LMFDB - Embedded newform 950.2.e.f.501.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(201,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("950.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.e (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:	$7.58578819202$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			501.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	950.501
Dual form			950.2.e.f.201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +5.00000 q^{11} +(1.00000 - 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +3.00000 q^{18} +(-0.500000 - 4.33013i) q^{19} +(2.50000 + 4.33013i) q^{22} +(0.500000 - 0.866025i) q^{23} +2.00000 q^{26} +(0.500000 - 0.866025i) q^{28} +(-3.00000 + 5.19615i) q^{29} +4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{36} +11.0000 q^{37} +(3.50000 - 2.59808i) q^{38} +(4.50000 + 7.79423i) q^{41} +(3.00000 + 5.19615i) q^{43} +(-2.50000 + 4.33013i) q^{44} +1.00000 q^{46} -6.00000 q^{49} +(1.00000 + 1.73205i) q^{52} +(2.50000 - 4.33013i) q^{53} +1.00000 q^{56} -6.00000 q^{58} +(2.00000 + 3.46410i) q^{62} +(-1.50000 + 2.59808i) q^{63} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{67} +(-3.00000 - 5.19615i) q^{71} +(-1.50000 + 2.59808i) q^{72} +(7.00000 + 12.1244i) q^{73} +(5.50000 + 9.52628i) q^{74} +(4.00000 + 1.73205i) q^{76} -5.00000 q^{77} +(-5.00000 - 8.66025i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{82} -14.0000 q^{83} +(-3.00000 + 5.19615i) q^{86} -5.00000 q^{88} +(3.50000 - 6.06218i) q^{89} +(-1.00000 + 1.73205i) q^{91} +(0.500000 + 0.866025i) q^{92} +(-1.00000 - 1.73205i) q^{97} +(-3.00000 - 5.19615i) q^{98} +(7.50000 - 12.9904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - 2 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + q^2 - q^4 - 2 * q^7 - 2 * q^8 + 3 * q^9	$ 2 q + q^{2} - q^{4} - 2 q^{7} - 2 q^{8} + 3 q^{9} + 10 q^{11} + 2 q^{13} - q^{14} - q^{16} + 6 q^{18} - q^{19} + 5 q^{22} + q^{23} + 4 q^{26} + q^{28} - 6 q^{29} + 8 q^{31} + q^{32} + 3 q^{36} + 22 q^{37} + 7 q^{38} + 9 q^{41} + 6 q^{43} - 5 q^{44} + 2 q^{46} - 12 q^{49} + 2 q^{52} + 5 q^{53} + 2 q^{56} - 12 q^{58} + 4 q^{62} - 3 q^{63} + 2 q^{64} + 12 q^{67} - 6 q^{71} - 3 q^{72} + 14 q^{73} + 11 q^{74} + 8 q^{76} - 10 q^{77} - 10 q^{79} - 9 q^{81} - 9 q^{82} - 28 q^{83} - 6 q^{86} - 10 q^{88} + 7 q^{89} - 2 q^{91} + q^{92} - 2 q^{97} - 6 q^{98} + 15 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^4 - 2 * q^7 - 2 * q^8 + 3 * q^9 + 10 * q^11 + 2 * q^13 - q^14 - q^16 + 6 * q^18 - q^19 + 5 * q^22 + q^23 + 4 * q^26 + q^28 - 6 * q^29 + 8 * q^31 + q^32 + 3 * q^36 + 22 * q^37 + 7 * q^38 + 9 * q^41 + 6 * q^43 - 5 * q^44 + 2 * q^46 - 12 * q^49 + 2 * q^52 + 5 * q^53 + 2 * q^56 - 12 * q^58 + 4 * q^62 - 3 * q^63 + 2 * q^64 + 12 * q^67 - 6 * q^71 - 3 * q^72 + 14 * q^73 + 11 * q^74 + 8 * q^76 - 10 * q^77 - 10 * q^79 - 9 * q^81 - 9 * q^82 - 28 * q^83 - 6 * q^86 - 10 * q^88 + 7 * q^89 - 2 * q^91 + q^92 - 2 * q^97 - 6 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$3$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$	−1.00000			−0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	5.00000			1.50756			0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000			1.50756			0.753778	+	0.657129i	$0.228229\pi$
