LMFDB - Embedded newform 1184.2.i.b.417.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1184,2,Mod(417,1184)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1184, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1184.417"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1184 = 2^{5} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1184.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,2,0,3,0,-2,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$9.45428759932$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			417.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1184.417
Dual form			1184.2.i.b.1025.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.73205i) q^{3} +(1.50000 + 2.59808i) q^{5} +(-1.00000 - 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +4.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +(-3.00000 + 5.19615i) q^{15} +(-3.50000 + 6.06218i) q^{17} +(2.00000 - 3.46410i) q^{21} -2.00000 q^{23} +(-2.00000 + 3.46410i) q^{25} +4.00000 q^{27} -3.00000 q^{29} +8.00000 q^{31} +(4.00000 + 6.92820i) q^{33} +(3.00000 - 5.19615i) q^{35} +(-5.50000 - 2.59808i) q^{37} +(-2.00000 + 3.46410i) q^{39} +(0.500000 + 0.866025i) q^{41} +10.0000 q^{43} -3.00000 q^{45} -8.00000 q^{47} +(1.50000 - 2.59808i) q^{49} -14.0000 q^{51} +(-5.00000 + 8.66025i) q^{53} +(6.00000 + 10.3923i) q^{55} +(-2.00000 + 3.46410i) q^{59} +(1.50000 + 2.59808i) q^{61} +2.00000 q^{63} +(-3.00000 + 5.19615i) q^{65} +(-2.00000 - 3.46410i) q^{67} +(-2.00000 - 3.46410i) q^{69} +(-7.00000 - 12.1244i) q^{71} -2.00000 q^{73} -8.00000 q^{75} +(-4.00000 - 6.92820i) q^{77} +(-8.00000 - 13.8564i) q^{79} +(5.50000 + 9.52628i) q^{81} +(-1.00000 + 1.73205i) q^{83} -21.0000 q^{85} +(-3.00000 - 5.19615i) q^{87} +(0.500000 - 0.866025i) q^{89} +(2.00000 - 3.46410i) q^{91} +(8.00000 + 13.8564i) q^{93} +19.0000 q^{97} +(-2.00000 + 3.46410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 3 q^{5} - 2 q^{7} - q^{9} + 8 q^{11} + 2 q^{13} - 6 q^{15} - 7 q^{17} + 4 q^{21} - 4 q^{23} - 4 q^{25} + 8 q^{27} - 6 q^{29} + 16 q^{31} + 8 q^{33} + 6 q^{35} - 11 q^{37} - 4 q^{39} + q^{41}+ \cdots - 4 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 + 3 * q^5 - 2 * q^7 - q^9 + 8 * q^11 + 2 * q^13 - 6 * q^15 - 7 * q^17 + 4 * q^21 - 4 * q^23 - 4 * q^25 + 8 * q^27 - 6 * q^29 + 16 * q^31 + 8 * q^33 + 6 * q^35 - 11 * q^37 - 4 * q^39 + q^41 + 20 * q^43 - 6 * q^45 - 16 * q^47 + 3 * q^49 - 28 * q^51 - 10 * q^53 + 12 * q^55 - 4 * q^59 + 3 * q^61 + 4 * q^63 - 6 * q^65 - 4 * q^67 - 4 * q^69 - 14 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 - 16 * q^79 + 11 * q^81 - 2 * q^83 - 42 * q^85 - 6 * q^87 + q^89 + 4 * q^91 + 16 * q^93 + 38 * q^97 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1184\mathbb{Z}\right)^\times$.

$n$	$223$	$705$	$741$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.00000	+	1.73205i	0.577350	+	1.00000i	0.995782	+	0.0917517i	$0.0292466\pi$
$3$	1.00000	+	1.73205i	0.577350	+	1.00000i	−0.418432	+	0.908248i	$0.637420\pi$
$4$		0			0
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		0			0
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	4.00000			1.20605			0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000			1.20605			0.603023	+	0.797724i	$0.293963\pi$
$12$		0			0
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$	−3.00000	+	5.19615i	−0.774597	+	1.34164i
$16$		0			0
$17$	−3.50000	+	6.06218i	−0.848875	+	1.47029i	0.0333386	+	0.999444i	$0.489386\pi$
$17$	−3.50000	+	6.06218i	−0.848875	+	1.47029i	−0.882213	+	0.470850i	$0.843947\pi$
$18$		0			0
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$		0			0
$21$	2.00000	−	3.46410i	0.436436	−	0.755929i
$22$		0			0
$23$	−2.00000			−0.417029			−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000			−0.417029			−0.208514	+	0.978019i	$0.566863\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$		0			0
$27$	4.00000			0.769800
$28$		0			0
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$		0			0
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$		0			0
$33$	4.00000	+	6.92820i	0.696311	+	1.20605i
$34$		0			0
$35$	3.00000	−	5.19615i	0.507093	−	0.878310i
$36$		0			0
$37$	−5.50000	−	2.59808i	−0.904194	−	0.427121i
$37$	−5.50000	−	2.59808i	−0.904194	−	0.427121i
$38$		0			0
$39$	−2.00000	+	3.46410i	−0.320256	+	0.554700i
$40$		0			0
$41$	0.500000	+	0.866025i	0.0780869	+	0.135250i	0.902424	−	0.430848i	$-0.141786\pi$
$41$	0.500000	+	0.866025i	0.0780869	+	0.135250i	−0.824338	+	0.566099i	$0.808452\pi$
$42$		0			0
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$		0			0
$45$	−3.00000			−0.447214
$46$		0			0
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$		0			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$		0			0
$51$	−14.0000			−1.96039
$52$		0			0
$53$	−5.00000	+	8.66025i	−0.686803	+	1.18958i	0.286064	+	0.958211i	$0.407653\pi$
$53$	−5.00000	+	8.66025i	−0.686803	+	1.18958i	−0.972867	+	0.231367i	$0.925680\pi$
$54$		0			0
$55$	6.00000	+	10.3923i	0.809040	+	1.40130i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	1.50000	+	2.59808i	0.192055	+	0.332650i	0.945931	−	0.324367i	$-0.105151\pi$
$61$	1.50000	+	2.59808i	0.192055	+	0.332650i	−0.753876	+	0.657017i	$0.771818\pi$
$62$		0			0
$63$	2.00000			0.251976
$64$		0			0
$65$	−3.00000	+	5.19615i	−0.372104	+	0.644503i
$66$		0			0
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$		0			0
$69$	−2.00000	−	3.46410i	−0.240772	−	0.417029i
$70$		0			0
$71$	−7.00000	−	12.1244i	−0.830747	−	1.43890i	−0.897447	−	0.441123i	$-0.854580\pi$
$71$	−7.00000	−	12.1244i	−0.830747	−	1.43890i	0.0666994	−	0.997773i	$-0.478753\pi$
$72$		0			0
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$		0			0
$75$	−8.00000			−0.923760
$76$		0			0
$77$	−4.00000	−	6.92820i	−0.455842	−	0.789542i
$78$		0			0
$79$	−8.00000	−	13.8564i	−0.900070	−	1.55897i	−0.827401	−	0.561611i	$-0.810182\pi$
$79$	−8.00000	−	13.8564i	−0.900070	−	1.55897i	−0.0726692	−	0.997356i	$-0.523152\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$		0			0
$83$	−1.00000	+	1.73205i	−0.109764	+	0.190117i	−0.915675	−	0.401920i	$-0.868343\pi$
