
$664$		0			0
$665$	−19.3923	+	11.1962i	−0.752001	+	0.434168i
$666$		0			0
$667$	32.4904	−	56.2750i	1.25803	−	2.17898i
$668$		0			0
$669$	−14.5359	−	8.39230i	−0.561990	−	0.324465i
$670$		0			0
$671$			17.1244i			0.661078i
$672$		0			0
$673$	−23.8923	−	41.3827i	−0.920981	−	1.59519i	−0.797901	−	0.602789i	$-0.794056\pi$
$673$	−23.8923	−	41.3827i	−0.920981	−	1.59519i	−0.123080	−	0.992397i	$-0.539277\pi$
$674$		0			0
$675$	−2.00000			−0.0769800
$676$		0			0
$677$	21.4641			0.824932			0.412466	−	0.910973i	$-0.364667\pi$
$677$	21.4641			0.824932			0.412466	+	0.910973i	$0.364667\pi$
$678$		0			0
$679$	13.6603	+	23.6603i	0.524232	+	0.907997i
$680$		0			0
$681$		−	22.0526i		−	0.845056i
$682$		0			0
$683$	−32.7846	−	18.9282i	−1.25447	−	0.724268i	−0.282475	−	0.959275i	$-0.591155\pi$
$683$	−32.7846	−	18.9282i	−1.25447	−	0.724268i	−0.971994	+	0.235007i	$0.924489\pi$
$684$		0			0
$685$	−4.79423	+	8.30385i	−0.183178	+	0.317274i
$686$		0			0
$687$	0.124356	−	0.0717968i	0.00474446	−	0.00273922i
$688$		0			0
$689$	20.5981	+	19.8205i	0.784724	+	0.755101i
$690$		0			0
$691$	−23.9545	+	13.8301i	−0.911271	+	0.526123i	−0.880840	−	0.473414i	$-0.843021\pi$
$691$	−23.9545	+	13.8301i	−0.911271	+	0.526123i	−0.0304314	+	0.999537i	$0.509688\pi$
$692$		0			0
$693$	3.73205	−	6.46410i	0.141769	−	0.245551i
$694$		0			0
$695$	−30.0000	−	17.3205i	−1.13796	−	0.657004i
$696$		0			0
$697$			1.33975i			0.0507465i
$698$		0			0
$699$	1.00000	+	1.73205i	0.0378235	+	0.0655122i
$700$		0			0
$701$	44.1051			1.66583			0.832914	−	0.553403i	$-0.186671\pi$
$701$	44.1051			1.66583			0.832914	+	0.553403i	$0.186671\pi$
$702$		0			0
$703$	−7.26795			−0.274116
$704$		0			0
$705$	−2.83013	−	4.90192i	−0.106589	−	0.184617i
$706$		0			0
$707$		−	20.5885i		−	0.774309i
$708$		0			0
$709$	6.18653	+	3.57180i	0.232340	+	0.134142i	0.611651	−	0.791128i	$-0.290506\pi$
$709$	6.18653	+	3.57180i	0.232340	+	0.134142i	−0.379311	+	0.925269i	$0.623839\pi$
$710$		0			0
$711$	4.19615	−	7.26795i	0.157368	−	0.272569i
$712$		0			0
$713$	10.3923	−	6.00000i	0.389195	−	0.224702i
$714$		0			0
$715$	−4.09808	+	16.5622i	−0.153259	+	0.619390i
$716$		0			0
$717$	−20.1506	+	11.6340i	−0.752539	+	0.434479i
$718$		0			0
$719$	−12.5885	+	21.8038i	−0.469470	+	0.813146i	−0.999391	−	0.0349010i	$-0.988888\pi$
$719$	−12.5885	+	21.8038i	−0.469470	+	0.813146i	0.529921	+	0.848047i	$0.322222\pi$
$720$		0			0
$721$	−1.73205	−	1.00000i	−0.0645049	−	0.0372419i
$722$		0			0
$723$			5.33975i			0.198587i
$724$		0			0
$725$	−7.92820	−	13.7321i	−0.294446	−	0.509996i
