LMFDB - Embedded newform 1148.2.i.c.821.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(165,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1148.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.i (of order $3$, 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:	$9.16682615204$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			821.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1148.821
Dual form			1148.2.i.c.165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} +2.00000 q^{13} +1.00000 q^{15} +(-0.500000 - 0.866025i) q^{17} +(1.50000 - 2.59808i) q^{19} +(-0.500000 + 2.59808i) q^{21} +(2.50000 - 4.33013i) q^{23} +(2.00000 + 3.46410i) q^{25} +5.00000 q^{27} -2.00000 q^{29} +(-2.50000 - 4.33013i) q^{31} +(1.50000 - 2.59808i) q^{33} +(2.50000 - 0.866025i) q^{35} +(-3.50000 + 6.06218i) q^{37} +(1.00000 + 1.73205i) q^{39} +1.00000 q^{41} +4.00000 q^{43} +(-1.00000 - 1.73205i) q^{45} +(1.50000 - 2.59808i) q^{47} +(1.00000 + 6.92820i) q^{49} +(0.500000 - 0.866025i) q^{51} +(1.50000 + 2.59808i) q^{53} -3.00000 q^{55} +3.00000 q^{57} +(-2.50000 - 4.33013i) q^{59} +(-1.50000 + 2.59808i) q^{61} +(5.00000 - 1.73205i) q^{63} +(1.00000 - 1.73205i) q^{65} +(6.50000 + 11.2583i) q^{67} +5.00000 q^{69} +(0.500000 + 0.866025i) q^{73} +(-2.00000 + 3.46410i) q^{75} +(1.50000 - 7.79423i) q^{77} +(5.50000 - 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{81} +4.00000 q^{83} -1.00000 q^{85} +(-1.00000 - 1.73205i) q^{87} +(-2.50000 + 4.33013i) q^{89} +(4.00000 + 3.46410i) q^{91} +(2.50000 - 4.33013i) q^{93} +(-1.50000 - 2.59808i) q^{95} +2.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} + q^{5} + 4 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + q^3 + q^5 + 4 * q^7 + 2 * q^9	$ 2 q + q^{3} + q^{5} + 4 q^{7} + 2 q^{9} - 3 q^{11} + 4 q^{13} + 2 q^{15} - q^{17} + 3 q^{19} - q^{21} + 5 q^{23} + 4 q^{25} + 10 q^{27} - 4 q^{29} - 5 q^{31} + 3 q^{33} + 5 q^{35} - 7 q^{37} + 2 q^{39} + 2 q^{41} + 8 q^{43} - 2 q^{45} + 3 q^{47} + 2 q^{49} + q^{51} + 3 q^{53} - 6 q^{55} + 6 q^{57} - 5 q^{59} - 3 q^{61} + 10 q^{63} + 2 q^{65} + 13 q^{67} + 10 q^{69} + q^{73} - 4 q^{75} + 3 q^{77} + 11 q^{79} - q^{81} + 8 q^{83} - 2 q^{85} - 2 q^{87} - 5 q^{89} + 8 q^{91} + 5 q^{93} - 3 q^{95} + 4 q^{97} - 12 q^{99}+O(q^{100}) $ 2 * q + q^3 + q^5 + 4 * q^7 + 2 * q^9 - 3 * q^11 + 4 * q^13 + 2 * q^15 - q^17 + 3 * q^19 - q^21 + 5 * q^23 + 4 * q^25 + 10 * q^27 - 4 * q^29 - 5 * q^31 + 3 * q^33 + 5 * q^35 - 7 * q^37 + 2 * q^39 + 2 * q^41 + 8 * q^43 - 2 * q^45 + 3 * q^47 + 2 * q^49 + q^51 + 3 * q^53 - 6 * q^55 + 6 * q^57 - 5 * q^59 - 3 * q^61 + 10 * q^63 + 2 * q^65 + 13 * q^67 + 10 * q^69 + q^73 - 4 * q^75 + 3 * q^77 + 11 * q^79 - q^81 + 8 * q^83 - 2 * q^85 - 2 * q^87 - 5 * q^89 + 8 * q^91 + 5 * q^93 - 3 * q^95 + 4 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$		0			0
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$		0			0
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i	0.799000	−	0.601331i	$-0.205363\pi$
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i	−0.920268	+	0.391289i	$0.872029\pi$
$18$		0			0
$19$	1.50000	−	2.59808i	0.344124	−	0.596040i	−0.641071	−	0.767482i	$-0.721509\pi$
$19$	1.50000	−	2.59808i	0.344124	−	0.596040i	0.985194	+	0.171442i	$0.0548427\pi$
$20$		0			0
$21$	−0.500000	+	2.59808i	−0.109109	+	0.566947i
$22$		0			0
$23$	2.50000	−	4.33013i	0.521286	−	0.902894i	−0.478407	−	0.878138i	$-0.658786\pi$
$23$	2.50000	−	4.33013i	0.521286	−	0.902894i	0.999694	−	0.0247559i	$-0.00788087\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$		0			0
$27$	5.00000			0.962250
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$		0			0
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$		0			0
$35$	2.50000	−	0.866025i	0.422577	−	0.146385i
$36$		0			0
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	0.420602	+	0.907245i	$0.361819\pi$
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	−0.995998	+	0.0893706i	$0.971514\pi$
$38$		0			0
$39$	1.00000	+	1.73205i	0.160128	+	0.277350i
$40$		0			0
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$	−1.00000	−	1.73205i	−0.149071	−	0.258199i
$46$		0			0
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	−0.735643	−	0.677369i	$-0.763120\pi$
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	0.954441	+	0.298401i	$0.0964533\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$	0.500000	−	0.866025i	0.0700140	−	0.121268i
$52$		0			0
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	0.950464	−	0.310835i	$-0.100609\pi$
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	−0.744423	+	0.667708i	$0.767275\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$		0			0
$57$	3.00000			0.397360
$58$		0			0
$59$	−2.50000	−	4.33013i	−0.325472	−	0.563735i	0.656136	−	0.754643i	$-0.272190\pi$
$59$	−2.50000	−	4.33013i	−0.325472	−	0.563735i	−0.981608	+	0.190909i	$0.938857\pi$
$60$		0			0
$61$	−1.50000	+	2.59808i	−0.192055	+	0.332650i	−0.945931	−	0.324367i	$-0.894849\pi$
$61$	−1.50000	+	2.59808i	−0.192055	+	0.332650i	0.753876	+	0.657017i	$0.228182\pi$
$62$		0			0
$63$	5.00000	−	1.73205i	0.629941	−	0.218218i
$64$		0			0
$65$	1.00000	−	1.73205i	0.124035	−	0.214834i
$66$		0			0
$67$	6.50000	+	11.2583i	0.794101	+	1.37542i	0.923408	+	0.383819i	$0.125391\pi$
$67$	6.50000	+	11.2583i	0.794101	+	1.37542i	−0.129307	+	0.991605i	$0.541275\pi$
$68$		0			0
$69$	5.00000			0.601929
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	0.500000	+	0.866025i	0.0585206	+	0.101361i	0.893801	−	0.448463i	$-0.148028\pi$
$73$	0.500000	+	0.866025i	0.0585206	+	0.101361i	−0.835281	+	0.549823i	$0.814695\pi$
$74$		0			0
$75$	−2.00000	+	3.46410i	−0.230940	+	0.400000i
$76$		0			0
$77$	1.50000	−	7.79423i	0.170941	−	0.888235i
$78$		0			0
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	−0.370907	−	0.928670i	$-0.620953\pi$
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	0.989705	−	0.143120i	$-0.0457135\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	4.00000			0.439057			0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000			0.439057			0.219529	+	0.975606i	$0.429548\pi$