$83$	−1.00000	+	1.73205i	−0.109764	+	0.190117i	0.805910	+	0.592037i	$0.201676\pi$
$84$		0			0
$85$	−21.0000			−2.27777
$86$		0			0
$87$	−3.00000	−	5.19615i	−0.321634	−	0.557086i
$88$		0			0
$89$	0.500000	−	0.866025i	0.0529999	−	0.0917985i	−0.838308	−	0.545197i	$-0.816455\pi$
$89$	0.500000	−	0.866025i	0.0529999	−	0.0917985i	0.891308	+	0.453398i	$0.149788\pi$
$90$		0			0
$91$	2.00000	−	3.46410i	0.209657	−	0.363137i
$92$		0			0
$93$	8.00000	+	13.8564i	0.829561	+	1.43684i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	19.0000			1.92916			0.964579	−	0.263795i	$-0.0849741\pi$
$97$	19.0000			1.92916			0.964579	+	0.263795i	$0.0849741\pi$
$98$		0			0
$99$	−2.00000	+	3.46410i	−0.201008	+	0.348155i
$100$		0			0
$101$	−3.00000			−0.298511			−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000			−0.298511			−0.149256	+	0.988799i	$0.547688\pi$
$102$		0			0
$103$	6.00000			0.591198			0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000			0.591198			0.295599	+	0.955312i	$0.404481\pi$
$104$		0			0
$105$	12.0000			1.17108
$106$		0			0
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	0.683793	−	0.729676i	$-0.260329\pi$
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	−0.973814	+	0.227345i	$0.926996\pi$
$108$		0			0
$109$	5.50000	−	9.52628i	0.526804	−	0.912452i	−0.472708	−	0.881219i	$-0.656723\pi$
$109$	5.50000	−	9.52628i	0.526804	−	0.912452i	0.999512	−	0.0312328i	$-0.00994332\pi$
$110$		0			0
$111$	−1.00000	−	12.1244i	−0.0949158	−	1.15079i
$112$		0			0
$113$	−7.00000	+	12.1244i	−0.658505	+	1.14056i	0.322498	+	0.946570i	$0.395477\pi$
$113$	−7.00000	+	12.1244i	−0.658505	+	1.14056i	−0.981003	+	0.193993i	$0.937856\pi$
$114$		0			0
$115$	−3.00000	−	5.19615i	−0.279751	−	0.484544i
$116$		0			0
$117$	−2.00000			−0.184900
$118$		0			0
$119$	14.0000			1.28338
$120$		0			0
$121$	5.00000			0.454545
$122$		0			0
$123$	−1.00000	+	1.73205i	−0.0901670	+	0.156174i
$124$		0			0
$125$	3.00000			0.268328
$126$		0			0
$127$	−5.00000	+	8.66025i	−0.443678	+	0.768473i	−0.997959	−	0.0638564i	$-0.979660\pi$
$127$	−5.00000	+	8.66025i	−0.443678	+	0.768473i	0.554281	+	0.832330i	$0.312993\pi$
$128$		0			0
$129$	10.0000	+	17.3205i	0.880451	+	1.52499i
$130$		0			0
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	6.00000	+	10.3923i	0.516398	+	0.894427i
$136$		0			0
$137$	3.00000			0.256307			0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000			0.256307			0.128154	+	0.991754i	$0.459095\pi$
$138$		0			0
$139$	−5.00000	+	8.66025i	−0.424094	+	0.734553i	−0.996335	−	0.0855324i	$-0.972741\pi$
$139$	−5.00000	+	8.66025i	−0.424094	+	0.734553i	0.572241	+	0.820086i	$0.306074\pi$
$140$		0			0
$141$	−8.00000	−	13.8564i	−0.673722	−	1.16692i
$142$		0			0
$143$	4.00000	+	6.92820i	0.334497	+	0.579365i
$144$		0			0
$145$	−4.50000	−	7.79423i	−0.373705	−	0.647275i
$146$		0			0
$147$	6.00000			0.494872
$148$		0			0
$149$	1.00000			0.0819232			0.0409616	−	0.999161i	$-0.486958\pi$
$149$	1.00000			0.0819232			0.0409616	+	0.999161i	$0.486958\pi$
$150$		0			0
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	0.822464	−	0.568818i	$-0.192599\pi$
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	−0.903842	+	0.427865i	$0.859266\pi$
$152$		0			0
$153$	−3.50000	−	6.06218i	−0.282958	−	0.490098i
$154$		0			0
$155$	12.0000	+	20.7846i	0.963863	+	1.66946i
$156$		0			0
$157$	−2.50000	+	4.33013i	−0.199522	+	0.345582i	−0.948373	−	0.317156i	$-0.897272\pi$
$157$	−2.50000	+	4.33013i	−0.199522	+	0.345582i	0.748852	+	0.662738i	$0.230606\pi$
$158$		0			0
$159$	−20.0000			−1.58610
$160$		0			0
$161$	2.00000	+	3.46410i	0.157622	+	0.273009i
$162$		0			0
$163$	9.00000	−	15.5885i	0.704934	−	1.22098i	−0.261781	−	0.965127i	$-0.584310\pi$
$163$	9.00000	−	15.5885i	0.704934	−	1.22098i	0.966715	−	0.255855i	$-0.0823569\pi$
$164$		0			0
$165$	−12.0000	+	20.7846i	−0.934199	+	1.61808i
$166$		0			0
$167$	4.00000	+	6.92820i	0.309529	+	0.536120i	0.978259	−	0.207385i	$-0.0664952\pi$
$167$	4.00000	+	6.92820i	0.309529	+	0.536120i	−0.668730	+	0.743505i	$0.733162\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.50000	−	16.4545i	0.722272	−	1.25101i	−0.237816	−	0.971310i	$-0.576431\pi$
$173$	9.50000	−	16.4545i	0.722272	−	1.25101i	0.960087	−	0.279701i	$-0.0902353\pi$
$174$		0			0
$175$	8.00000			0.604743
$176$		0			0
$177$	−8.00000			−0.601317
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	−2.50000	−	4.33013i	−0.185824	−	0.321856i	0.758030	−	0.652219i	$-0.226162\pi$
$181$	−2.50000	−	4.33013i	−0.185824	−	0.321856i	−0.943854	+	0.330364i	$0.892829\pi$
$182$		0			0
$183$	−3.00000	+	5.19615i	−0.221766	+	0.384111i
$184$		0			0
$185$	−1.50000	−	18.1865i	−0.110282	−	1.33710i
$186$		0			0
$187$	−14.0000	+	24.2487i	−1.02378	+	1.77324i
$188$		0			0
$189$	−4.00000	−	6.92820i	−0.290957	−	0.503953i
$190$		0			0
$191$	18.0000			1.30243			0.651217	−	0.758891i	$-0.274259\pi$
$191$	18.0000			1.30243			0.651217	+	0.758891i	$0.274259\pi$
$192$		0			0
$193$	7.00000			0.503871			0.251936	−	0.967744i	$-0.418933\pi$
$193$	7.00000			0.503871			0.251936	+	0.967744i	$0.418933\pi$
$194$		0			0
$195$	−12.0000			−0.859338
$196$		0			0
$197$	7.50000	−	12.9904i	0.534353	−	0.925526i	−0.464841	−	0.885394i	$-0.653889\pi$
$197$	7.50000	−	12.9904i	0.534353	−	0.925526i	0.999194	−	0.0401324i	$-0.0127780\pi$
$198$		0			0
$199$	10.0000			0.708881			0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000			0.708881			0.354441	+	0.935079i	$0.384671\pi$
$200$		0			0
$201$	4.00000	−	6.92820i	0.282138	−	0.488678i
$202$		0			0
$203$	3.00000	+	5.19615i	0.210559	+	0.364698i
$204$		0			0
$205$	−1.50000	+	2.59808i	−0.104765	+	0.181458i
$206$		0			0
$207$	1.00000	−	1.73205i	0.0695048	−	0.120386i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	22.0000			1.51454			0.757271	−	0.653101i	$-0.226532\pi$
$211$	22.0000			1.51454			0.757271	+	0.653101i	$0.226532\pi$
$212$		0			0
$213$	14.0000	−	24.2487i	0.959264	−	1.66149i
$214$		0			0
$215$	15.0000	+	25.9808i	1.02299	+	1.77187i
$216$		0			0
$217$	−8.00000	−	13.8564i	−0.543075	−	0.940634i
$218$		0			0
$219$	−2.00000	−	3.46410i	−0.135147	−	0.234082i
$220$		0			0
$221$	−14.0000			−0.941742
$222$		0			0
$223$	14.0000			0.937509			0.468755	−	0.883328i	$-0.344703\pi$