$726$		0			0
$727$	−4.73205			−0.175502			−0.0877510	−	0.996142i	$-0.527968\pi$
$727$	−4.73205			−0.175502			−0.0877510	+	0.996142i	$0.527968\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	1.63397	+	2.83013i	0.0604347	+	0.104676i
$732$		0			0
$733$		−	35.0000i		−	1.29275i	−0.763018	−	0.646377i	$-0.776283\pi$
$733$		−	35.0000i		−	1.29275i	0.763018	−	0.646377i	$-0.223717\pi$
$734$		0			0
$735$	−0.696152	−	0.401924i	−0.0256780	−	0.0148252i
$736$		0			0
$737$	−11.9282	+	20.6603i	−0.439381	+	0.761030i
$738$		0			0
$739$	−14.5359	+	8.39230i	−0.534712	+	0.308716i	−0.742933	−	0.669366i	$-0.766566\pi$
$739$	−14.5359	+	8.39230i	−0.534712	+	0.308716i	0.208221	+	0.978082i	$0.433233\pi$
$740$		0			0
$741$	11.8301	−	12.2942i	0.434591	−	0.451640i
$742$		0			0
$743$	38.1962	−	22.0526i	1.40128	−	0.809030i	0.406757	−	0.913537i	$-0.366660\pi$
$743$	38.1962	−	22.0526i	1.40128	−	0.809030i	0.994524	+	0.104507i	$0.0333263\pi$
$744$		0			0
$745$	−18.6962	+	32.3827i	−0.684974	+	1.18641i
$746$		0			0
$747$	1.43782	+	0.830127i	0.0526072	+	0.0303728i
$748$		0			0
$749$		−	24.9282i		−	0.910857i
$750$		0			0
$751$	7.83013	+	13.5622i	0.285725	+	0.494891i	0.972785	−	0.231710i	$-0.0744321\pi$
$751$	7.83013	+	13.5622i	0.285725	+	0.494891i	−0.687059	+	0.726601i	$0.741099\pi$
$752$		0			0
$753$	−2.53590			−0.0924133
$754$		0			0
$755$	29.9090			1.08850
$756$		0			0
$757$	3.39230	+	5.87564i	0.123295	+	0.213554i	0.921065	−	0.389408i	$-0.127320\pi$
$757$	3.39230	+	5.87564i	0.123295	+	0.213554i	−0.797770	+	0.602962i	$0.793987\pi$
$758$		0			0
$759$		−	22.3923i		−	0.812789i
$760$		0			0
$761$	−2.19615	−	1.26795i	−0.0796105	−	0.0459631i	0.459666	−	0.888092i	$-0.347969\pi$
$761$	−2.19615	−	1.26795i	−0.0796105	−	0.0459631i	−0.539277	+	0.842129i	$0.681302\pi$
$762$		0			0
$763$	−27.8564	+	48.2487i	−1.00847	+	1.74672i
$764$		0			0
$765$	0.401924	−	0.232051i	0.0145316	−	0.00838981i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−37.7321	+	21.7846i	−1.36065	+	0.785573i	−0.989711	−	0.143083i	$-0.954298\pi$
$769$	−37.7321	+	21.7846i	−1.36065	+	0.785573i	−0.370942	+	0.928656i	$0.620965\pi$
$770$		0			0
$771$	7.13397	−	12.3564i	0.256924	−	0.445005i
$772$		0			0
$773$	−4.51666	−	2.60770i	−0.162453	−	0.0937923i	0.416569	−	0.909104i	$-0.363232\pi$
$773$	−4.51666	−	2.60770i	−0.162453	−	0.0937923i	−0.579022	+	0.815312i	$0.696566\pi$
$774$		0			0
$775$		−	2.92820i		−	0.105184i
$776$		0			0
$777$	−2.09808	−	3.63397i	−0.0752681	−	0.130368i
$778$		0			0
$779$	23.6603			0.847717
$780$		0			0