$84$		0			0
$85$	−1.00000			−0.108465
$86$		0			0
$87$	−1.00000	−	1.73205i	−0.107211	−	0.185695i
$88$		0			0
$89$	−2.50000	+	4.33013i	−0.264999	+	0.458993i	−0.967563	−	0.252628i	$-0.918705\pi$
$89$	−2.50000	+	4.33013i	−0.264999	+	0.458993i	0.702564	+	0.711621i	$0.252038\pi$
$90$		0			0
$91$	4.00000	+	3.46410i	0.419314	+	0.363137i
$92$		0			0
$93$	2.50000	−	4.33013i	0.259238	−	0.449013i
$94$		0			0
$95$	−1.50000	−	2.59808i	−0.153897	−	0.266557i
$96$		0			0
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$		0			0
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$		0			0
$103$	−3.50000	+	6.06218i	−0.344865	+	0.597324i	−0.985329	−	0.170664i	$-0.945409\pi$
$103$	−3.50000	+	6.06218i	−0.344865	+	0.597324i	0.640464	+	0.767988i	$0.278742\pi$
$104$		0			0
$105$	2.00000	+	1.73205i	0.195180	+	0.169031i
$106$		0			0
$107$	0.500000	−	0.866025i	0.0483368	−	0.0837218i	−0.840845	−	0.541276i	$-0.817941\pi$
$107$	0.500000	−	0.866025i	0.0483368	−	0.0837218i	0.889182	+	0.457555i	$0.151275\pi$
$108$		0			0
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	0.983531	−	0.180741i	$-0.0578495\pi$
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	−0.648292	+	0.761392i	$0.724516\pi$
$110$		0			0
$111$	−7.00000			−0.664411
$112$		0			0
$113$	−2.00000			−0.188144			−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000			−0.188144			−0.0940721	+	0.995565i	$0.529988\pi$
$114$		0			0
$115$	−2.50000	−	4.33013i	−0.233126	−	0.403786i
$116$		0			0
$117$	2.00000	−	3.46410i	0.184900	−	0.320256i
$118$		0			0
$119$	0.500000	−	2.59808i	0.0458349	−	0.238165i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$	0.500000	+	0.866025i	0.0450835	+	0.0780869i
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$		0			0
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$		0			0
$131$	−3.50000	+	6.06218i	−0.305796	+	0.529655i	−0.977438	−	0.211221i	$-0.932256\pi$
$131$	−3.50000	+	6.06218i	−0.305796	+	0.529655i	0.671642	+	0.740876i	$0.265589\pi$
$132$		0			0
$133$	7.50000	−	2.59808i	0.650332	−	0.225282i
$134$		0			0
$135$	2.50000	−	4.33013i	0.215166	−	0.372678i
$136$		0			0
$137$	−2.50000	−	4.33013i	−0.213589	−	0.369948i	0.739246	−	0.673436i	$-0.235182\pi$
$137$	−2.50000	−	4.33013i	−0.213589	−	0.369948i	−0.952835	+	0.303488i	$0.901849\pi$
$138$		0			0
$139$	−12.0000			−1.01783			−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000			−1.01783			−0.508913	+	0.860818i	$0.669953\pi$
$140$		0			0
$141$	3.00000			0.252646
$142$		0			0
$143$	−3.00000	−	5.19615i	−0.250873	−	0.434524i
$144$		0			0
$145$	−1.00000	+	1.73205i	−0.0830455	+	0.143839i
$146$		0			0
$147$	−5.50000	+	4.33013i	−0.453632	+	0.357143i
$148$		0			0
$149$	−10.5000	+	18.1865i	−0.860194	+	1.48990i	0.0115483	+	0.999933i	$0.496324\pi$
$149$	−10.5000	+	18.1865i	−0.860194	+	1.48990i	−0.871742	+	0.489966i	$0.837009\pi$
$150$		0			0
$151$	−1.50000	−	2.59808i	−0.122068	−	0.211428i	0.798515	−	0.601975i	$-0.205619\pi$
$151$	−1.50000	−	2.59808i	−0.122068	−	0.211428i	−0.920583	+	0.390547i	$0.872286\pi$
$152$		0			0
$153$	−2.00000			−0.161690
$154$		0			0
$155$	−5.00000			−0.401610
$156$		0			0
$157$	1.50000	+	2.59808i	0.119713	+	0.207349i	0.919654	−	0.392730i	$-0.128469\pi$
$157$	1.50000	+	2.59808i	0.119713	+	0.207349i	−0.799941	+	0.600079i	$0.795136\pi$
$158$		0			0
$159$	−1.50000	+	2.59808i	−0.118958	+	0.206041i
$160$		0			0
$161$	12.5000	−	4.33013i	0.985138	−	0.341262i
$162$		0			0
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	−0.845780	−	0.533533i	$-0.820864\pi$
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	0.884943	+	0.465700i	$0.154198\pi$
$164$		0			0
$165$	−1.50000	−	2.59808i	−0.116775	−	0.202260i
$166$		0			0
$167$	−8.00000			−0.619059			−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000			−0.619059			−0.309529	+	0.950890i	$0.600171\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	−3.00000	−	5.19615i	−0.229416	−	0.397360i
$172$		0			0
$173$	−5.50000	+	9.52628i	−0.418157	+	0.724270i	−0.995754	−	0.0920525i	$-0.970657\pi$
$173$	−5.50000	+	9.52628i	−0.418157	+	0.724270i	0.577597	+	0.816322i	$0.303991\pi$
$174$		0			0
$175$	−2.00000	+	10.3923i	−0.151186	+	0.785584i
$176$		0			0
$177$	2.50000	−	4.33013i	0.187912	−	0.325472i
$178$		0			0
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	0.804508	−	0.593942i	$-0.202429\pi$
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	−0.916623	+	0.399753i	$0.869096\pi$
$180$		0			0
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$		0			0
$183$	−3.00000			−0.221766
$184$		0			0
$185$	3.50000	+	6.06218i	0.257325	+	0.445700i
$186$		0			0
$187$	−1.50000	+	2.59808i	−0.109691	+	0.189990i
$188$		0			0
$189$	10.0000	+	8.66025i	0.727393	+	0.629941i
$190$		0			0
$191$	3.50000	−	6.06218i	0.253251	−	0.438644i	−0.711168	−	0.703022i	$-0.751833\pi$
$191$	3.50000	−	6.06218i	0.253251	−	0.438644i	0.964419	+	0.264378i	$0.0851668\pi$
$192$		0			0
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	0.964059	−	0.265689i	$-0.0855996\pi$
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	−0.712123	+	0.702055i	$0.752266\pi$
$194$		0			0
$195$	2.00000			0.143223
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	−9.50000	−	16.4545i	−0.673437	−	1.16643i	−0.976923	−	0.213591i	$-0.931484\pi$
$199$	−9.50000	−	16.4545i	−0.673437	−	1.16643i	0.303486	−	0.952836i	$-0.401849\pi$
$200$		0			0
$201$	−6.50000	+	11.2583i	−0.458475	+	0.794101i
$202$		0			0
$203$	−4.00000	−	3.46410i	−0.280745	−	0.243132i
$204$		0			0
$205$	0.500000	−	0.866025i	0.0349215	−	0.0604858i
$206$		0			0
$207$	−5.00000	−	8.66025i	−0.347524	−	0.601929i
$208$		0			0
$209$	−9.00000			−0.622543
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.00000	−	3.46410i	0.136399	−	0.236250i
$216$		0			0
$217$	2.50000	−	12.9904i	0.169711	−	0.881845i
$218$		0			0
$219$	−0.500000	+	0.866025i	−0.0337869	+	0.0585206i
$220$		0			0
$221$	−1.00000	−	1.73205i	−0.0672673	−	0.116510i
$222$		0			0
$223$	−12.0000			−0.803579			−0.401790	−	0.915732i	$-0.631612\pi$
$223$	−12.0000			−0.803579			−0.401790	+	0.915732i	$0.631612\pi$
$224$		0			0
$225$	8.00000			0.533333
$226$		0			0