$223$	14.0000			0.937509			0.468755	+	0.883328i	$0.344703\pi$
$224$		0			0
$225$	−2.00000	−	3.46410i	−0.133333	−	0.230940i
$226$		0			0
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	−0.921903	−	0.387421i	$-0.873366\pi$
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	0.125435	−	0.992102i	$-0.459967\pi$
$228$		0			0
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	0.849032	−	0.528341i	$-0.177186\pi$
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	−0.882073	+	0.471113i	$0.843853\pi$
$230$		0			0
$231$	8.00000	−	13.8564i	0.526361	−	0.911685i
$232$		0			0
$233$	11.0000			0.720634			0.360317	−	0.932830i	$-0.382669\pi$
$233$	11.0000			0.720634			0.360317	+	0.932830i	$0.382669\pi$
$234$		0			0
$235$	−12.0000	−	20.7846i	−0.782794	−	1.35584i
$236$		0			0
$237$	16.0000	−	27.7128i	1.03931	−	1.80014i
$238$		0			0
$239$	7.00000	−	12.1244i	0.452792	−	0.784259i	−0.545766	−	0.837938i	$-0.683761\pi$
$239$	7.00000	−	12.1244i	0.452792	−	0.784259i	0.998558	+	0.0536783i	$0.0170946\pi$
$240$		0			0
$241$	−11.0000	−	19.0526i	−0.708572	−	1.22728i	−0.965387	−	0.260822i	$-0.916006\pi$
$241$	−11.0000	−	19.0526i	−0.708572	−	1.22728i	0.256814	−	0.966461i	$-0.417327\pi$
$242$		0			0
$243$	−5.00000	+	8.66025i	−0.320750	+	0.555556i
$244$		0			0
$245$	9.00000			0.574989
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−4.00000			−0.253490
$250$		0			0
$251$	30.0000			1.89358			0.946792	−	0.321847i	$-0.104304\pi$
$251$	30.0000			1.89358			0.946792	+	0.321847i	$0.104304\pi$
$252$		0			0
$253$	−8.00000			−0.502956
$254$		0			0
$255$	−21.0000	−	36.3731i	−1.31507	−	2.27777i
$256$		0			0
$257$	−13.5000	+	23.3827i	−0.842107	+	1.45857i	0.0460033	+	0.998941i	$0.485352\pi$
$257$	−13.5000	+	23.3827i	−0.842107	+	1.45857i	−0.888110	+	0.459631i	$0.847982\pi$
$258$		0			0
$259$	1.00000	+	12.1244i	0.0621370	+	0.753371i
$260$		0			0
$261$	1.50000	−	2.59808i	0.0928477	−	0.160817i
$262$		0			0
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$		0			0
$265$	−30.0000			−1.84289
$266$		0			0
$267$	2.00000			0.122398
$268$		0			0
$269$	14.0000			0.853595			0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000			0.853595			0.426798	+	0.904347i	$0.359642\pi$
$270$		0			0
$271$	−14.0000	+	24.2487i	−0.850439	+	1.47300i	0.0303728	+	0.999539i	$0.490331\pi$
$271$	−14.0000	+	24.2487i	−0.850439	+	1.47300i	−0.880812	+	0.473466i	$0.843003\pi$
$272$		0			0
$273$	8.00000			0.484182
$274$		0			0
$275$	−8.00000	+	13.8564i	−0.482418	+	0.835573i
$276$		0			0
$277$	1.50000	+	2.59808i	0.0901263	+	0.156103i	0.907564	−	0.419914i	$-0.137940\pi$
$277$	1.50000	+	2.59808i	0.0901263	+	0.156103i	−0.817438	+	0.576017i	$0.804606\pi$
$278$		0			0
$279$	−4.00000	+	6.92820i	−0.239474	+	0.414781i
$280$		0			0
$281$	−9.50000	+	16.4545i	−0.566722	+	0.981592i	0.430165	+	0.902750i	$0.358455\pi$
$281$	−9.50000	+	16.4545i	−0.566722	+	0.981592i	−0.996887	+	0.0788417i	$0.974878\pi$
$282$		0			0
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	0.579437	−	0.815017i	$-0.303272\pi$
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	−0.995544	+	0.0942988i	$0.969939\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.00000	−	1.73205i	0.0590281	−	0.102240i
$288$		0			0
$289$	−16.0000	−	27.7128i	−0.941176	−	1.63017i
$290$		0			0
$291$	19.0000	+	32.9090i	1.11380	+	1.92916i
$292$		0			0
$293$	7.50000	+	12.9904i	0.438155	+	0.758906i	0.997547	−	0.0699967i	$-0.0222989\pi$
$293$	7.50000	+	12.9904i	0.438155	+	0.758906i	−0.559393	+	0.828903i	$0.688966\pi$
$294$		0			0
$295$	−12.0000			−0.698667
$296$		0			0
$297$	16.0000			0.928414
$298$		0			0
$299$	−2.00000	−	3.46410i	−0.115663	−	0.200334i
$300$		0			0
$301$	−10.0000	−	17.3205i	−0.576390	−	0.998337i
$302$		0			0
$303$	−3.00000	−	5.19615i	−0.172345	−	0.298511i
$304$		0			0
$305$	−4.50000	+	7.79423i	−0.257669	+	0.446296i
$306$		0			0
$307$	−22.0000			−1.25561			−0.627803	−	0.778372i	$-0.716046\pi$
$307$	−22.0000			−1.25561			−0.627803	+	0.778372i	$0.716046\pi$
$308$		0			0
$309$	6.00000	+	10.3923i	0.341328	+	0.591198i
$310$		0			0
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	0.489585	+	0.871956i	$0.337148\pi$
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	−0.999928	+	0.0119847i	$0.996185\pi$
$312$		0			0
$313$	12.5000	−	21.6506i	0.706542	−	1.22377i	−0.259590	−	0.965719i	$-0.583588\pi$
$313$	12.5000	−	21.6506i	0.706542	−	1.22377i	0.966132	−	0.258047i	$-0.0830791\pi$
$314$		0			0
$315$	3.00000	+	5.19615i	0.169031	+	0.292770i
$316$		0			0
$317$	11.5000	−	19.9186i	0.645904	−	1.11874i	−0.338188	−	0.941079i	$-0.609814\pi$
$317$	11.5000	−	19.9186i	0.645904	−	1.11874i	0.984092	−	0.177660i	$-0.0568529\pi$
$318$		0			0
$319$	−12.0000			−0.671871
$320$		0			0
$321$	6.00000	−	10.3923i	0.334887	−	0.580042i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−8.00000			−0.443760
$326$		0			0
$327$	22.0000			1.21660
$328$		0			0
$329$	8.00000	+	13.8564i	0.441054	+	0.763928i
$330$		0			0
$331$	16.0000	−	27.7128i	0.879440	−	1.52323i	0.0274825	−	0.999622i	$-0.491251\pi$
$331$	16.0000	−	27.7128i	0.879440	−	1.52323i	0.851957	−	0.523612i	$-0.175416\pi$
$332$		0			0
$333$	5.00000	−	3.46410i	0.273998	−	0.189832i
$334$		0			0
$335$	6.00000	−	10.3923i	0.327815	−	0.567792i
$336$		0			0
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	0.986960	−	0.160968i	$-0.0514616\pi$
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	−0.632882	+	0.774248i	$0.718128\pi$
$338$		0			0
$339$	−28.0000			−1.52075
$340$		0			0
$341$	32.0000			1.73290
$342$		0			0
$343$	−20.0000			−1.07990
$344$		0			0
$345$	6.00000	−	10.3923i	0.323029	−	0.559503i
$346$		0			0
$347$	−18.0000			−0.966291			−0.483145	−	0.875540i	$-0.660506\pi$
$347$	−18.0000			−0.966291			−0.483145	+	0.875540i	$0.660506\pi$
$348$		0			0
$349$	−4.50000	+	7.79423i	−0.240879	+	0.417215i	−0.960965	−	0.276670i	$-0.910769\pi$
$349$	−4.50000	+	7.79423i	−0.240879	+	0.417215i	0.720086	+	0.693885i	$0.244103\pi$
$350$		0			0
$351$	4.00000	+	6.92820i	0.213504	+	0.369800i
$352$		0			0
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	−0.903179	−	0.429263i	$-0.858773\pi$