$781$	6.00000			0.214697
$782$		0			0
$783$	3.96410	+	6.86603i	0.141665	+	0.245372i
$784$		0			0
$785$		−	39.9282i		−	1.42510i
$786$		0			0
$787$	37.5167	+	21.6603i	1.33732	+	0.772105i	0.986410	−	0.164303i	$-0.0525374\pi$
$787$	37.5167	+	21.6603i	1.33732	+	0.772105i	0.350915	+	0.936407i	$0.385871\pi$
$788$		0			0
$789$	14.8301	−	25.6865i	0.527967	−	0.914465i
$790$		0			0
$791$	29.9545	−	17.2942i	1.06506	−	0.614912i
$792$		0			0
$793$	−21.7128	+	6.26795i	−0.771045	+	0.222581i
$794$		0			0
$795$	11.8923	−	6.86603i	0.421777	−	0.243513i
$796$		0			0
$797$	3.00000	−	5.19615i	0.106265	−	0.184057i	−0.807989	−	0.589197i	$-0.799444\pi$
$797$	3.00000	−	5.19615i	0.106265	−	0.184057i	0.914255	+	0.405140i	$0.132777\pi$
$798$		0			0
$799$	−0.758330	−	0.437822i	−0.0268278	−	0.0154890i
$800$		0			0
$801$			9.46410i			0.334398i
$802$		0			0
$803$	12.5622	+	21.7583i	0.443310	+	0.767835i
$804$		0			0
$805$	−38.7846			−1.36698
$806$		0			0
$807$	−2.53590			−0.0892679
$808$		0			0
$809$	−2.86603	−	4.96410i	−0.100764	−	0.174529i	0.811236	−	0.584719i	$-0.198795\pi$
$809$	−2.86603	−	4.96410i	−0.100764	−	0.174529i	−0.912000	+	0.410191i	$0.865462\pi$
$810$		0			0
$811$		−	1.75129i		−	0.0614961i	−0.999527	−	0.0307480i	$-0.990211\pi$
$811$		−	1.75129i		−	0.0614961i	0.999527	−	0.0307480i	$-0.00978895\pi$
$812$		0			0
$813$	−13.8564	−	8.00000i	−0.485965	−	0.280572i
$814$		0			0
$815$	−11.6603	+	20.1962i	−0.408441	+	0.707440i
$816$		0			0
$817$	49.9808	−	28.8564i	1.74861	−	1.00956i
$818$		0			0
$819$	9.56218	+	2.36603i	0.334130	+	0.0826756i
$820$		0			0
$821$	−13.0526	+	7.53590i	−0.455537	+	0.263005i	−0.710166	−	0.704034i	$-0.751380\pi$
$821$	−13.0526	+	7.53590i	−0.455537	+	0.263005i	0.254629	+	0.967039i	$0.418047\pi$
$822$		0			0
$823$	−12.0000	+	20.7846i	−0.418294	+	0.724506i	−0.995768	−	0.0919029i	$-0.970705\pi$
$823$	−12.0000	+	20.7846i	−0.418294	+	0.724506i	0.577474	+	0.816409i	$0.304038\pi$
$824$		0			0
$825$	−4.73205	−	2.73205i	−0.164749	−	0.0951178i
$826$		0			0
$827$			56.3923i			1.96095i	0.196637	+	0.980476i	$0.436998\pi$
$827$			56.3923i			1.96095i	−0.196637	+	0.980476i	$0.563002\pi$
$828$		0			0
$829$	12.8660	+	22.2846i	0.446856	+	0.773976i	0.998179	−	0.0603148i	$-0.0192105\pi$
$829$	12.8660	+	22.2846i	0.446856	+	0.773976i	−0.551324	+	0.834291i	$0.685877\pi$
$830$		0			0
$831$	16.1244			0.559348
$832$		0			0
$833$	−0.124356			−0.00430867
$834$		0			0
$835$	−1.26795	−	2.19615i	−0.0438792	−	0.0760010i
$836$		0			0
$837$			1.46410i			0.0506068i
$838$		0			0