$227$	−13.5000	−	23.3827i	−0.896026	−	1.55196i	−0.832529	−	0.553981i	$-0.813108\pi$
$227$	−13.5000	−	23.3827i	−0.896026	−	1.55196i	−0.0634974	−	0.997982i	$-0.520225\pi$
$228$		0			0
$229$	−0.500000	+	0.866025i	−0.0330409	+	0.0572286i	−0.882073	−	0.471113i	$-0.843853\pi$
$229$	−0.500000	+	0.866025i	−0.0330409	+	0.0572286i	0.849032	+	0.528341i	$0.177186\pi$
$230$		0			0
$231$	7.50000	−	2.59808i	0.493464	−	0.170941i
$232$		0			0
$233$	13.5000	−	23.3827i	0.884414	−	1.53185i	0.0380310	−	0.999277i	$-0.487891\pi$
$233$	13.5000	−	23.3827i	0.884414	−	1.53185i	0.846383	−	0.532574i	$-0.178775\pi$
$234$		0			0
$235$	−1.50000	−	2.59808i	−0.0978492	−	0.169480i
$236$		0			0
$237$	11.0000			0.714527
$238$		0			0
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	−1.50000	−	2.59808i	−0.0966235	−	0.167357i	0.813662	−	0.581339i	$-0.197471\pi$
$241$	−1.50000	−	2.59808i	−0.0966235	−	0.167357i	−0.910285	+	0.413982i	$0.864138\pi$
$242$		0			0
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$		0			0
$245$	6.50000	+	2.59808i	0.415270	+	0.165985i
$246$		0			0
$247$	3.00000	−	5.19615i	0.190885	−	0.330623i
$248$		0			0
$249$	2.00000	+	3.46410i	0.126745	+	0.219529i
$250$		0			0
$251$	−8.00000			−0.504956			−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000			−0.504956			−0.252478	+	0.967603i	$0.581245\pi$
$252$		0			0
$253$	−15.0000			−0.943042
$254$		0			0
$255$	−0.500000	−	0.866025i	−0.0313112	−	0.0542326i
$256$		0			0
$257$	−0.500000	+	0.866025i	−0.0311891	+	0.0540212i	−0.881199	−	0.472746i	$-0.843263\pi$
$257$	−0.500000	+	0.866025i	−0.0311891	+	0.0540212i	0.850010	+	0.526767i	$0.176596\pi$
$258$		0			0
$259$	−17.5000	+	6.06218i	−1.08740	+	0.376685i
$260$		0			0
$261$	−2.00000	+	3.46410i	−0.123797	+	0.214423i
$262$		0			0
$263$	12.5000	+	21.6506i	0.770783	+	1.33504i	0.937134	+	0.348969i	$0.113468\pi$
$263$	12.5000	+	21.6506i	0.770783	+	1.33504i	−0.166351	+	0.986067i	$0.553199\pi$
$264$		0			0
$265$	3.00000			0.184289
$266$		0			0
$267$	−5.00000			−0.305995
$268$		0			0
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	0.969976	−	0.243201i	$-0.0781974\pi$
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	−0.695606	+	0.718423i	$0.744864\pi$
$270$		0			0
$271$	−13.5000	+	23.3827i	−0.820067	+	1.42040i	0.0855654	+	0.996333i	$0.472730\pi$
$271$	−13.5000	+	23.3827i	−0.820067	+	1.42040i	−0.905632	+	0.424064i	$0.860603\pi$
$272$		0			0
$273$	−1.00000	+	5.19615i	−0.0605228	+	0.314485i
$274$		0			0
$275$	6.00000	−	10.3923i	0.361814	−	0.626680i
$276$		0			0
$277$	8.50000	+	14.7224i	0.510716	+	0.884585i	0.999923	+	0.0124177i	$0.00395278\pi$
$277$	8.50000	+	14.7224i	0.510716	+	0.884585i	−0.489207	+	0.872167i	$0.662714\pi$
$278$		0			0
$279$	−10.0000			−0.598684
$280$		0			0
$281$	−22.0000			−1.31241			−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000			−1.31241			−0.656205	+	0.754583i	$0.727839\pi$
$282$		0			0
$283$	−4.50000	−	7.79423i	−0.267497	−	0.463319i	0.700718	−	0.713439i	$-0.252863\pi$
$283$	−4.50000	−	7.79423i	−0.267497	−	0.463319i	−0.968215	+	0.250120i	$0.919530\pi$
$284$		0			0
$285$	1.50000	−	2.59808i	0.0888523	−	0.153897i
$286$		0			0
$287$	2.00000	+	1.73205i	0.118056	+	0.102240i
$288$		0			0
$289$	8.00000	−	13.8564i	0.470588	−	0.815083i
$290$		0			0
$291$	1.00000	+	1.73205i	0.0586210	+	0.101535i
$292$		0			0
$293$	−26.0000			−1.51894			−0.759468	−	0.650545i	$-0.774541\pi$
$293$	−26.0000			−1.51894			−0.759468	+	0.650545i	$0.774541\pi$
$294$		0			0
$295$	−5.00000			−0.291111
$296$		0			0
$297$	−7.50000	−	12.9904i	−0.435194	−	0.753778i
$298$		0			0
$299$	5.00000	−	8.66025i	0.289157	−	0.500835i
$300$		0			0
$301$	8.00000	+	6.92820i	0.461112	+	0.399335i
$302$		0			0
$303$	−1.50000	+	2.59808i	−0.0861727	+	0.149256i
$304$		0			0
$305$	1.50000	+	2.59808i	0.0858898	+	0.148765i
$306$		0			0
$307$	−16.0000			−0.913168			−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000			−0.913168			−0.456584	+	0.889680i	$0.650927\pi$
$308$		0			0
$309$	−7.00000			−0.398216
$310$		0			0
$311$	6.50000	+	11.2583i	0.368581	+	0.638401i	0.989344	−	0.145597i	$-0.0465103\pi$
$311$	6.50000	+	11.2583i	0.368581	+	0.638401i	−0.620763	+	0.783998i	$0.713177\pi$
$312$		0			0
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	−0.879810	−	0.475325i	$-0.842331\pi$
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	0.851549	+	0.524276i	$0.175664\pi$
$314$		0			0
$315$	1.00000	−	5.19615i	0.0563436	−	0.292770i
$316$		0			0
$317$	−2.50000	+	4.33013i	−0.140414	+	0.243204i	−0.927653	−	0.373444i	$-0.878177\pi$
$317$	−2.50000	+	4.33013i	−0.140414	+	0.243204i	0.787239	+	0.616649i	$0.211510\pi$
$318$		0			0
$319$	3.00000	+	5.19615i	0.167968	+	0.290929i
$320$		0			0
$321$	1.00000			0.0558146
$322$		0			0
$323$	−3.00000			−0.166924
$324$		0			0
$325$	4.00000	+	6.92820i	0.221880	+	0.384308i
$326$		0			0
$327$	−3.50000	+	6.06218i	−0.193550	+	0.335239i
$328$		0			0
$329$	7.50000	−	2.59808i	0.413488	−	0.143237i
$330$		0			0
$331$	−10.5000	+	18.1865i	−0.577132	+	0.999622i	0.418674	+	0.908137i	$0.362495\pi$
$331$	−10.5000	+	18.1865i	−0.577132	+	0.999622i	−0.995806	+	0.0914858i	$0.970838\pi$
$332$		0			0
$333$	7.00000	+	12.1244i	0.383598	+	0.664411i
$334$		0			0
$335$	13.0000			0.710266
$336$		0			0
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$		0			0
$339$	−1.00000	−	1.73205i	−0.0543125	−	0.0940721i
$340$		0			0
$341$	−7.50000	+	12.9904i	−0.406148	+	0.703469i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$	2.50000	−	4.33013i	0.134595	−	0.233126i
$346$		0			0
$347$	−3.50000	−	6.06218i	−0.187890	−	0.325435i	0.756657	−	0.653812i	$-0.226831\pi$
$347$	−3.50000	−	6.06218i	−0.187890	−	0.325435i	−0.944547	+	0.328378i	$0.893498\pi$
$348$		0			0
$349$	−30.0000			−1.60586			−0.802932	−	0.596071i	$-0.796728\pi$
$349$	−30.0000			−1.60586			−0.802932	+	0.596071i	$0.796728\pi$
$350$		0			0
$351$	10.0000			0.533761
$352$		0			0
$353$	6.50000	+	11.2583i	0.345960	+	0.599220i	0.985528	−	0.169514i	$-0.0542199\pi$
$353$	6.50000	+	11.2583i	0.345960	+	0.599220i	−0.639568	+	0.768735i	$0.720887\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.50000	−	0.866025i	0.132314	−	0.0458349i