$12$		0			0
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	3.00000			0.707107
$19$	−0.500000	−	4.33013i	−0.114708	−	0.993399i
$19$	−0.500000	−	4.33013i	−0.114708	−	0.993399i
$20$		0			0
$21$		0			0
$22$	2.50000	+	4.33013i	0.533002	+	0.923186i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$		0			0
$25$		0			0
$26$	2.00000			0.392232
$27$		0			0
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	11.0000			1.80839			0.904194	−	0.427121i	$-0.140472\pi$
$37$	11.0000			1.80839			0.904194	+	0.427121i	$0.140472\pi$
$38$	3.50000	−	2.59808i	0.567775	−	0.421464i
$39$		0			0
$40$		0			0
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$		0			0
$43$	3.00000	+	5.19615i	0.457496	+	0.792406i	0.998828	−	0.0484030i	$-0.0154132\pi$
$43$	3.00000	+	5.19615i	0.457496	+	0.792406i	−0.541332	+	0.840809i	$0.682080\pi$
$44$	−2.50000	+	4.33013i	−0.376889	+	0.652791i
$45$		0			0
$46$	1.00000			0.147442
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	−6.00000			−0.857143
$50$		0			0
$51$		0			0
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	2.50000	−	4.33013i	0.343401	−	0.594789i	−0.641661	−	0.766989i	$-0.721754\pi$
$53$	2.50000	−	4.33013i	0.343401	−	0.594789i	0.985062	+	0.172200i	$0.0550875\pi$
$54$		0			0
$55$		0			0
$56$	1.00000			0.133631
$57$		0			0
$58$	−6.00000			−0.787839
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$	2.00000	+	3.46410i	0.254000	+	0.439941i
$63$	−1.50000	+	2.59808i	−0.188982	+	0.327327i
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	−0.222571	−	0.974916i	$-0.571445\pi$
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	0.955588	−	0.294706i	$-0.0952216\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$	−1.50000	+	2.59808i	−0.176777	+	0.306186i
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	0.906208	+	0.422833i	$0.138964\pi$
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	−0.0869195	+	0.996215i	$0.527702\pi$
$74$	5.50000	+	9.52628i	0.639362	+	1.10741i
$75$		0			0
$76$	4.00000	+	1.73205i	0.458831	+	0.198680i
$77$	−5.00000			−0.569803
$78$		0			0
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	−0.997274	−	0.0737937i	$-0.976489\pi$
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	0.434730	−	0.900561i	$-0.356844\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−4.50000	+	7.79423i	−0.496942	+	0.860729i
$83$	−14.0000			−1.53670			−0.768350	−	0.640030i	$-0.778922\pi$
$83$	−14.0000			−1.53670			−0.768350	+	0.640030i	$0.778922\pi$
$84$		0			0
$85$		0			0
$86$	−3.00000	+	5.19615i	−0.323498	+	0.560316i
$87$		0			0
$88$	−5.00000			−0.533002
$89$	3.50000	−	6.06218i	0.370999	−	0.642590i	−0.618720	−	0.785611i	$-0.712349\pi$
$89$	3.50000	−	6.06218i	0.370999	−	0.642590i	0.989720	+	0.143022i	$0.0456819\pi$
$90$		0			0
$91$	−1.00000	+	1.73205i	−0.104828	+	0.181568i
$92$	0.500000	+	0.866025i	0.0521286	+	0.0902894i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	−3.00000	−	5.19615i	−0.303046	−	0.524891i
$99$	7.50000	−	12.9904i	0.753778	−	1.30558i
$100$		0			0
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$		0			0