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	0.823343	+	0.567545i	$0.192107\pi$
$354$		0			0
$355$	21.0000	−	36.3731i	1.11456	−	1.93048i
$356$		0			0
$357$	14.0000	+	24.2487i	0.740959	+	1.28338i
$358$		0			0
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$		0			0
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$		0			0
$363$	5.00000	+	8.66025i	0.262432	+	0.454545i
$364$		0			0
$365$	−3.00000	−	5.19615i	−0.157027	−	0.271979i
$366$		0			0
$367$	8.00000	+	13.8564i	0.417597	+	0.723299i	0.995697	−	0.0926670i	$-0.0295392\pi$
$367$	8.00000	+	13.8564i	0.417597	+	0.723299i	−0.578101	+	0.815966i	$0.696206\pi$
$368$		0			0
$369$	−1.00000			−0.0520579
$370$		0			0
$371$	20.0000			1.03835
$372$		0			0
$373$	9.50000	+	16.4545i	0.491891	+	0.851981i	0.999956	−	0.00933789i	$-0.00297238\pi$
$373$	9.50000	+	16.4545i	0.491891	+	0.851981i	−0.508065	+	0.861319i	$0.669639\pi$
$374$		0			0
$375$	3.00000	+	5.19615i	0.154919	+	0.268328i
$376$		0			0
$377$	−3.00000	−	5.19615i	−0.154508	−	0.267615i
$378$		0			0
$379$	−9.00000	+	15.5885i	−0.462299	+	0.800725i	−0.999075	−	0.0429994i	$-0.986309\pi$
$379$	−9.00000	+	15.5885i	−0.462299	+	0.800725i	0.536776	+	0.843725i	$0.319642\pi$
$380$		0			0
$381$	−20.0000			−1.02463
$382$		0			0
$383$	1.00000	+	1.73205i	0.0510976	+	0.0885037i	0.890443	−	0.455095i	$-0.150395\pi$
$383$	1.00000	+	1.73205i	0.0510976	+	0.0885037i	−0.839345	+	0.543599i	$0.817061\pi$
$384$		0			0
$385$	12.0000	−	20.7846i	0.611577	−	1.05928i
$386$		0			0
$387$	−5.00000	+	8.66025i	−0.254164	+	0.440225i
$388$		0			0
$389$	9.50000	+	16.4545i	0.481669	+	0.834275i	0.999779	−	0.0210389i	$-0.00669738\pi$
$389$	9.50000	+	16.4545i	0.481669	+	0.834275i	−0.518110	+	0.855314i	$0.673364\pi$
$390$		0			0
$391$	7.00000	−	12.1244i	0.354005	−	0.613155i
$392$		0			0
$393$	12.0000			0.605320
$394$		0			0
$395$	24.0000	−	41.5692i	1.20757	−	2.09157i
$396$		0			0
$397$	−7.00000			−0.351320			−0.175660	−	0.984451i	$-0.556206\pi$
$397$	−7.00000			−0.351320			−0.175660	+	0.984451i	$0.556206\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	30.0000			1.49813			0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000			1.49813			0.749064	+	0.662497i	$0.230503\pi$
$402$		0			0
$403$	8.00000	+	13.8564i	0.398508	+	0.690237i
$404$		0			0
$405$	−16.5000	+	28.5788i	−0.819892	+	1.42009i
$406$		0			0
$407$	−22.0000	−	10.3923i	−1.09050	−	0.515127i
$408$		0			0
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	0.173064	+	0.984911i	$0.444633\pi$
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	−0.939490	+	0.342578i	$0.888700\pi$
$410$		0			0
$411$	3.00000	+	5.19615i	0.147979	+	0.256307i
$412$		0			0
$413$	8.00000			0.393654
$414$		0			0
$415$	−6.00000			−0.294528
$416$		0			0
$417$	−20.0000			−0.979404
$418$		0			0
$419$	15.0000	−	25.9808i	0.732798	−	1.26924i	−0.222885	−	0.974845i	$-0.571547\pi$
$419$	15.0000	−	25.9808i	0.732798	−	1.26924i	0.955683	−	0.294398i	$-0.0951193\pi$
$420$		0			0
$421$	−27.0000			−1.31590			−0.657950	−	0.753062i	$-0.728576\pi$
$421$	−27.0000			−1.31590			−0.657950	+	0.753062i	$0.728576\pi$
$422$		0			0
$423$	4.00000	−	6.92820i	0.194487	−	0.336861i
$424$		0			0
$425$	−14.0000	−	24.2487i	−0.679100	−	1.17624i
$426$		0			0
$427$	3.00000	−	5.19615i	0.145180	−	0.251459i
$428$		0			0
$429$	−8.00000	+	13.8564i	−0.386244	+	0.668994i
$430$		0			0
$431$	−8.00000	−	13.8564i	−0.385346	−	0.667440i	0.606471	−	0.795106i	$-0.292585\pi$
$431$	−8.00000	−	13.8564i	−0.385346	−	0.667440i	−0.991817	+	0.127666i	$0.959251\pi$
$432$		0			0
$433$	−21.0000			−1.00920			−0.504598	−	0.863355i	$-0.668359\pi$
$433$	−21.0000			−1.00920			−0.504598	+	0.863355i	$0.668359\pi$
$434$		0			0
$435$	9.00000	−	15.5885i	0.431517	−	0.747409i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−10.0000	−	17.3205i	−0.477274	−	0.826663i	0.522387	−	0.852709i	$-0.325042\pi$
$439$	−10.0000	−	17.3205i	−0.477274	−	0.826663i	−0.999661	+	0.0260459i	$0.991708\pi$
$440$		0			0
$441$	1.50000	+	2.59808i	0.0714286	+	0.123718i
$442$		0			0
$443$	−24.0000			−1.14027			−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000			−1.14027			−0.570137	+	0.821549i	$0.693110\pi$
$444$		0			0
$445$	3.00000			0.142214
$446$		0			0
$447$	1.00000	+	1.73205i	0.0472984	+	0.0819232i
$448$		0			0
$449$	−15.0000	−	25.9808i	−0.707894	−	1.22611i	−0.965637	−	0.259895i	$-0.916312\pi$
$449$	−15.0000	−	25.9808i	−0.707894	−	1.22611i	0.257743	−	0.966213i	$-0.417021\pi$
$450$		0			0
$451$	2.00000	+	3.46410i	0.0941763	+	0.163118i
$452$		0			0
$453$	2.00000	−	3.46410i	0.0939682	−	0.162758i
$454$		0			0
$455$	12.0000			0.562569
$456$		0			0
$457$	−13.5000	−	23.3827i	−0.631503	−	1.09380i	−0.987245	−	0.159211i	$-0.949105\pi$
$457$	−13.5000	−	23.3827i	−0.631503	−	1.09380i	0.355741	−	0.934585i	$-0.384228\pi$
$458$		0			0
$459$	−14.0000	+	24.2487i	−0.653464	+	1.13183i
$460$		0			0
$461$	1.00000	−	1.73205i	0.0465746	−	0.0806696i	−0.841798	−	0.539792i	$-0.818503\pi$
$461$	1.00000	−	1.73205i	0.0465746	−	0.0806696i	0.888373	+	0.459123i	$0.151836\pi$
$462$		0			0
$463$	13.0000	+	22.5167i	0.604161	+	1.04644i	0.992183	+	0.124788i	$0.0398251\pi$
$463$	13.0000	+	22.5167i	0.604161	+	1.04644i	−0.388022	+	0.921650i	$0.626842\pi$
$464$		0			0
$465$	−24.0000	+	41.5692i	−1.11297	+	1.92773i
$466$		0			0
$467$	−20.0000			−0.925490			−0.462745	−	0.886492i	$-0.653135\pi$
$467$	−20.0000			−0.925490			−0.462745	+	0.886492i	$0.653135\pi$
$468$		0			0
$469$	−4.00000	+	6.92820i	−0.184703	+	0.319915i
$470$		0			0
$471$	−10.0000			−0.460776
$472$		0			0
$473$	40.0000			1.83920
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−5.00000	−	8.66025i	−0.228934	−	0.396526i
$478$		0			0
$479$	−6.00000	+	10.3923i	−0.274147	+	0.474837i	−0.969920	−	0.243426i	$-0.921729\pi$
$479$	−6.00000	+	10.3923i	−0.274147	+	0.474837i	0.695773	+	0.718262i	$0.255062\pi$
$480$		0			0
$481$	−1.00000	−	12.1244i	−0.0455961	−	0.552823i
$482$		0			0
$483$	−4.00000	+	6.92820i	−0.182006	+	0.315244i
$484$		0			0
$485$	28.5000	+	49.3634i	1.29412	+	2.24148i
$486$		0			0
$487$	−38.0000			−1.72194			−0.860972	−	0.508652i	$-0.830144\pi$
$487$	−38.0000			−1.72194			−0.860972	+	0.508652i	$0.830144\pi$
$488$		0			0