$358$		0			0
$359$	12.5000	−	21.6506i	0.659725	−	1.14268i	−0.320962	−	0.947092i	$-0.604006\pi$
$359$	12.5000	−	21.6506i	0.659725	−	1.14268i	0.980687	−	0.195585i	$-0.0626605\pi$
$360$		0			0
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$		0			0
$363$	2.00000			0.104973
$364$		0			0
$365$	1.00000			0.0523424
$366$		0			0
$367$	13.5000	+	23.3827i	0.704694	+	1.22057i	0.966802	+	0.255528i	$0.0822492\pi$
$367$	13.5000	+	23.3827i	0.704694	+	1.22057i	−0.262108	+	0.965039i	$0.584418\pi$
$368$		0			0
$369$	1.00000	−	1.73205i	0.0520579	−	0.0901670i
$370$		0			0
$371$	−1.50000	+	7.79423i	−0.0778761	+	0.404656i
$372$		0			0
$373$	−9.50000	+	16.4545i	−0.491891	+	0.851981i	−0.999956	−	0.00933789i	$-0.997028\pi$
$373$	−9.50000	+	16.4545i	−0.491891	+	0.851981i	0.508065	+	0.861319i	$0.330361\pi$
$374$		0			0
$375$	4.50000	+	7.79423i	0.232379	+	0.402492i
$376$		0			0
$377$	−4.00000			−0.206010
$378$		0			0
$379$	−4.00000			−0.205466			−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000			−0.205466			−0.102733	+	0.994709i	$0.532759\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−4.50000	+	7.79423i	−0.229939	+	0.398266i	−0.957790	−	0.287469i	$-0.907186\pi$
$383$	−4.50000	+	7.79423i	−0.229939	+	0.398266i	0.727851	+	0.685736i	$0.240519\pi$
$384$		0			0
$385$	−6.00000	−	5.19615i	−0.305788	−	0.264820i
$386$		0			0
$387$	4.00000	−	6.92820i	0.203331	−	0.352180i
$388$		0			0
$389$	12.5000	+	21.6506i	0.633775	+	1.09773i	0.986773	+	0.162107i	$0.0518289\pi$
$389$	12.5000	+	21.6506i	0.633775	+	1.09773i	−0.352998	+	0.935624i	$0.614838\pi$
$390$		0			0
$391$	−5.00000			−0.252861
$392$		0			0
$393$	−7.00000			−0.353103
$394$		0			0
$395$	−5.50000	−	9.52628i	−0.276735	−	0.479319i
$396$		0			0
$397$	7.50000	−	12.9904i	0.376414	−	0.651969i	−0.614123	−	0.789210i	$-0.710490\pi$
$397$	7.50000	−	12.9904i	0.376414	−	0.651969i	0.990538	+	0.137241i	$0.0438236\pi$
$398$		0			0
$399$	6.00000	+	5.19615i	0.300376	+	0.260133i
$400$		0			0
$401$	6.50000	−	11.2583i	0.324595	−	0.562214i	−0.656836	−	0.754034i	$-0.728105\pi$
$401$	6.50000	−	11.2583i	0.324595	−	0.562214i	0.981430	+	0.191820i	$0.0614388\pi$
$402$		0			0
$403$	−5.00000	−	8.66025i	−0.249068	−	0.431398i
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	21.0000			1.04093
$408$		0			0
$409$	4.50000	+	7.79423i	0.222511	+	0.385400i	0.955570	−	0.294765i	$-0.0952414\pi$
$409$	4.50000	+	7.79423i	0.222511	+	0.385400i	−0.733059	+	0.680165i	$0.761908\pi$
$410$		0			0
$411$	2.50000	−	4.33013i	0.123316	−	0.213589i
$412$		0			0
$413$	2.50000	−	12.9904i	0.123017	−	0.639215i
$414$		0			0
$415$	2.00000	−	3.46410i	0.0981761	−	0.170046i
$416$		0			0
$417$	−6.00000	−	10.3923i	−0.293821	−	0.508913i
$418$		0			0
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$		0			0
$421$	6.00000			0.292422			0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000			0.292422			0.146211	+	0.989253i	$0.453292\pi$
$422$		0			0
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$		0			0
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$		0			0
$427$	−7.50000	+	2.59808i	−0.362950	+	0.125730i
$428$		0			0
$429$	3.00000	−	5.19615i	0.144841	−	0.250873i
$430$		0			0
$431$	9.50000	+	16.4545i	0.457599	+	0.792585i	0.998833	−	0.0482871i	$-0.0153762\pi$
$431$	9.50000	+	16.4545i	0.457599	+	0.792585i	−0.541235	+	0.840872i	$0.682043\pi$
$432$		0			0
$433$	6.00000			0.288342			0.144171	−	0.989553i	$-0.453949\pi$
$433$	6.00000			0.288342			0.144171	+	0.989553i	$0.453949\pi$
$434$		0			0
$435$	−2.00000			−0.0958927
$436$		0			0
$437$	−7.50000	−	12.9904i	−0.358774	−	0.621414i
$438$		0			0
$439$	17.5000	−	30.3109i	0.835229	−	1.44666i	−0.0586141	−	0.998281i	$-0.518668\pi$
$439$	17.5000	−	30.3109i	0.835229	−	1.44666i	0.893843	−	0.448379i	$-0.147999\pi$
$440$		0			0
$441$	13.0000	+	5.19615i	0.619048	+	0.247436i
$442$		0			0
$443$	4.50000	−	7.79423i	0.213801	−	0.370315i	−0.739100	−	0.673596i	$-0.764749\pi$
$443$	4.50000	−	7.79423i	0.213801	−	0.370315i	0.952901	+	0.303281i	$0.0980821\pi$
$444$		0			0
$445$	2.50000	+	4.33013i	0.118511	+	0.205268i
$446$		0			0
$447$	−21.0000			−0.993266
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$	−1.50000	−	2.59808i	−0.0706322	−	0.122339i
$452$		0			0
$453$	1.50000	−	2.59808i	0.0704761	−	0.122068i
$454$		0			0
$455$	5.00000	−	1.73205i	0.234404	−	0.0811998i
$456$		0			0
$457$	1.50000	−	2.59808i	0.0701670	−	0.121533i	−0.828807	−	0.559534i	$-0.810980\pi$
$457$	1.50000	−	2.59808i	0.0701670	−	0.121533i	0.898974	+	0.438001i	$0.144313\pi$
$458$		0			0
$459$	−2.50000	−	4.33013i	−0.116690	−	0.202113i
$460$		0			0
$461$	26.0000			1.21094			0.605470	−	0.795868i	$-0.292985\pi$
$461$	26.0000			1.21094			0.605470	+	0.795868i	$0.292985\pi$
$462$		0			0
$463$	32.0000			1.48717			0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000			1.48717			0.743583	+	0.668644i	$0.233125\pi$
$464$		0			0
$465$	−2.50000	−	4.33013i	−0.115935	−	0.200805i
$466$		0			0
$467$	16.5000	−	28.5788i	0.763529	−	1.32247i	−0.177492	−	0.984122i	$-0.556798\pi$
$467$	16.5000	−	28.5788i	0.763529	−	1.32247i	0.941021	−	0.338349i	$-0.109868\pi$
$468$		0			0
$469$	−6.50000	+	33.7750i	−0.300142	+	1.55958i
$470$		0			0
$471$	−1.50000	+	2.59808i	−0.0691164	+	0.119713i
$472$		0			0
$473$	−6.00000	−	10.3923i	−0.275880	−	0.477839i
$474$		0			0
$475$	12.0000			0.550598
$476$		0			0
$477$	6.00000			0.274721
$478$		0			0
$479$	−9.50000	−	16.4545i	−0.434066	−	0.751825i	0.563153	−	0.826353i	$-0.309588\pi$
$479$	−9.50000	−	16.4545i	−0.434066	−	0.751825i	−0.997219	+	0.0745283i	$0.976255\pi$
$480$		0			0
$481$	−7.00000	+	12.1244i	−0.319173	+	0.552823i
$482$		0			0
$483$	10.0000	+	8.66025i	0.455016	+	0.394055i
$484$		0			0
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$		0			0
$487$	5.50000	+	9.52628i	0.249229	+	0.431677i	0.963312	−	0.268384i	$-0.0864896\pi$
$487$	5.50000	+	9.52628i	0.249229	+	0.431677i	−0.714083	+	0.700061i	$0.753156\pi$
$488$		0			0
$489$	1.00000			0.0452216
$490$		0			0
$491$	36.0000			1.62466			0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000			1.62466			0.812329	+	0.583200i	$0.198200\pi$