$839$	15.4641	+	8.92820i	0.533880	+	0.308236i	0.742595	−	0.669741i	$-0.233595\pi$
$839$	15.4641	+	8.92820i	0.533880	+	0.308236i	−0.208715	+	0.977977i	$0.566928\pi$
$840$		0			0
$841$	−16.9282	+	29.3205i	−0.583731	+	1.01105i
$842$		0			0
$843$	26.5981	−	15.3564i	0.916086	−	0.528903i
$844$		0			0
$845$	−22.5000	+	0.866025i	−0.774024	+	0.0297922i
$846$		0			0
$847$	−8.36603	+	4.83013i	−0.287460	+	0.165965i
$848$		0			0
$849$	−11.7583	+	20.3660i	−0.403545	+	0.698960i
$850$		0			0
$851$	−10.9019	−	6.29423i	−0.373713	−	0.215763i
$852$		0			0
$853$			34.0333i			1.16528i	0.812731	+	0.582639i	$0.197980\pi$
$853$			34.0333i			1.16528i	−0.812731	+	0.582639i	$0.802020\pi$
$854$		0			0
$855$	−4.09808	−	7.09808i	−0.140151	−	0.242749i
$856$		0			0
$857$	34.5167			1.17907			0.589533	−	0.807744i	$-0.299312\pi$
$857$	34.5167			1.17907			0.589533	+	0.807744i	$0.299312\pi$
$858$		0			0
$859$	34.4449			1.17524			0.587622	−	0.809136i	$-0.300064\pi$
$859$	34.4449			1.17524			0.587622	+	0.809136i	$0.300064\pi$
$860$		0			0
$861$	6.83013	+	11.8301i	0.232770	+	0.403170i
$862$		0			0
$863$		−	27.6603i		−	0.941566i	−0.882249	−	0.470783i	$-0.843971\pi$
$863$		−	27.6603i		−	0.941566i	0.882249	−	0.470783i	$-0.156029\pi$
$864$		0			0
$865$	26.1962	+	15.1244i	0.890696	+	0.514244i
$866$		0			0
$867$	−8.46410	+	14.6603i	−0.287456	+	0.497888i
$868$		0			0
$869$	19.8564	−	11.4641i	0.673582	−	0.388893i
$870$		0			0
$871$	−30.5622	−	7.56218i	−1.03556	−	0.256235i
$872$		0			0
$873$	−8.66025	+	5.00000i	−0.293105	+	0.169224i
$874$		0			0
$875$	−16.5622	+	28.6865i	−0.559904	+	0.969782i
$876$		0			0
$877$	−16.4545	−	9.50000i	−0.555628	−	0.320792i	0.195761	−	0.980652i	$-0.437282\pi$
$877$	−16.4545	−	9.50000i	−0.555628	−	0.320792i	−0.751389	+	0.659860i	$0.770616\pi$
$878$		0			0
$879$		−	22.1244i		−	0.746236i
$880$		0			0
$881$	−12.2583	−	21.2321i	−0.412994	−	0.715326i	0.582222	−	0.813030i	$-0.302183\pi$
$881$	−12.2583	−	21.2321i	−0.412994	−	0.715326i	−0.995216	+	0.0977040i	$0.968850\pi$
$882$		0			0
$883$	8.78461			0.295626			0.147813	−	0.989015i	$-0.452777\pi$
$883$	8.78461			0.295626			0.147813	+	0.989015i	$0.452777\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.9282	+	25.8564i	0.501240	+	0.868173i	0.999999	+	0.00143243i	$0.000455957\pi$
$887$	14.9282	+	25.8564i	0.501240	+	0.868173i	−0.498759	+	0.866741i	$0.666211\pi$
$888$		0			0
$889$			10.9282i			0.366520i
$890$		0			0
$891$	2.36603	+	1.36603i	0.0792648	+	0.0457636i
$892$		0			0
$893$	−7.73205	+	13.3923i	−0.258743	+	0.448156i
$894$		0			0