$489$	36.0000			1.62798
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$		0			0
$493$	10.5000	−	18.1865i	0.472896	−	0.819080i
$494$		0			0
$495$	−12.0000			−0.539360
$496$		0			0
$497$	−14.0000	+	24.2487i	−0.627986	+	1.08770i
$498$		0			0
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	0.962472	+	0.271380i	$0.0874801\pi$
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	−0.246214	+	0.969216i	$0.579187\pi$
$500$		0			0
$501$	−8.00000	+	13.8564i	−0.357414	+	0.619059i
$502$		0			0
$503$	6.00000	−	10.3923i	0.267527	−	0.463370i	−0.700696	−	0.713460i	$-0.747127\pi$
$503$	6.00000	−	10.3923i	0.267527	−	0.463370i	0.968223	+	0.250090i	$0.0804603\pi$
$504$		0			0
$505$	−4.50000	−	7.79423i	−0.200247	−	0.346839i
$506$		0			0
$507$	18.0000			0.799408
$508$		0			0
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	−0.650556	−	0.759458i	$-0.725464\pi$
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	0.982988	+	0.183669i	$0.0587976\pi$
$510$		0			0
$511$	2.00000	+	3.46410i	0.0884748	+	0.153243i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	9.00000	+	15.5885i	0.396587	+	0.686909i
$516$		0			0
$517$	−32.0000			−1.40736
$518$		0			0
$519$	38.0000			1.66801
$520$		0			0
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	0.792797	−	0.609486i	$-0.208624\pi$
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	−0.924229	+	0.381839i	$0.875291\pi$
$522$		0			0
$523$	−13.0000	−	22.5167i	−0.568450	−	0.984585i	−0.996719	−	0.0809336i	$-0.974210\pi$
$523$	−13.0000	−	22.5167i	−0.568450	−	0.984585i	0.428269	−	0.903651i	$-0.359124\pi$
$524$		0			0
$525$	8.00000	+	13.8564i	0.349149	+	0.604743i
$526$		0			0
$527$	−28.0000	+	48.4974i	−1.21970	+	2.11258i
$528$		0			0
$529$	−19.0000			−0.826087
$530$		0			0
$531$	−2.00000	−	3.46410i	−0.0867926	−	0.150329i
$532$		0			0
$533$	−1.00000	+	1.73205i	−0.0433148	+	0.0750234i
$534$		0			0
$535$	9.00000	−	15.5885i	0.389104	−	0.673948i
$536$		0			0
$537$	−12.0000	−	20.7846i	−0.517838	−	0.896922i
$538$		0			0
$539$	6.00000	−	10.3923i	0.258438	−	0.447628i
$540$		0			0
$541$	5.00000			0.214967			0.107483	−	0.994207i	$-0.465721\pi$
$541$	5.00000			0.214967			0.107483	+	0.994207i	$0.465721\pi$
$542$		0			0
$543$	5.00000	−	8.66025i	0.214571	−	0.371647i
$544$		0			0
$545$	33.0000			1.41356
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$		0			0
$549$	−3.00000			−0.128037
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−16.0000	+	27.7128i	−0.680389	+	1.17847i
$554$		0			0
$555$	30.0000	−	20.7846i	1.27343	−	0.882258i
$556$		0			0
$557$	15.5000	−	26.8468i	0.656756	−	1.13753i	−0.324694	−	0.945819i	$-0.605261\pi$
$557$	15.5000	−	26.8468i	0.656756	−	1.13753i	0.981450	−	0.191716i	$-0.0614052\pi$
$558$		0			0
$559$	10.0000	+	17.3205i	0.422955	+	0.732579i
$560$		0			0
$561$	−56.0000			−2.36432
$562$		0			0
$563$	14.0000			0.590030			0.295015	−	0.955493i	$-0.404675\pi$
$563$	14.0000			0.590030			0.295015	+	0.955493i	$0.404675\pi$
$564$		0			0
$565$	−42.0000			−1.76695
$566$		0			0
$567$	11.0000	−	19.0526i	0.461957	−	0.800132i
$568$		0			0
$569$	−33.0000			−1.38343			−0.691716	−	0.722170i	$-0.743145\pi$
$569$	−33.0000			−1.38343			−0.691716	+	0.722170i	$0.743145\pi$
$570$		0			0
$571$	−13.0000	+	22.5167i	−0.544033	+	0.942293i	0.454634	+	0.890678i	$0.349770\pi$
$571$	−13.0000	+	22.5167i	−0.544033	+	0.942293i	−0.998667	+	0.0516146i	$0.983563\pi$
$572$		0			0
$573$	18.0000	+	31.1769i	0.751961	+	1.30243i
$574$		0			0
$575$	4.00000	−	6.92820i	0.166812	−	0.288926i
$576$		0			0
$577$	−9.00000	+	15.5885i	−0.374675	+	0.648956i	−0.990278	−	0.139100i	$-0.955579\pi$
$577$	−9.00000	+	15.5885i	−0.374675	+	0.648956i	0.615603	+	0.788056i	$0.288912\pi$
$578$		0			0
$579$	7.00000	+	12.1244i	0.290910	+	0.503871i
$580$		0			0
$581$	4.00000			0.165948
$582$		0			0
$583$	−20.0000	+	34.6410i	−0.828315	+	1.43468i
$584$		0			0
$585$	−3.00000	−	5.19615i	−0.124035	−	0.214834i
$586$		0			0
$587$	−5.00000	−	8.66025i	−0.206372	−	0.357447i	0.744197	−	0.667960i	$-0.232832\pi$
$587$	−5.00000	−	8.66025i	−0.206372	−	0.357447i	−0.950569	+	0.310513i	$0.899499\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	30.0000			1.23404
$592$		0			0
$593$	−21.0000			−0.862367			−0.431183	−	0.902264i	$-0.641904\pi$
$593$	−21.0000			−0.862367			−0.431183	+	0.902264i	$0.641904\pi$
$594$		0			0
$595$	21.0000	+	36.3731i	0.860916	+	1.49115i
$596$		0			0
$597$	10.0000	+	17.3205i	0.409273	+	0.708881i
$598$		0			0
$599$	14.0000	+	24.2487i	0.572024	+	0.990775i	0.996358	+	0.0852695i	$0.0271751\pi$
$599$	14.0000	+	24.2487i	0.572024	+	0.990775i	−0.424333	+	0.905506i	$0.639492\pi$
$600$		0			0
$601$	2.50000	−	4.33013i	0.101977	−	0.176630i	−0.810522	−	0.585708i	$-0.800816\pi$
$601$	2.50000	−	4.33013i	0.101977	−	0.176630i	0.912499	+	0.409079i	$0.134150\pi$
$602$		0			0
$603$	4.00000			0.162893
$604$		0			0
$605$	7.50000	+	12.9904i	0.304918	+	0.528134i
$606$		0			0
$607$	−6.00000	+	10.3923i	−0.243532	+	0.421811i	−0.961718	−	0.274041i	$-0.911640\pi$
$607$	−6.00000	+	10.3923i	−0.243532	+	0.421811i	0.718186	+	0.695852i	$0.244973\pi$
$608$		0			0
$609$	−6.00000	+	10.3923i	−0.243132	+	0.421117i
$610$		0			0
$611$	−8.00000	−	13.8564i	−0.323645	−	0.560570i
$612$		0			0
$613$	1.50000	−	2.59808i	0.0605844	−	0.104935i	−0.834142	−	0.551549i	$-0.814037\pi$
$613$	1.50000	−	2.59808i	0.0605844	−	0.104935i	0.894727	+	0.446614i	$0.147370\pi$
$614$		0			0
$615$	−6.00000			−0.241943
$616$		0			0
$617$	9.00000	−	15.5885i	0.362326	−	0.627568i	−0.626017	−	0.779809i	$-0.715316\pi$
$617$	9.00000	−	15.5885i	0.362326	−	0.627568i	0.988343	+	0.152242i	$0.0486493\pi$
$618$		0			0
$619$	10.0000			0.401934			0.200967	−	0.979598i	$-0.435592\pi$
$619$	10.0000			0.401934			0.200967	+	0.979598i	$0.435592\pi$
$620$		0			0
$621$	−8.00000			−0.321029
$622$		0			0
$623$	−2.00000			−0.0801283
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	35.0000	−	24.2487i	1.39554	−	0.966859i
$630$		0			0
$631$	25.0000	−	43.3013i	0.995234	−	1.72380i	0.413169	−	0.910654i	$-0.364422\pi$
$631$	25.0000	−	43.3013i	0.995234	−	1.72380i	0.582066	−	0.813142i	$-0.302245\pi$
$632$		0			0
$633$	22.0000	+	38.1051i	0.874421	+	1.51454i
$634$		0			0