$492$		0			0
$493$	1.00000	+	1.73205i	0.0450377	+	0.0780076i
$494$		0			0
$495$	−3.00000	+	5.19615i	−0.134840	+	0.233550i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	3.50000	−	6.06218i	0.156682	−	0.271380i	−0.776989	−	0.629515i	$-0.783254\pi$
$499$	3.50000	−	6.06218i	0.156682	−	0.271380i	0.933670	+	0.358134i	$0.116587\pi$
$500$		0			0
$501$	−4.00000	−	6.92820i	−0.178707	−	0.309529i
$502$		0			0
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	3.00000			0.133498
$506$		0			0
$507$	−4.50000	−	7.79423i	−0.199852	−	0.346154i
$508$		0			0
$509$	5.50000	−	9.52628i	0.243783	−	0.422245i	−0.718006	−	0.696037i	$-0.754945\pi$
$509$	5.50000	−	9.52628i	0.243783	−	0.422245i	0.961789	+	0.273792i	$0.0882781\pi$
$510$		0			0
$511$	−0.500000	+	2.59808i	−0.0221187	+	0.114932i
$512$		0			0
$513$	7.50000	−	12.9904i	0.331133	−	0.573539i
$514$		0			0
$515$	3.50000	+	6.06218i	0.154228	+	0.267131i
$516$		0			0
$517$	−9.00000			−0.395820
$518$		0			0
$519$	−11.0000			−0.482846
$520$		0			0
$521$	−6.50000	−	11.2583i	−0.284770	−	0.493236i	0.687783	−	0.725916i	$-0.258584\pi$
$521$	−6.50000	−	11.2583i	−0.284770	−	0.493236i	−0.972553	+	0.232680i	$0.925251\pi$
$522$		0			0
$523$	−5.50000	+	9.52628i	−0.240498	+	0.416555i	−0.960856	−	0.277047i	$-0.910644\pi$
$523$	−5.50000	+	9.52628i	−0.240498	+	0.416555i	0.720358	+	0.693602i	$0.243977\pi$
$524$		0			0
$525$	−10.0000	+	3.46410i	−0.436436	+	0.151186i
$526$		0			0
$527$	−2.50000	+	4.33013i	−0.108902	+	0.188623i
$528$		0			0
$529$	−1.00000	−	1.73205i	−0.0434783	−	0.0753066i
$530$		0			0
$531$	−10.0000			−0.433963
$532$		0			0
$533$	2.00000			0.0866296
$534$		0			0
$535$	−0.500000	−	0.866025i	−0.0216169	−	0.0374415i
$536$		0			0
$537$	1.50000	−	2.59808i	0.0647298	−	0.112115i
$538$		0			0
$539$	16.5000	−	12.9904i	0.710705	−	0.559535i
$540$		0			0
$541$	0.500000	−	0.866025i	0.0214967	−	0.0372333i	−0.855077	−	0.518501i	$-0.826490\pi$
$541$	0.500000	−	0.866025i	0.0214967	−	0.0372333i	0.876574	+	0.481268i	$0.159824\pi$
$542$		0			0
$543$	−11.0000	−	19.0526i	−0.472055	−	0.817624i
$544$		0			0
$545$	7.00000			0.299847
$546$		0			0
$547$	4.00000			0.171028			0.0855138	−	0.996337i	$-0.472747\pi$
$547$	4.00000			0.171028			0.0855138	+	0.996337i	$0.472747\pi$
$548$		0			0
$549$	3.00000	+	5.19615i	0.128037	+	0.221766i
$550$		0			0
$551$	−3.00000	+	5.19615i	−0.127804	+	0.221364i
$552$		0			0
$553$	27.5000	−	9.52628i	1.16942	−	0.405099i
$554$		0			0
$555$	−3.50000	+	6.06218i	−0.148567	+	0.257325i
$556$		0			0
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	0.896053	−	0.443947i	$-0.146422\pi$
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	−0.832496	+	0.554031i	$0.813089\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$		0			0
$561$	−3.00000			−0.126660
$562$		0			0
$563$	10.5000	+	18.1865i	0.442522	+	0.766471i	0.997876	−	0.0651433i	$-0.0207504\pi$
$563$	10.5000	+	18.1865i	0.442522	+	0.766471i	−0.555354	+	0.831614i	$0.687417\pi$
$564$		0			0
$565$	−1.00000	+	1.73205i	−0.0420703	+	0.0728679i
$566$		0			0
$567$	0.500000	−	2.59808i	0.0209980	−	0.109109i
$568$		0			0
$569$	22.5000	−	38.9711i	0.943249	−	1.63376i	0.184030	−	0.982921i	$-0.441086\pi$
$569$	22.5000	−	38.9711i	0.943249	−	1.63376i	0.759220	−	0.650835i	$-0.225581\pi$
$570$		0			0
$571$	2.50000	+	4.33013i	0.104622	+	0.181210i	0.913584	−	0.406651i	$-0.133303\pi$
$571$	2.50000	+	4.33013i	0.104622	+	0.181210i	−0.808962	+	0.587861i	$0.799970\pi$
$572$		0			0
$573$	7.00000			0.292429
$574$		0			0
$575$	20.0000			0.834058
$576$		0			0
$577$	−8.50000	−	14.7224i	−0.353860	−	0.612903i	0.633062	−	0.774101i	$-0.281798\pi$
$577$	−8.50000	−	14.7224i	−0.353860	−	0.612903i	−0.986922	+	0.161198i	$0.948464\pi$
$578$		0			0
$579$	−3.50000	+	6.06218i	−0.145455	+	0.251936i
$580$		0			0
$581$	8.00000	+	6.92820i	0.331896	+	0.287430i
$582$		0			0
$583$	4.50000	−	7.79423i	0.186371	−	0.322804i
$584$		0			0
$585$	−2.00000	−	3.46410i	−0.0826898	−	0.143223i
$586$		0			0
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	−15.0000			−0.618064
$590$		0			0
$591$	3.00000	+	5.19615i	0.123404	+	0.213741i
$592$		0			0
$593$	−4.50000	+	7.79423i	−0.184793	+	0.320071i	−0.943507	−	0.331353i	$-0.892495\pi$
$593$	−4.50000	+	7.79423i	−0.184793	+	0.320071i	0.758714	+	0.651424i	$0.225828\pi$
$594$		0			0
$595$	−2.00000	−	1.73205i	−0.0819920	−	0.0710072i
$596$		0			0
$597$	9.50000	−	16.4545i	0.388809	−	0.673437i
$598$		0			0
$599$	−8.50000	−	14.7224i	−0.347301	−	0.601542i	0.638468	−	0.769648i	$-0.279568\pi$
$599$	−8.50000	−	14.7224i	−0.347301	−	0.601542i	−0.985769	+	0.168106i	$0.946235\pi$
$600$		0			0
$601$	42.0000			1.71322			0.856608	−	0.515968i	$-0.172568\pi$
$601$	42.0000			1.71322			0.856608	+	0.515968i	$0.172568\pi$
$602$		0			0
$603$	26.0000			1.05880
$604$		0			0
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$		0			0
$607$	−11.5000	+	19.9186i	−0.466771	+	0.808470i	−0.999279	−	0.0379540i	$-0.987916\pi$
$607$	−11.5000	+	19.9186i	−0.466771	+	0.808470i	0.532509	+	0.846424i	$0.321249\pi$
$608$		0			0
$609$	1.00000	−	5.19615i	0.0405220	−	0.210559i
$610$		0			0
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$		0			0
$613$	14.5000	+	25.1147i	0.585649	+	1.01437i	0.994794	+	0.101905i	$0.0324938\pi$
$613$	14.5000	+	25.1147i	0.585649	+	1.01437i	−0.409145	+	0.912470i	$0.634173\pi$
$614$		0			0
$615$	1.00000			0.0403239
$616$		0			0
$617$	22.0000			0.885687			0.442843	−	0.896599i	$-0.353970\pi$
$617$	22.0000			0.885687			0.442843	+	0.896599i	$0.353970\pi$
$618$		0			0
$619$	−0.500000	−	0.866025i	−0.0200967	−	0.0348085i	0.855802	−	0.517303i	$-0.173064\pi$
$619$	−0.500000	−	0.866025i	−0.0200967	−	0.0348085i	−0.875899	+	0.482495i	$0.839731\pi$
$620$		0			0
$621$	12.5000	−	21.6506i	0.501608	−	0.868810i
$622$		0			0
$623$	−12.5000	+	4.33013i	−0.500802	+	0.173483i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$		0			0
$627$	−4.50000	−	7.79423i	−0.179713	−	0.311272i
$628$		0			0
$629$	7.00000			0.279108
$630$		0			0
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$		0			0