$895$	−31.0981	+	17.9545i	−1.03949	+	0.600152i
$896$		0			0
$897$	28.3923	−	8.19615i	0.947991	−	0.273662i
$898$		0			0
$899$	−10.0526	+	5.80385i	−0.335272	+	0.193569i
$900$		0			0
$901$	1.06218	−	1.83975i	0.0353863	−	0.0612908i
$902$		0			0
$903$	28.8564	+	16.6603i	0.960281	+	0.554419i
$904$		0			0
$905$		−	33.2487i		−	1.10522i
$906$		0			0
$907$	−25.5167	−	44.1962i	−0.847267	−	1.46751i	−0.883638	−	0.468171i	$-0.844913\pi$
$907$	−25.5167	−	44.1962i	−0.847267	−	1.46751i	0.0363712	−	0.999338i	$-0.488420\pi$
$908$		0			0
$909$	7.53590			0.249950
$910$		0			0
$911$	−2.53590			−0.0840181			−0.0420090	−	0.999117i	$-0.513376\pi$
$911$	−2.53590			−0.0840181			−0.0420090	+	0.999117i	$0.513376\pi$
$912$		0			0
$913$	2.26795	+	3.92820i	0.0750582	+	0.130005i
$914$		0			0
$915$			10.8564i			0.358902i
$916$		0			0
$917$	−36.2487	−	20.9282i	−1.19704	−	0.691110i
$918$		0			0
$919$	−6.19615	+	10.7321i	−0.204392	+	0.354018i	−0.949939	−	0.312436i	$-0.898855\pi$
$919$	−6.19615	+	10.7321i	−0.204392	+	0.354018i	0.745547	+	0.666453i	$0.232188\pi$
$920$		0			0
$921$	−6.29423	+	3.63397i	−0.207402	+	0.119744i
$922$		0			0
$923$	2.19615	+	7.60770i	0.0722872	+	0.250410i
$924$		0			0
$925$	−2.66025	+	1.53590i	−0.0874686	+	0.0505000i
$926$		0			0
$927$	0.366025	−	0.633975i	0.0120219	−	0.0208225i
$928$		0			0
$929$	−34.5788	−	19.9641i	−1.13449	−	0.655001i	−0.189433	−	0.981894i	$-0.560665\pi$
$929$	−34.5788	−	19.9641i	−1.13449	−	0.655001i	−0.945061	+	0.326893i	$0.893998\pi$
$930$		0			0
$931$			2.19615i			0.0719760i
$932$		0			0
$933$	10.8301	+	18.7583i	0.354562	+	0.614120i
$934$		0			0
$935$	1.26795			0.0414664
$936$		0			0
$937$	−19.6795			−0.642901			−0.321450	−	0.946926i	$-0.604170\pi$
$937$	−19.6795			−0.642901			−0.321450	+	0.946926i	$0.604170\pi$
$938$		0			0
$939$	−15.6603	−	27.1244i	−0.511053	−	0.885170i
$940$		0			0
$941$			26.7846i			0.873153i	0.899667	+	0.436577i	$0.143809\pi$
$941$			26.7846i			0.873153i	−0.899667	+	0.436577i	$0.856191\pi$
$942$		0			0
$943$	35.4904	+	20.4904i	1.15573	+	0.667259i
$944$		0			0
$945$	2.36603	−	4.09808i	0.0769668	−	0.133310i
$946$		0			0
$947$	23.3205	−	13.4641i	0.757815	−	0.437525i	−0.0706959	−	0.997498i	$-0.522522\pi$
$947$	23.3205	−	13.4641i	0.757815	−	0.437525i	0.828511	+	0.559973i	$0.189189\pi$
$948$		0			0
$949$	−22.9904	+	23.8923i	−0.746299	+	0.775577i
$950$		0			0
$951$	−0.696152	+	0.401924i	−0.0225743	+	0.0130333i
$952$		0			0
$953$	16.3923	−	28.3923i	0.530999	−	0.919717i	−0.468347	−	0.883545i	$-0.655150\pi$