$635$	−30.0000			−1.19051
$636$		0			0
$637$	6.00000			0.237729
$638$		0			0
$639$	14.0000			0.553831
$640$		0			0
$641$	−17.5000	+	30.3109i	−0.691208	+	1.19721i	0.280234	+	0.959932i	$0.409588\pi$
$641$	−17.5000	+	30.3109i	−0.691208	+	1.19721i	−0.971442	+	0.237276i	$0.923745\pi$
$642$		0			0
$643$	−16.0000			−0.630978			−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000			−0.630978			−0.315489	+	0.948929i	$0.602169\pi$
$644$		0			0
$645$	−30.0000	+	51.9615i	−1.18125	+	2.04598i
$646$		0			0
$647$	21.0000	+	36.3731i	0.825595	+	1.42997i	0.901464	+	0.432855i	$0.142494\pi$
$647$	21.0000	+	36.3731i	0.825595	+	1.42997i	−0.0758684	+	0.997118i	$0.524173\pi$
$648$		0			0
$649$	−8.00000	+	13.8564i	−0.314027	+	0.543912i
$650$		0			0
$651$	16.0000	−	27.7128i	0.627089	−	1.08615i
$652$		0			0
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	0.941248	+	0.337715i	$0.109654\pi$
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	−0.178154	+	0.984003i	$0.557013\pi$
$654$		0			0
$655$	18.0000			0.703318
$656$		0			0
$657$	1.00000	−	1.73205i	0.0390137	−	0.0675737i
$658$		0			0
$659$	8.00000	+	13.8564i	0.311636	+	0.539769i	0.978717	−	0.205216i	$-0.0657898\pi$
$659$	8.00000	+	13.8564i	0.311636	+	0.539769i	−0.667081	+	0.744985i	$0.732456\pi$
$660$		0			0
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	0.813302	−	0.581842i	$-0.197668\pi$
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	−0.910541	+	0.413419i	$0.864334\pi$
$662$		0			0
$663$	−14.0000	−	24.2487i	−0.543715	−	0.941742i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	6.00000			0.232321
$668$		0			0
$669$	14.0000	+	24.2487i	0.541271	+	0.937509i
$670$		0			0
$671$	6.00000	+	10.3923i	0.231627	+	0.401190i
$672$		0			0
$673$	13.0000	+	22.5167i	0.501113	+	0.867953i	0.999999	+	0.00128586i	$0.000409302\pi$
$673$	13.0000	+	22.5167i	0.501113	+	0.867953i	−0.498886	+	0.866668i	$0.666257\pi$
$674$		0			0
$675$	−8.00000	+	13.8564i	−0.307920	+	0.533333i
$676$		0			0
$677$	41.0000			1.57576			0.787879	−	0.615830i	$-0.211179\pi$
$677$	41.0000			1.57576			0.787879	+	0.615830i	$0.211179\pi$
$678$		0			0
$679$	−19.0000	−	32.9090i	−0.729153	−	1.26293i
$680$		0			0
$681$	24.0000	−	41.5692i	0.919682	−	1.59294i
$682$		0			0
$683$	−17.0000	+	29.4449i	−0.650487	+	1.12668i	0.332518	+	0.943097i	$0.392102\pi$
$683$	−17.0000	+	29.4449i	−0.650487	+	1.12668i	−0.983005	+	0.183579i	$0.941232\pi$
$684$		0			0
$685$	4.50000	+	7.79423i	0.171936	+	0.297802i
$686$		0			0
$687$	1.00000	−	1.73205i	0.0381524	−	0.0660819i
$688$		0			0
$689$	−20.0000			−0.761939
$690$		0			0
$691$	16.0000	−	27.7128i	0.608669	−	1.05425i	−0.382791	−	0.923835i	$-0.625037\pi$
$691$	16.0000	−	27.7128i	0.608669	−	1.05425i	0.991460	−	0.130410i	$-0.0416295\pi$
$692$		0			0
$693$	8.00000			0.303895
$694$		0			0
$695$	−30.0000			−1.13796
$696$		0			0
$697$	−7.00000			−0.265144
$698$		0			0
$699$	11.0000	+	19.0526i	0.416058	+	0.720634i
$700$		0			0
$701$	−15.0000	+	25.9808i	−0.566542	+	0.981280i	0.430362	+	0.902656i	$0.358386\pi$
$701$	−15.0000	+	25.9808i	−0.566542	+	0.981280i	−0.996904	+	0.0786236i	$0.974947\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	24.0000	−	41.5692i	0.903892	−	1.56559i
$706$		0			0
$707$	3.00000	+	5.19615i	0.112827	+	0.195421i
$708$		0			0
$709$	22.0000			0.826227			0.413114	−	0.910679i	$-0.364441\pi$
$709$	22.0000			0.826227			0.413114	+	0.910679i	$0.364441\pi$
$710$		0			0
$711$	16.0000			0.600047
$712$		0			0
$713$	−16.0000			−0.599205
$714$		0			0
$715$	−12.0000	+	20.7846i	−0.448775	+	0.777300i
$716$		0			0
$717$	28.0000			1.04568
$718$		0			0
$719$	19.0000	−	32.9090i	0.708580	−	1.22730i	−0.256803	−	0.966464i	$-0.582669\pi$
$719$	19.0000	−	32.9090i	0.708580	−	1.22730i	0.965384	−	0.260834i	$-0.0839974\pi$
$720$		0			0
$721$	−6.00000	−	10.3923i	−0.223452	−	0.387030i
$722$		0			0
$723$	22.0000	−	38.1051i	0.818189	−	1.41714i
$724$		0			0
$725$	6.00000	−	10.3923i	0.222834	−	0.385961i
$726$		0			0
$727$	10.0000	+	17.3205i	0.370879	+	0.642382i	0.989701	−	0.143149i	$-0.0457230\pi$
$727$	10.0000	+	17.3205i	0.370879	+	0.642382i	−0.618822	+	0.785532i	$0.712390\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−35.0000	+	60.6218i	−1.29452	+	2.24218i
$732$		0			0
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	0.588177	−	0.808732i	$-0.299846\pi$
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	−0.994471	+	0.105010i	$0.966513\pi$
$734$		0			0
$735$	9.00000	+	15.5885i	0.331970	+	0.574989i
$736$		0			0
$737$	−8.00000	−	13.8564i	−0.294684	−	0.510407i
$738$		0			0
$739$	−54.0000			−1.98642			−0.993211	−	0.116326i	$-0.962888\pi$
$739$	−54.0000			−1.98642			−0.993211	+	0.116326i	$0.962888\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−24.0000	−	41.5692i	−0.880475	−	1.52503i	−0.850814	−	0.525467i	$-0.823891\pi$
$743$	−24.0000	−	41.5692i	−0.880475	−	1.52503i	−0.0296605	−	0.999560i	$-0.509443\pi$
$744$		0			0
$745$	1.50000	+	2.59808i	0.0549557	+	0.0951861i
$746$		0			0
$747$	−1.00000	−	1.73205i	−0.0365881	−	0.0633724i
$748$		0			0
$749$	−6.00000	+	10.3923i	−0.219235	+	0.379727i
$750$		0			0
$751$	22.0000			0.802791			0.401396	−	0.915905i	$-0.368525\pi$
$751$	22.0000			0.802791			0.401396	+	0.915905i	$0.368525\pi$
$752$		0			0
$753$	30.0000	+	51.9615i	1.09326	+	1.89358i
$754$		0			0
$755$	3.00000	−	5.19615i	0.109181	−	0.189107i
$756$		0			0
$757$	−24.5000	+	42.4352i	−0.890468	+	1.54234i	−0.0511519	+	0.998691i	$0.516289\pi$
$757$	−24.5000	+	42.4352i	−0.890468	+	1.54234i	−0.839316	+	0.543644i	$0.817044\pi$
$758$		0			0
$759$	−8.00000	−	13.8564i	−0.290382	−	0.502956i
$760$		0			0
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	−0.999925	−	0.0122260i	$-0.996108\pi$
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	0.510551	+	0.859848i	$0.329442\pi$
$762$		0			0
$763$	−22.0000			−0.796453
$764$		0			0
$765$	10.5000	−	18.1865i	0.379628	−	0.657536i
$766$		0			0
$767$	−8.00000			−0.288863
$768$		0			0
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$	−54.0000			−1.94476
$772$		0			0
$773$	19.5000	+	33.7750i	0.701366	+	1.21480i	0.967987	+	0.251000i	$0.0807596\pi$