$633$	2.00000	+	3.46410i	0.0794929	+	0.137686i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	2.00000	+	13.8564i	0.0792429	+	0.549011i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	17.5000	+	30.3109i	0.691208	+	1.19721i	0.971442	+	0.237276i	$0.0762547\pi$
$641$	17.5000	+	30.3109i	0.691208	+	1.19721i	−0.280234	+	0.959932i	$0.590412\pi$
$642$		0			0
$643$	−20.0000			−0.788723			−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000			−0.788723			−0.394362	+	0.918955i	$0.629034\pi$
$644$		0			0
$645$	4.00000			0.157500
$646$		0			0
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	0.763908	−	0.645325i	$-0.223278\pi$
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	−0.940822	+	0.338902i	$0.889945\pi$
$648$		0			0
$649$	−7.50000	+	12.9904i	−0.294401	+	0.509917i
$650$		0			0
$651$	12.5000	−	4.33013i	0.489914	−	0.169711i
$652$		0			0
$653$	21.5000	−	37.2391i	0.841360	−	1.45728i	−0.0473852	−	0.998877i	$-0.515089\pi$
$653$	21.5000	−	37.2391i	0.841360	−	1.45728i	0.888745	−	0.458402i	$-0.151578\pi$
$654$		0			0
$655$	3.50000	+	6.06218i	0.136756	+	0.236869i
$656$		0			0
$657$	2.00000			0.0780274
$658$		0			0
$659$	−24.0000			−0.934907			−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000			−0.934907			−0.467454	+	0.884018i	$0.654829\pi$
$660$		0			0
$661$	22.5000	+	38.9711i	0.875149	+	1.51580i	0.856604	+	0.515974i	$0.172570\pi$
$661$	22.5000	+	38.9711i	0.875149	+	1.51580i	0.0185442	+	0.999828i	$0.494097\pi$
$662$		0			0
$663$	1.00000	−	1.73205i	0.0388368	−	0.0672673i
$664$		0			0
$665$	1.50000	−	7.79423i	0.0581675	−	0.302247i
$666$		0			0
$667$	−5.00000	+	8.66025i	−0.193601	+	0.335326i
$668$		0			0
$669$	−6.00000	−	10.3923i	−0.231973	−	0.401790i
$670$		0			0
$671$	9.00000			0.347441
$672$		0			0
$673$	−34.0000			−1.31060			−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000			−1.31060			−0.655302	+	0.755367i	$0.727459\pi$
$674$		0			0
$675$	10.0000	+	17.3205i	0.384900	+	0.666667i
$676$		0			0
$677$	−13.5000	+	23.3827i	−0.518847	+	0.898670i	0.480913	+	0.876768i	$0.340305\pi$
$677$	−13.5000	+	23.3827i	−0.518847	+	0.898670i	−0.999760	+	0.0219013i	$0.993028\pi$
$678$		0			0
$679$	4.00000	+	3.46410i	0.153506	+	0.132940i
$680$		0			0
$681$	13.5000	−	23.3827i	0.517321	−	0.896026i
$682$		0			0
$683$	2.50000	+	4.33013i	0.0956598	+	0.165688i	0.909884	−	0.414863i	$-0.136171\pi$
$683$	2.50000	+	4.33013i	0.0956598	+	0.165688i	−0.814224	+	0.580551i	$0.802837\pi$
$684$		0			0
$685$	−5.00000			−0.191040
$686$		0			0
$687$	−1.00000			−0.0381524
$688$		0			0
$689$	3.00000	+	5.19615i	0.114291	+	0.197958i
$690$		0			0
$691$	5.50000	−	9.52628i	0.209230	−	0.362397i	−0.742242	−	0.670132i	$-0.766238\pi$
$691$	5.50000	−	9.52628i	0.209230	−	0.362397i	0.951472	+	0.307735i	$0.0995710\pi$
$692$		0			0
$693$	−12.0000	−	10.3923i	−0.455842	−	0.394771i
$694$		0			0
$695$	−6.00000	+	10.3923i	−0.227593	+	0.394203i
$696$		0			0
$697$	−0.500000	−	0.866025i	−0.0189389	−	0.0328031i
$698$		0			0
$699$	27.0000			1.02123
$700$		0			0
$701$	−14.0000			−0.528773			−0.264386	−	0.964417i	$-0.585169\pi$
$701$	−14.0000			−0.528773			−0.264386	+	0.964417i	$0.585169\pi$
$702$		0			0
$703$	10.5000	+	18.1865i	0.396015	+	0.685918i
$704$		0			0
$705$	1.50000	−	2.59808i	0.0564933	−	0.0978492i
$706$		0			0
$707$	−1.50000	+	7.79423i	−0.0564133	+	0.293132i
$708$		0			0
$709$	−2.50000	+	4.33013i	−0.0938895	+	0.162621i	−0.909145	−	0.416481i	$-0.863263\pi$
$709$	−2.50000	+	4.33013i	−0.0938895	+	0.162621i	0.815255	+	0.579102i	$0.196597\pi$
$710$		0			0
$711$	−11.0000	−	19.0526i	−0.412532	−	0.714527i
$712$		0			0
$713$	−25.0000			−0.936257
$714$		0			0
$715$	−6.00000			−0.224387
$716$		0			0
$717$	−8.00000	−	13.8564i	−0.298765	−	0.517477i
$718$		0			0
$719$	−22.5000	+	38.9711i	−0.839108	+	1.45338i	0.0515326	+	0.998671i	$0.483589\pi$
$719$	−22.5000	+	38.9711i	−0.839108	+	1.45338i	−0.890641	+	0.454707i	$0.849744\pi$
$720$		0			0
$721$	−17.5000	+	6.06218i	−0.651734	+	0.225767i
$722$		0			0
$723$	1.50000	−	2.59808i	0.0557856	−	0.0966235i
$724$		0			0
$725$	−4.00000	−	6.92820i	−0.148556	−	0.257307i
$726$		0			0
$727$	32.0000			1.18681			0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−2.00000	−	3.46410i	−0.0739727	−	0.128124i
$732$		0			0
$733$	−3.50000	+	6.06218i	−0.129275	+	0.223912i	−0.923396	−	0.383849i	$-0.874598\pi$
$733$	−3.50000	+	6.06218i	−0.129275	+	0.223912i	0.794121	+	0.607760i	$0.207932\pi$
$734$		0			0
$735$	1.00000	+	6.92820i	0.0368856	+	0.255551i
$736$		0			0
$737$	19.5000	−	33.7750i	0.718292	−	1.24412i
$738$		0			0
$739$	11.5000	+	19.9186i	0.423034	+	0.732717i	0.996235	−	0.0866983i	$-0.0276316\pi$
$739$	11.5000	+	19.9186i	0.423034	+	0.732717i	−0.573200	+	0.819415i	$0.694298\pi$
$740$		0			0
$741$	6.00000			0.220416
$742$		0			0
$743$	36.0000			1.32071			0.660356	−	0.750953i	$-0.270405\pi$
$743$	36.0000			1.32071			0.660356	+	0.750953i	$0.270405\pi$
$744$		0			0
$745$	10.5000	+	18.1865i	0.384690	+	0.666303i
$746$		0			0
$747$	4.00000	−	6.92820i	0.146352	−	0.253490i
$748$		0			0
$749$	2.50000	−	0.866025i	0.0913480	−	0.0316439i
$750$		0			0
$751$	11.5000	−	19.9186i	0.419641	−	0.726839i	−0.576262	−	0.817265i	$-0.695489\pi$
$751$	11.5000	−	19.9186i	0.419641	−	0.726839i	0.995903	+	0.0904254i	$0.0288227\pi$
$752$		0			0
$753$	−4.00000	−	6.92820i	−0.145768	−	0.252478i
$754$		0			0
$755$	−3.00000			−0.109181
$756$		0			0
$757$	−34.0000			−1.23575			−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000			−1.23575			−0.617876	+	0.786276i	$0.712006\pi$
$758$		0			0
$759$	−7.50000	−	12.9904i	−0.272233	−	0.471521i
$760$		0			0
$761$	6.50000	−	11.2583i	0.235625	−	0.408114i	−0.723829	−	0.689979i	$-0.757620\pi$
$761$	6.50000	−	11.2583i	0.235625	−	0.408114i	0.959454	+	0.281865i	$0.0909530\pi$
$762$		0			0
$763$	−3.50000	+	18.1865i	−0.126709	+	0.658397i
$764$		0			0
$765$	−1.00000	+	1.73205i	−0.0361551	+	0.0626224i
$766$		0			0
$767$	−5.00000	−	8.66025i	−0.180540	−	0.312704i
$768$		0			0
$769$	2.00000			0.0721218			0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000			0.0721218			0.0360609	+	0.999350i	$0.488519\pi$
$770$		0			0
$771$	−1.00000			−0.0360141
$772$		0			0