$953$	16.3923	−	28.3923i	0.530999	−	0.919717i	0.999346	−	0.0361722i	$-0.0115165\pi$
$954$		0			0
$955$	22.3923	+	12.9282i	0.724598	+	0.418347i
$956$		0			0
$957$			21.6603i			0.700177i
$958$		0			0
$959$	7.56218	+	13.0981i	0.244195	+	0.422959i
$960$		0			0
$961$	28.8564			0.930852
$962$		0			0
$963$	9.12436			0.294028
$964$		0			0
$965$	−10.1603	−	17.5981i	−0.327070	−	0.566502i
$966$		0			0
$967$		−	2.73205i		−	0.0878568i	−0.999035	−	0.0439284i	$-0.986013\pi$
$967$		−	2.73205i		−	0.0878568i	0.999035	−	0.0439284i	$-0.0139873\pi$
$968$		0			0
$969$	−1.09808	−	0.633975i	−0.0352753	−	0.0203662i
$970$		0			0
$971$	−0.196152	+	0.339746i	−0.00629483	+	0.0109030i	−0.869156	−	0.494539i	$-0.835337\pi$
$971$	−0.196152	+	0.339746i	−0.00629483	+	0.0109030i	0.862861	+	0.505442i	$0.168670\pi$
$972$		0			0
$973$	−47.3205	+	27.3205i	−1.51703	+	0.875855i
$974$		0			0
$975$	1.73205	−	7.00000i	0.0554700	−	0.224179i
$976$		0			0
$977$	−42.4019	+	24.4808i	−1.35656	+	0.783209i	−0.989158	−	0.146854i	$-0.953085\pi$
$977$	−42.4019	+	24.4808i	−1.35656	+	0.783209i	−0.367400	+	0.930063i	$0.619752\pi$
$978$		0			0
$979$	−12.9282	+	22.3923i	−0.413187	+	0.715661i
$980$		0			0
$981$	−17.6603	−	10.1962i	−0.563849	−	0.325538i
$982$		0			0
$983$			42.6410i			1.36004i	0.733195	+	0.680019i	$0.238028\pi$
$983$			42.6410i			1.36004i	−0.733195	+	0.680019i	$0.761972\pi$
$984$		0			0
$985$	−0.928203	−	1.60770i	−0.0295750	−	0.0512254i
$986$		0			0
$987$	−8.92820			−0.284188
$988$		0			0
$989$	99.9615			3.17859
$990$		0			0
$991$	18.5622	+	32.1506i	0.589647	+	1.02130i	0.994279	+	0.106819i	$0.0340665\pi$
$991$	18.5622	+	32.1506i	0.589647	+	1.02130i	−0.404631	+	0.914480i	$0.632600\pi$
$992$		0			0
$993$		−	12.0000i		−	0.380808i
$994$		0			0
$995$	−0.509619	−	0.294229i	−0.0161560	−	0.00932767i
$996$		0			0
$997$	−9.99038	+	17.3038i	−0.316399	+	0.548018i	−0.979734	−	0.200304i	$-0.935807\pi$
$997$	−9.99038	+	17.3038i	−0.316399	+	0.548018i	0.663335	+	0.748322i	$0.269140\pi$
$998$		0			0
$999$	1.33013	−	0.767949i	0.0420834	−	0.0242968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bf.a.49.2	✓	4
3.2	odd	2		936.2.bi.a.361.2		4
4.3	odd	2		624.2.bv.c.49.1		4
12.11	even	2		1872.2.by.g.1297.1		4
13.2	odd	12		4056.2.a.u.1.2		2
13.3	even	3		4056.2.c.k.337.3		4
13.4	even	6	inner	312.2.bf.a.121.2	yes	4
13.10	even	6		4056.2.c.k.337.2		4
13.11	odd	12		4056.2.a.t.1.1		2
39.17	odd	6		936.2.bi.a.433.2		4
52.11	even	12		8112.2.a.bw.1.1		2
52.15	even	12		8112.2.a.br.1.2		2
52.43	odd	6		624.2.bv.c.433.1		4