$773$	19.5000	+	33.7750i	0.701366	+	1.21480i	−0.266621	+	0.963802i	$0.585907\pi$
$774$		0			0
$775$	−16.0000	+	27.7128i	−0.574737	+	0.995474i
$776$		0			0
$777$	−20.0000	+	13.8564i	−0.717496	+	0.497096i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−28.0000	−	48.4974i	−1.00192	−	1.73537i
$782$		0			0
$783$	−12.0000			−0.428845
$784$		0			0
$785$	−15.0000			−0.535373
$786$		0			0
$787$	32.0000			1.14068			0.570338	−	0.821410i	$-0.306812\pi$
$787$	32.0000			1.14068			0.570338	+	0.821410i	$0.306812\pi$
$788$		0			0
$789$	12.0000	−	20.7846i	0.427211	−	0.739952i
$790$		0			0
$791$	28.0000			0.995565
$792$		0			0
$793$	−3.00000	+	5.19615i	−0.106533	+	0.184521i
$794$		0			0
$795$	−30.0000	−	51.9615i	−1.06399	−	1.84289i
$796$		0			0
$797$	−19.0000	+	32.9090i	−0.673015	+	1.16570i	0.304030	+	0.952662i	$0.401668\pi$
$797$	−19.0000	+	32.9090i	−0.673015	+	1.16570i	−0.977045	+	0.213033i	$0.931666\pi$
$798$		0			0
$799$	28.0000	−	48.4974i	0.990569	−	1.71572i
$800$		0			0
$801$	0.500000	+	0.866025i	0.0176666	+	0.0305995i
$802$		0			0
$803$	−8.00000			−0.282314
$804$		0			0
$805$	−6.00000	+	10.3923i	−0.211472	+	0.366281i
$806$		0			0
$807$	14.0000	+	24.2487i	0.492823	+	0.853595i
$808$		0			0
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	−0.999491	−	0.0319002i	$-0.989844\pi$
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	0.472119	−	0.881535i	$-0.343489\pi$
$810$		0			0
$811$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$811$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$812$		0			0
$813$	−56.0000			−1.96401
$814$		0			0
$815$	54.0000			1.89154
$816$		0			0
$817$		0			0
$818$		0			0
$819$	2.00000	+	3.46410i	0.0698857	+	0.121046i
$820$		0			0
$821$	−3.00000	−	5.19615i	−0.104701	−	0.181347i	0.808915	−	0.587925i	$-0.200055\pi$
$821$	−3.00000	−	5.19615i	−0.104701	−	0.181347i	−0.913616	+	0.406578i	$0.866722\pi$
$822$		0			0
$823$	−13.0000	+	22.5167i	−0.453152	+	0.784881i	−0.998580	−	0.0532760i	$-0.983034\pi$
$823$	−13.0000	+	22.5167i	−0.453152	+	0.784881i	0.545428	+	0.838157i	$0.316367\pi$
$824$		0			0
$825$	−32.0000			−1.11410
$826$		0			0
$827$	−8.00000	−	13.8564i	−0.278187	−	0.481834i	0.692747	−	0.721181i	$-0.256400\pi$
$827$	−8.00000	−	13.8564i	−0.278187	−	0.481834i	−0.970934	+	0.239346i	$0.923067\pi$
$828$		0			0
$829$	17.0000	−	29.4449i	0.590434	−	1.02266i	−0.403739	−	0.914874i	$-0.632290\pi$
$829$	17.0000	−	29.4449i	0.590434	−	1.02266i	0.994174	−	0.107788i	$-0.0343769\pi$
$830$		0			0
$831$	−3.00000	+	5.19615i	−0.104069	+	0.180253i
$832$		0			0
$833$	10.5000	+	18.1865i	0.363803	+	0.630126i
$834$		0			0
$835$	−12.0000	+	20.7846i	−0.415277	+	0.719281i
$836$		0			0
$837$	32.0000			1.10608
$838$		0			0
$839$	3.00000	−	5.19615i	0.103572	−	0.179391i	−0.809582	−	0.587007i	$-0.800306\pi$
$839$	3.00000	−	5.19615i	0.103572	−	0.179391i	0.913154	+	0.407615i	$0.133640\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$		0			0
$843$	−38.0000			−1.30879
$844$		0			0
$845$	27.0000			0.928828
$846$		0			0
$847$	−5.00000	−	8.66025i	−0.171802	−	0.297570i
$848$		0			0
$849$	14.0000	−	24.2487i	0.480479	−	0.832214i
$850$		0			0
$851$	11.0000	+	5.19615i	0.377075	+	0.178122i
$852$		0			0
$853$	7.50000	−	12.9904i	0.256795	−	0.444782i	−0.708586	−	0.705624i	$-0.750667\pi$
$853$	7.50000	−	12.9904i	0.256795	−	0.444782i	0.965382	+	0.260842i	$0.0840001\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−57.0000			−1.94708			−0.973541	−	0.228510i	$-0.926614\pi$
$857$	−57.0000			−1.94708			−0.973541	+	0.228510i	$0.926614\pi$
$858$		0			0
$859$	−10.0000			−0.341196			−0.170598	−	0.985341i	$-0.554570\pi$
$859$	−10.0000			−0.341196			−0.170598	+	0.985341i	$0.554570\pi$
$860$		0			0
$861$	4.00000			0.136320
$862$		0			0
$863$	2.00000	−	3.46410i	0.0680808	−	0.117919i	−0.829976	−	0.557800i	$-0.811646\pi$
$863$	2.00000	−	3.46410i	0.0680808	−	0.117919i	0.898056	+	0.439880i	$0.144979\pi$
$864$		0			0
$865$	57.0000			1.93806
$866$		0			0
$867$	32.0000	−	55.4256i	1.08678	−	1.88235i
$868$		0			0
$869$	−32.0000	−	55.4256i	−1.08553	−	1.88019i
$870$		0			0
$871$	4.00000	−	6.92820i	0.135535	−	0.234753i
$872$		0			0
$873$	−9.50000	+	16.4545i	−0.321526	+	0.556900i
$874$		0			0
$875$	−3.00000	−	5.19615i	−0.101419	−	0.175662i
$876$		0			0
$877$	1.00000			0.0337676			0.0168838	−	0.999857i	$-0.494625\pi$
$877$	1.00000			0.0337676			0.0168838	+	0.999857i	$0.494625\pi$
$878$		0			0
$879$	−15.0000	+	25.9808i	−0.505937	+	0.876309i
$880$		0			0
$881$	−3.50000	−	6.06218i	−0.117918	−	0.204240i	0.801024	−	0.598632i	$-0.204289\pi$
$881$	−3.50000	−	6.06218i	−0.117918	−	0.204240i	−0.918942	+	0.394392i	$0.870955\pi$
$882$		0			0
$883$	−9.00000	−	15.5885i	−0.302874	−	0.524593i	0.673912	−	0.738812i	$-0.264613\pi$
$883$	−9.00000	−	15.5885i	−0.302874	−	0.524593i	−0.976786	+	0.214219i	$0.931280\pi$
$884$		0			0
$885$	−12.0000	−	20.7846i	−0.403376	−	0.698667i
$886$		0			0
$887$	−54.0000			−1.81314			−0.906571	−	0.422053i	$-0.861310\pi$
$887$	−54.0000			−1.81314			−0.906571	+	0.422053i	$0.861310\pi$
$888$		0			0
$889$	20.0000			0.670778
$890$		0			0
$891$	22.0000	+	38.1051i	0.737028	+	1.27657i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−18.0000	−	31.1769i	−0.601674	−	1.04213i
$896$		0			0
$897$	4.00000	−	6.92820i	0.133556	−	0.231326i
$898$		0			0
$899$	−24.0000			−0.800445
$900$		0			0
$901$	−35.0000	−	60.6218i	−1.16602	−	2.01960i
$902$		0			0
$903$	20.0000	−	34.6410i	0.665558	−	1.15278i
$904$		0			0
$905$	7.50000	−	12.9904i	0.249308	−	0.431815i
$906$		0			0
$907$	−26.0000	−	45.0333i	−0.863316	−	1.49531i	−0.868710	−	0.495321i	$-0.835050\pi$
$907$	−26.0000	−	45.0333i	−0.863316	−	1.49531i	0.00539395	−	0.999985i	$-0.498283\pi$
$908$		0			0
$909$	1.50000	−	2.59808i	0.0497519	−	0.0861727i
$910$		0			0
$911$	−22.0000			−0.728893			−0.364446	−	0.931224i	$-0.618742\pi$
$911$	−22.0000			−0.728893			−0.364446	+	0.931224i	$0.618742\pi$
$912$		0			0
$913$	−4.00000	+	6.92820i	−0.132381	+	0.229290i
$914$		0			0
$915$	−18.0000			−0.595062
$916$		0			0
$917$	−12.0000			−0.396275
$918$		0			0
$919$	−2.00000			−0.0659739			−0.0329870	−	0.999456i	$-0.510502\pi$
$919$	−2.00000			−0.0659739			−0.0329870	+	0.999456i	$0.510502\pi$
$920$		0			0