$773$	1.50000	+	2.59808i	0.0539513	+	0.0934463i	0.891740	−	0.452549i	$-0.149485\pi$
$773$	1.50000	+	2.59808i	0.0539513	+	0.0934463i	−0.837788	+	0.545995i	$0.816152\pi$
$774$		0			0
$775$	10.0000	−	17.3205i	0.359211	−	0.622171i
$776$		0			0
$777$	−14.0000	−	12.1244i	−0.502247	−	0.434959i
$778$		0			0
$779$	1.50000	−	2.59808i	0.0537431	−	0.0930857i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−10.0000			−0.357371
$784$		0			0
$785$	3.00000			0.107075
$786$		0			0
$787$	5.50000	+	9.52628i	0.196054	+	0.339575i	0.947245	−	0.320509i	$-0.103854\pi$
$787$	5.50000	+	9.52628i	0.196054	+	0.339575i	−0.751192	+	0.660084i	$0.770521\pi$
$788$		0			0
$789$	−12.5000	+	21.6506i	−0.445012	+	0.770783i
$790$		0			0
$791$	−4.00000	−	3.46410i	−0.142224	−	0.123169i
$792$		0			0
$793$	−3.00000	+	5.19615i	−0.106533	+	0.184521i
$794$		0			0
$795$	1.50000	+	2.59808i	0.0531995	+	0.0921443i
$796$		0			0
$797$	−34.0000			−1.20434			−0.602171	−	0.798367i	$-0.705697\pi$
$797$	−34.0000			−1.20434			−0.602171	+	0.798367i	$0.705697\pi$
$798$		0			0
$799$	−3.00000			−0.106132
$800$		0			0
$801$	5.00000	+	8.66025i	0.176666	+	0.305995i
$802$		0			0
$803$	1.50000	−	2.59808i	0.0529339	−	0.0916841i
$804$		0			0
$805$	2.50000	−	12.9904i	0.0881134	−	0.457851i
$806$		0			0
$807$	−4.50000	+	7.79423i	−0.158408	+	0.274370i
$808$		0			0
$809$	−20.5000	−	35.5070i	−0.720742	−	1.24836i	−0.960703	−	0.277579i	$-0.910468\pi$
$809$	−20.5000	−	35.5070i	−0.720742	−	1.24836i	0.239961	−	0.970782i	$-0.422865\pi$
$810$		0			0
$811$	36.0000			1.26413			0.632065	−	0.774915i	$-0.282207\pi$
$811$	36.0000			1.26413			0.632065	+	0.774915i	$0.282207\pi$
$812$		0			0
$813$	−27.0000			−0.946931
$814$		0			0
$815$	−0.500000	−	0.866025i	−0.0175142	−	0.0303355i
$816$		0			0
$817$	6.00000	−	10.3923i	0.209913	−	0.363581i
$818$		0			0
$819$	10.0000	−	3.46410i	0.349428	−	0.121046i
$820$		0			0
$821$	−15.5000	+	26.8468i	−0.540954	+	0.936959i	0.457896	+	0.889006i	$0.348603\pi$
$821$	−15.5000	+	26.8468i	−0.540954	+	0.936959i	−0.998850	+	0.0479535i	$0.984730\pi$
$822$		0			0
$823$	6.50000	+	11.2583i	0.226576	+	0.392441i	0.956791	−	0.290776i	$-0.0939136\pi$
$823$	6.50000	+	11.2583i	0.226576	+	0.392441i	−0.730215	+	0.683217i	$0.760580\pi$
$824$		0			0
$825$	12.0000			0.417786
$826$		0			0
$827$	40.0000			1.39094			0.695468	−	0.718557i	$-0.255197\pi$
$827$	40.0000			1.39094			0.695468	+	0.718557i	$0.255197\pi$
$828$		0			0
$829$	−3.50000	−	6.06218i	−0.121560	−	0.210548i	0.798823	−	0.601566i	$-0.205456\pi$
$829$	−3.50000	−	6.06218i	−0.121560	−	0.210548i	−0.920383	+	0.391018i	$0.872123\pi$
$830$		0			0
$831$	−8.50000	+	14.7224i	−0.294862	+	0.510716i
$832$		0			0
$833$	5.50000	−	4.33013i	0.190564	−	0.150030i
$834$		0			0
$835$	−4.00000	+	6.92820i	−0.138426	+	0.239760i
$836$		0			0
$837$	−12.5000	−	21.6506i	−0.432063	−	0.748355i
$838$		0			0
$839$	−28.0000			−0.966667			−0.483334	−	0.875436i	$-0.660574\pi$
$839$	−28.0000			−0.966667			−0.483334	+	0.875436i	$0.660574\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		0			0
$843$	−11.0000	−	19.0526i	−0.378860	−	0.656205i
$844$		0			0
$845$	−4.50000	+	7.79423i	−0.154805	+	0.268130i
$846$		0			0
$847$	5.00000	−	1.73205i	0.171802	−	0.0595140i
$848$		0			0
$849$	4.50000	−	7.79423i	0.154440	−	0.267497i
$850$		0			0
$851$	17.5000	+	30.3109i	0.599892	+	1.03904i
$852$		0			0
$853$	−46.0000			−1.57501			−0.787505	−	0.616308i	$-0.788628\pi$
$853$	−46.0000			−1.57501			−0.787505	+	0.616308i	$0.788628\pi$
$854$		0			0
$855$	−6.00000			−0.205196
$856$		0			0
$857$	4.50000	+	7.79423i	0.153717	+	0.266246i	0.932591	−	0.360935i	$-0.117542\pi$
$857$	4.50000	+	7.79423i	0.153717	+	0.266246i	−0.778874	+	0.627180i	$0.784209\pi$
$858$		0			0
$859$	12.5000	−	21.6506i	0.426494	−	0.738710i	−0.570064	−	0.821600i	$-0.693082\pi$
$859$	12.5000	−	21.6506i	0.426494	−	0.738710i	0.996559	+	0.0828900i	$0.0264150\pi$
$860$		0			0
$861$	−0.500000	+	2.59808i	−0.0170400	+	0.0885422i
$862$		0			0
$863$	−13.5000	+	23.3827i	−0.459545	+	0.795956i	−0.998937	−	0.0460992i	$-0.985321\pi$
$863$	−13.5000	+	23.3827i	−0.459545	+	0.795956i	0.539392	+	0.842055i	$0.318654\pi$
$864$		0			0
$865$	5.50000	+	9.52628i	0.187006	+	0.323903i
$866$		0			0
$867$	16.0000			0.543388
$868$		0			0
$869$	−33.0000			−1.11945
$870$		0			0
$871$	13.0000	+	22.5167i	0.440488	+	0.762948i
$872$		0			0
$873$	2.00000	−	3.46410i	0.0676897	−	0.117242i
$874$		0			0
$875$	18.0000	+	15.5885i	0.608511	+	0.526986i
$876$		0			0
$877$	2.50000	−	4.33013i	0.0844190	−	0.146218i	−0.820724	−	0.571324i	$-0.806430\pi$
$877$	2.50000	−	4.33013i	0.0844190	−	0.146218i	0.905143	+	0.425106i	$0.139763\pi$
$878$		0			0
$879$	−13.0000	−	22.5167i	−0.438479	−	0.759468i
$880$		0			0
$881$	38.0000			1.28025			0.640126	−	0.768270i	$-0.278882\pi$
$881$	38.0000			1.28025			0.640126	+	0.768270i	$0.278882\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$		0			0
$885$	−2.50000	−	4.33013i	−0.0840366	−	0.145556i
$886$		0			0
$887$	7.50000	−	12.9904i	0.251825	−	0.436174i	−0.712203	−	0.701974i	$-0.752302\pi$
$887$	7.50000	−	12.9904i	0.251825	−	0.436174i	0.964028	+	0.265799i	$0.0856358\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.50000	+	2.59808i	−0.0502519	+	0.0870388i
$892$		0			0
$893$	−4.50000	−	7.79423i	−0.150587	−	0.260824i
$894$		0			0
$895$	−3.00000			−0.100279
$896$		0			0
$897$	10.0000			0.333890
$898$		0			0
$899$	5.00000	+	8.66025i	0.166759	+	0.288836i
$900$		0			0
$901$	1.50000	−	2.59808i	0.0499722	−	0.0865545i
$902$		0			0
$903$	−2.00000	+	10.3923i	−0.0665558	+	0.345834i
$904$		0			0
$905$	−11.0000	+	19.0526i	−0.365652	+	0.633328i
$906$		0			0
$907$	−6.50000	−	11.2583i	−0.215829	−	0.373827i	0.737700	−	0.675129i	$-0.235912\pi$
$907$	−6.50000	−	11.2583i	−0.215829	−	0.373827i	−0.953529	+	0.301302i	$0.902579\pi$
$908$		0			0
$909$	6.00000			0.199007
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$		0			0
$913$	−6.00000	−	10.3923i	−0.198571	−	0.343935i
$914$		0			0
$915$	−1.50000	+	2.59808i	−0.0495885	+	0.0858898i
$916$		0			0
$917$	−17.5000	+	6.06218i	−0.577901	+	0.200191i
$918$		0			0
$919$	5.50000	−	9.52628i	0.181428	−	0.314243i	−0.760939	−	0.648824i	$-0.775261\pi$