156.95	even	6		1872.2.by.g.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bf.a.49.2	✓	4	1.1	even	1	trivial
312.2.bf.a.121.2	yes	4	13.4	even	6	inner
624.2.bv.c.49.1		4	4.3	odd	2
624.2.bv.c.433.1		4	52.43	odd	6
936.2.bi.a.361.2		4	3.2	odd	2
936.2.bi.a.433.2		4	39.17	odd	6
1872.2.by.g.433.1		4	156.95	even	6
1872.2.by.g.1297.1		4	12.11	even	2
4056.2.a.t.1.1		2	13.11	odd	12
4056.2.a.u.1.2		2	13.2	odd	12
4056.2.c.k.337.2		4	13.10	even	6
4056.2.c.k.337.3		4	13.3	even	3
8112.2.a.br.1.2		2	52.15	even	12
8112.2.a.bw.1.1		2	52.11	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +1.73205i q^{5} +(2.36603 + 1.36603i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-2.36603 + 1.36603i) q^{11} +(-2.59808 - 2.50000i) q^{13} +(-1.50000 + 0.866025i) q^{15} +(-0.133975 + 0.232051i) q^{17} +(4.09808 + 2.36603i) q^{19} +2.73205i q^{21} +(4.09808 + 7.09808i) q^{23} +2.00000 q^{25} -1.00000 q^{27} +(-3.96410 - 6.86603i) q^{29} -1.46410i q^{31} +(-2.36603 - 1.36603i) q^{33} +(-2.36603 + 4.09808i) q^{35} +(-1.33013 + 0.767949i) q^{37} +(0.866025 - 3.50000i) q^{39} +(4.33013 - 2.50000i) q^{41} +(6.09808 - 10.5622i) q^{43} +(-1.50000 - 0.866025i) q^{45} +3.26795i q^{47} +(0.232051 + 0.401924i) q^{49} -0.267949 q^{51} -7.92820 q^{53} +(-2.36603 - 4.09808i) q^{55} +4.73205i q^{57} +(3.13397 - 5.42820i) q^{61} +(-2.36603 + 1.36603i) q^{63} +(4.33013 - 4.50000i) q^{65} +(7.56218 - 4.36603i) q^{67} +(-4.09808 + 7.09808i) q^{69} +(-1.90192 - 1.09808i) q^{71} -9.19615i q^{73} +(1.00000 + 1.73205i) q^{75} -7.46410 q^{77} -8.39230 q^{79} +(-0.500000 - 0.866025i) q^{81} -1.66025i q^{83} +(-0.401924 - 0.232051i) q^{85} +(3.96410 - 6.86603i) q^{87} +(8.19615 - 4.73205i) q^{89} +(-2.73205 - 9.46410i) q^{91} +(1.26795 - 0.732051i) q^{93} +(-4.09808 + 7.09808i) q^{95} +(8.66025 + 5.00000i) q^{97} -2.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 6 q^{7} - 2 q^{9} - 6 q^{11} - 6 q^{15} - 4 q^{17} + 6 q^{19} + 6 q^{23} + 8 q^{25} - 4 q^{27} - 2 q^{29} - 6 q^{33} - 6 q^{35} + 12 q^{37} + 14 q^{43} - 6 q^{45} - 6 q^{49} - 8 q^{51} - 4 q^{53}+ \cdots - 6 q^{95}+O(q^{100}) \) 4 * q + 2 * q^3 + 6 * q^7 - 2 * q^9 - 6 * q^11 - 6 * q^15 - 4 * q^17 + 6 * q^19 + 6 * q^23 + 8 * q^25 - 4 * q^27 - 2 * q^29 - 6 * q^33 - 6 * q^35 + 12 * q^37 + 14 * q^43 - 6 * q^45 - 6 * q^49 - 8 * q^51 - 4 * q^53 - 6 * q^55 + 16 * q^61 - 6 * q^63 + 6 * q^67 - 6 * q^69 - 18 * q^71 + 4 * q^75 - 16 * q^77 + 8 * q^79 - 2 * q^81 - 12 * q^85 + 2 * q^87 + 12 * q^89 - 4 * q^91 + 12 * q^93 - 6 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more