$921$	−22.0000	−	38.1051i	−0.724925	−	1.25561i
$922$		0			0
$923$	14.0000	−	24.2487i	0.460816	−	0.798156i
$924$		0			0
$925$	20.0000	−	13.8564i	0.657596	−	0.455596i
$926$		0			0
$927$	−3.00000	+	5.19615i	−0.0985329	+	0.170664i
$928$		0			0
$929$	22.5000	+	38.9711i	0.738201	+	1.27860i	0.953305	+	0.302010i	$0.0976578\pi$
$929$	22.5000	+	38.9711i	0.738201	+	1.27860i	−0.215104	+	0.976591i	$0.569009\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−36.0000			−1.17859
$934$		0			0
$935$	−84.0000			−2.74709
$936$		0			0
$937$	12.5000	−	21.6506i	0.408357	−	0.707295i	−0.586349	−	0.810059i	$-0.699435\pi$
$937$	12.5000	−	21.6506i	0.408357	−	0.707295i	0.994706	+	0.102763i	$0.0327685\pi$
$938$		0			0
$939$	50.0000			1.63169
$940$		0			0
$941$	−18.5000	+	32.0429i	−0.603083	+	1.04457i	0.389269	+	0.921124i	$0.372728\pi$
$941$	−18.5000	+	32.0429i	−0.603083	+	1.04457i	−0.992351	+	0.123446i	$0.960606\pi$
$942$		0			0
$943$	−1.00000	−	1.73205i	−0.0325645	−	0.0564033i
$944$		0			0
$945$	12.0000	−	20.7846i	0.390360	−	0.676123i
$946$		0			0
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	−0.946892	−	0.321552i	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$		0			0
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$		0			0
$951$	46.0000			1.49165
$952$		0			0
$953$	9.00000	−	15.5885i	0.291539	−	0.504960i	−0.682635	−	0.730759i	$-0.739166\pi$
$953$	9.00000	−	15.5885i	0.291539	−	0.504960i	0.974174	+	0.225800i	$0.0724995\pi$
$954$		0			0
$955$	27.0000	+	46.7654i	0.873699	+	1.51329i
$956$		0			0
$957$	−12.0000	−	20.7846i	−0.387905	−	0.671871i
$958$		0			0
$959$	−3.00000	−	5.19615i	−0.0968751	−	0.167793i
$960$		0			0
$961$	33.0000			1.06452
$962$		0			0
$963$	6.00000			0.193347
$964$		0			0
$965$	10.5000	+	18.1865i	0.338007	+	0.585445i
$966$		0			0
$967$	2.00000	+	3.46410i	0.0643157	+	0.111398i	0.896390	−	0.443266i	$-0.146180\pi$
$967$	2.00000	+	3.46410i	0.0643157	+	0.111398i	−0.832075	+	0.554664i	$0.812847\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	23.0000	−	39.8372i	0.738105	−	1.27844i	−0.215242	−	0.976561i	$-0.569054\pi$
$971$	23.0000	−	39.8372i	0.738105	−	1.27844i	0.953348	−	0.301875i	$-0.0976125\pi$
$972$		0			0
$973$	20.0000			0.641171
$974$		0			0
$975$	−8.00000	−	13.8564i	−0.256205	−	0.443760i
$976$		0			0
$977$	−3.00000	+	5.19615i	−0.0959785	+	0.166240i	−0.910017	−	0.414572i	$-0.863931\pi$
$977$	−3.00000	+	5.19615i	−0.0959785	+	0.166240i	0.814038	+	0.580812i	$0.197265\pi$
$978$		0			0
$979$	2.00000	−	3.46410i	0.0639203	−	0.110713i
$980$		0			0
$981$	5.50000	+	9.52628i	0.175601	+	0.304151i
$982$		0			0
$983$	−4.00000	+	6.92820i	−0.127580	+	0.220975i	−0.922739	−	0.385426i	$-0.874054\pi$
$983$	−4.00000	+	6.92820i	−0.127580	+	0.220975i	0.795158	+	0.606402i	$0.207388\pi$
$984$		0			0
$985$	45.0000			1.43382
$986$		0			0
$987$	−16.0000	+	27.7128i	−0.509286	+	0.882109i
$988$		0			0
$989$	−20.0000			−0.635963
$990$		0			0
$991$	2.00000			0.0635321			0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000			0.0635321			0.0317660	+	0.999495i	$0.489887\pi$
$992$		0			0
$993$	64.0000			2.03098
$994$		0			0
$995$	15.0000	+	25.9808i	0.475532	+	0.823646i
$996$		0			0
$997$	21.0000	−	36.3731i	0.665077	−	1.15195i	−0.314188	−	0.949361i	$-0.601732\pi$
$997$	21.0000	−	36.3731i	0.665077	−	1.15195i	0.979265	−	0.202586i	$-0.0649345\pi$
$998$		0			0
$999$	−22.0000	−	10.3923i	−0.696049	−	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1184.2.i.b.417.1	yes	2
4.3	odd	2		1184.2.i.a.417.1	✓	2
37.26	even	3	inner	1184.2.i.b.1025.1	yes	2
148.63	odd	6		1184.2.i.a.1025.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1184.2.i.a.417.1	✓	2	4.3	odd	2
1184.2.i.a.1025.1	yes	2	148.63	odd	6
1184.2.i.b.417.1	yes	2	1.1	even	1	trivial
1184.2.i.b.1025.1	yes	2	37.26	even	3	inner

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:	\( N \)	\(=\)	\( 1184 = 2^{5} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1184.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{3} +(1.50000 + 2.59808i) q^{5} +(-1.00000 - 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +4.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +(-3.00000 + 5.19615i) q^{15} +(-3.50000 + 6.06218i) q^{17} +(2.00000 - 3.46410i) q^{21} -2.00000 q^{23} +(-2.00000 + 3.46410i) q^{25} +4.00000 q^{27} -3.00000 q^{29} +8.00000 q^{31} +(4.00000 + 6.92820i) q^{33} +(3.00000 - 5.19615i) q^{35} +(-5.50000 - 2.59808i) q^{37} +(-2.00000 + 3.46410i) q^{39} +(0.500000 + 0.866025i) q^{41} +10.0000 q^{43} -3.00000 q^{45} -8.00000 q^{47} +(1.50000 - 2.59808i) q^{49} -14.0000 q^{51} +(-5.00000 + 8.66025i) q^{53} +(6.00000 + 10.3923i) q^{55} +(-2.00000 + 3.46410i) q^{59} +(1.50000 + 2.59808i) q^{61} +2.00000 q^{63} +(-3.00000 + 5.19615i) q^{65} +(-2.00000 - 3.46410i) q^{67} +(-2.00000 - 3.46410i) q^{69} +(-7.00000 - 12.1244i) q^{71} -2.00000 q^{73} -8.00000 q^{75} +(-4.00000 - 6.92820i) q^{77} +(-8.00000 - 13.8564i) q^{79} +(5.50000 + 9.52628i) q^{81} +(-1.00000 + 1.73205i) q^{83} -21.0000 q^{85} +(-3.00000 - 5.19615i) q^{87} +(0.500000 - 0.866025i) q^{89} +(2.00000 - 3.46410i) q^{91} +(8.00000 + 13.8564i) q^{93} +19.0000 q^{97} +(-2.00000 + 3.46410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 3 q^{5} - 2 q^{7} - q^{9} + 8 q^{11} + 2 q^{13} - 6 q^{15} - 7 q^{17} + 4 q^{21} - 4 q^{23} - 4 q^{25} + 8 q^{27} - 6 q^{29} + 16 q^{31} + 8 q^{33} + 6 q^{35} - 11 q^{37} - 4 q^{39} + q^{41}+ \cdots - 4 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 + 3 * q^5 - 2 * q^7 - q^9 + 8 * q^11 + 2 * q^13 - 6 * q^15 - 7 * q^17 + 4 * q^21 - 4 * q^23 - 4 * q^25 + 8 * q^27 - 6 * q^29 + 16 * q^31 + 8 * q^33 + 6 * q^35 - 11 * q^37 - 4 * q^39 + q^41 + 20 * q^43 - 6 * q^45 - 16 * q^47 + 3 * q^49 - 28 * q^51 - 10 * q^53 + 12 * q^55 - 4 * q^59 + 3 * q^61 + 4 * q^63 - 6 * q^65 - 4 * q^67 - 4 * q^69 - 14 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 - 16 * q^79 + 11 * q^81 - 2 * q^83 - 42 * q^85 - 6 * q^87 + q^89 + 4 * q^91 + 16 * q^93 + 38 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

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Groups

Database

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