$919$	5.50000	−	9.52628i	0.181428	−	0.314243i	0.942367	+	0.334581i	$0.108595\pi$
$920$		0			0
$921$	−8.00000	−	13.8564i	−0.263609	−	0.456584i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−28.0000			−0.920634
$926$		0			0
$927$	7.00000	+	12.1244i	0.229910	+	0.398216i
$928$		0			0
$929$	19.5000	−	33.7750i	0.639774	−	1.10812i	−0.345708	−	0.938342i	$-0.612361\pi$
$929$	19.5000	−	33.7750i	0.639774	−	1.10812i	0.985482	−	0.169779i	$-0.0543055\pi$
$930$		0			0
$931$	19.5000	+	7.79423i	0.639087	+	0.255446i
$932$		0			0
$933$	−6.50000	+	11.2583i	−0.212800	+	0.368581i
$934$		0			0
$935$	1.50000	+	2.59808i	0.0490552	+	0.0849662i
$936$		0			0
$937$	−58.0000			−1.89478			−0.947389	−	0.320085i	$-0.896288\pi$
$937$	−58.0000			−1.89478			−0.947389	+	0.320085i	$0.896288\pi$
$938$		0			0
$939$	−1.00000			−0.0326338
$940$		0			0
$941$	24.5000	+	42.4352i	0.798677	+	1.38335i	0.920478	+	0.390795i	$0.127800\pi$
$941$	24.5000	+	42.4352i	0.798677	+	1.38335i	−0.121801	+	0.992555i	$0.538867\pi$
$942$		0			0
$943$	2.50000	−	4.33013i	0.0814112	−	0.141008i
$944$		0			0
$945$	12.5000	−	4.33013i	0.406625	−	0.140859i
$946$		0			0
$947$	−17.5000	+	30.3109i	−0.568674	+	0.984972i	0.428024	+	0.903767i	$0.359210\pi$
$947$	−17.5000	+	30.3109i	−0.568674	+	0.984972i	−0.996697	+	0.0812041i	$0.974123\pi$
$948$		0			0
$949$	1.00000	+	1.73205i	0.0324614	+	0.0562247i
$950$		0			0
$951$	−5.00000			−0.162136
$952$		0			0
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$		0			0
$955$	−3.50000	−	6.06218i	−0.113257	−	0.196167i
$956$		0			0
$957$	−3.00000	+	5.19615i	−0.0969762	+	0.167968i
$958$		0			0
$959$	2.50000	−	12.9904i	0.0807292	−	0.419481i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$		0			0
$963$	−1.00000	−	1.73205i	−0.0322245	−	0.0558146i
$964$		0			0
$965$	7.00000			0.225338
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$		0			0
$969$	−1.50000	−	2.59808i	−0.0481869	−	0.0834622i
$970$		0			0
$971$	−28.5000	+	49.3634i	−0.914609	+	1.58415i	−0.107135	+	0.994244i	$0.534168\pi$
$971$	−28.5000	+	49.3634i	−0.914609	+	1.58415i	−0.807473	+	0.589904i	$0.799166\pi$
$972$		0			0
$973$	−24.0000	−	20.7846i	−0.769405	−	0.666324i
$974$		0			0
$975$	−4.00000	+	6.92820i	−0.128103	+	0.221880i
$976$		0			0
$977$	−28.5000	−	49.3634i	−0.911796	−	1.57928i	−0.811526	−	0.584316i	$-0.801363\pi$
$977$	−28.5000	−	49.3634i	−0.911796	−	1.57928i	−0.100270	−	0.994960i	$-0.531971\pi$
$978$		0			0
$979$	15.0000			0.479402
$980$		0			0
$981$	14.0000			0.446986
$982$		0			0
$983$	−22.5000	−	38.9711i	−0.717639	−	1.24299i	−0.961933	−	0.273285i	$-0.911890\pi$
$983$	−22.5000	−	38.9711i	−0.717639	−	1.24299i	0.244294	−	0.969701i	$-0.421444\pi$
$984$		0			0
$985$	3.00000	−	5.19615i	0.0955879	−	0.165563i
$986$		0			0
$987$	6.00000	+	5.19615i	0.190982	+	0.165395i
$988$		0			0
$989$	10.0000	−	17.3205i	0.317982	−	0.550760i
$990$		0			0
$991$	28.5000	+	49.3634i	0.905332	+	1.56808i	0.820470	+	0.571689i	$0.193712\pi$
$991$	28.5000	+	49.3634i	0.905332	+	1.56808i	0.0848618	+	0.996393i	$0.472955\pi$
$992$		0			0
$993$	−21.0000			−0.666415
$994$		0			0
$995$	−19.0000			−0.602340
$996$		0			0
$997$	−6.50000	−	11.2583i	−0.205857	−	0.356555i	0.744548	−	0.667568i	$-0.232665\pi$
$997$	−6.50000	−	11.2583i	−0.205857	−	0.356555i	−0.950405	+	0.311014i	$0.899332\pi$
$998$		0			0
$999$	−17.5000	+	30.3109i	−0.553675	+	0.958994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.i.c.821.1	yes	2
7.2	even	3		8036.2.a.b.1.1		1
7.4	even	3	inner	1148.2.i.c.165.1	✓	2
7.5	odd	6		8036.2.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.i.c.165.1	✓	2	7.4	even	3	inner
1148.2.i.c.821.1	yes	2	1.1	even	1	trivial
8036.2.a.b.1.1		1	7.2	even	3
8036.2.a.f.1.1		1	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} +2.00000 q^{13} +1.00000 q^{15} +(-0.500000 - 0.866025i) q^{17} +(1.50000 - 2.59808i) q^{19} +(-0.500000 + 2.59808i) q^{21} +(2.50000 - 4.33013i) q^{23} +(2.00000 + 3.46410i) q^{25} +5.00000 q^{27} -2.00000 q^{29} +(-2.50000 - 4.33013i) q^{31} +(1.50000 - 2.59808i) q^{33} +(2.50000 - 0.866025i) q^{35} +(-3.50000 + 6.06218i) q^{37} +(1.00000 + 1.73205i) q^{39} +1.00000 q^{41} +4.00000 q^{43} +(-1.00000 - 1.73205i) q^{45} +(1.50000 - 2.59808i) q^{47} +(1.00000 + 6.92820i) q^{49} +(0.500000 - 0.866025i) q^{51} +(1.50000 + 2.59808i) q^{53} -3.00000 q^{55} +3.00000 q^{57} +(-2.50000 - 4.33013i) q^{59} +(-1.50000 + 2.59808i) q^{61} +(5.00000 - 1.73205i) q^{63} +(1.00000 - 1.73205i) q^{65} +(6.50000 + 11.2583i) q^{67} +5.00000 q^{69} +(0.500000 + 0.866025i) q^{73} +(-2.00000 + 3.46410i) q^{75} +(1.50000 - 7.79423i) q^{77} +(5.50000 - 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{81} +4.00000 q^{83} -1.00000 q^{85} +(-1.00000 - 1.73205i) q^{87} +(-2.50000 + 4.33013i) q^{89} +(4.00000 + 3.46410i) q^{91} +(2.50000 - 4.33013i) q^{93} +(-1.50000 - 2.59808i) q^{95} +2.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} + q^{5} + 4 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + q^3 + q^5 + 4 * q^7 + 2 * q^9	\( 2 q + q^{3} + q^{5} + 4 q^{7} + 2 q^{9} - 3 q^{11} + 4 q^{13} + 2 q^{15} - q^{17} + 3 q^{19} - q^{21} + 5 q^{23} + 4 q^{25} + 10 q^{27} - 4 q^{29} - 5 q^{31} + 3 q^{33} + 5 q^{35} - 7 q^{37} + 2 q^{39} + 2 q^{41} + 8 q^{43} - 2 q^{45} + 3 q^{47} + 2 q^{49} + q^{51} + 3 q^{53} - 6 q^{55} + 6 q^{57} - 5 q^{59} - 3 q^{61} + 10 q^{63} + 2 q^{65} + 13 q^{67} + 10 q^{69} + q^{73} - 4 q^{75} + 3 q^{77} + 11 q^{79} - q^{81} + 8 q^{83} - 2 q^{85} - 2 q^{87} - 5 q^{89} + 8 q^{91} + 5 q^{93} - 3 q^{95} + 4 q^{97} - 12 q^{99}+O(q^{100}) \) 2 * q + q^3 + q^5 + 4 * q^7 + 2 * q^9 - 3 * q^11 + 4 * q^13 + 2 * q^15 - q^17 + 3 * q^19 - q^21 + 5 * q^23 + 4 * q^25 + 10 * q^27 - 4 * q^29 - 5 * q^31 + 3 * q^33 + 5 * q^35 - 7 * q^37 + 2 * q^39 + 2 * q^41 + 8 * q^43 - 2 * q^45 + 3 * q^47 + 2 * q^49 + q^51 + 3 * q^53 - 6 * q^55 + 6 * q^57 - 5 * q^59 - 3 * q^61 + 10 * q^63 + 2 * q^65 + 13 * q^67 + 10 * q^69 + q^73 - 4 * q^75 + 3 * q^77 + 11 * q^79 - q^81 + 8 * q^83 - 2 * q^85 - 2 * q^87 - 5 * q^89 + 8 * q^91 + 5 * q^93 - 3 * q^95 + 4 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more