$103$	−13.0000			−1.28093			−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−13.0000			−1.28093			−0.640464	+	0.767988i	$0.721258\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$		0			0
$106$	5.00000			0.485643
$107$	4.00000			0.386695			0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000			0.386695			0.193347	+	0.981130i	$0.438066\pi$
$108$		0			0
$109$	−2.00000	−	3.46410i	−0.191565	−	0.331801i	0.754204	−	0.656640i	$-0.228023\pi$
$109$	−2.00000	−	3.46410i	−0.191565	−	0.331801i	−0.945769	+	0.324840i	$0.894690\pi$
$110$		0			0
$111$		0			0
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$		0			0
$115$		0			0
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$	−3.00000	−	5.19615i	−0.277350	−	0.480384i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	14.0000			1.27273
$122$		0			0
$123$		0			0
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$		0			0
$126$	−3.00000			−0.267261
$127$	−7.50000	+	12.9904i	−0.665517	+	1.15271i	0.313627	+	0.949546i	$0.398456\pi$
$127$	−7.50000	+	12.9904i	−0.665517	+	1.15271i	−0.979145	+	0.203164i	$0.934878\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	−0.500000	−	0.866025i	−0.0436852	−	0.0756650i	0.843356	−	0.537355i	$-0.180577\pi$
$131$	−0.500000	−	0.866025i	−0.0436852	−	0.0756650i	−0.887041	+	0.461690i	$0.847243\pi$
$132$		0			0
$133$	0.500000	+	4.33013i	0.0433555	+	0.375470i
$134$	12.0000			1.03664
$135$		0			0
$136$		0			0
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$		0			0
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	0.296866	+	0.954919i	$0.404058\pi$
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	−0.975417	+	0.220366i	$0.929275\pi$
$140$		0			0
$141$		0			0
$142$	3.00000	−	5.19615i	0.251754	−	0.436051i
$143$	5.00000	−	8.66025i	0.418121	−	0.724207i
$144$	−3.00000			−0.250000
$145$		0			0
$146$	−7.00000	+	12.1244i	−0.579324	+	1.00342i
$147$		0			0
$148$	−5.50000	+	9.52628i	−0.452097	+	0.783055i
$149$	2.00000	+	3.46410i	0.163846	+	0.283790i	0.936245	−	0.351348i	$-0.114277\pi$
$149$	2.00000	+	3.46410i	0.163846	+	0.283790i	−0.772399	+	0.635138i	$0.780943\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$	0.500000	+	4.33013i	0.0405554	+	0.351220i
$153$		0			0
$154$	−2.50000	−	4.33013i	−0.201456	−	0.348932i
$155$		0			0
$156$		0			0
$157$	−10.5000	−	18.1865i	−0.837991	−	1.45144i	−0.891572	−	0.452880i	$-0.850397\pi$
$157$	−10.5000	−	18.1865i	−0.837991	−	1.45144i	0.0535803	−	0.998564i	$-0.482937\pi$
$158$	5.00000	−	8.66025i	0.397779	−	0.688973i
$159$		0			0
$160$		0			0
$161$	−0.500000	+	0.866025i	−0.0394055	+	0.0682524i
$162$	4.50000	−	7.79423i	0.353553	−	0.612372i
$163$	−10.0000			−0.783260			−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000			−0.783260			−0.391630	+	0.920123i	$0.628089\pi$
$164$	−9.00000			−0.702782
$165$		0			0
$166$	−7.00000	−	12.1244i	−0.543305	−	0.941033i
$167$	−2.50000	+	4.33013i	−0.193456	+	0.335075i	−0.946393	−	0.323017i	$-0.895303\pi$
$167$	−2.50000	+	4.33013i	−0.193456	+	0.335075i	0.752937	+	0.658092i	$0.228636\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$	−12.0000	−	5.19615i	−0.917663	−	0.397360i
$172$	−6.00000			−0.457496
$173$	0.500000	+	0.866025i	0.0380143	+	0.0658427i	0.884407	−	0.466717i	$-0.154563\pi$
$173$	0.500000	+	0.866025i	0.0380143	+	0.0658427i	−0.846392	+	0.532560i	$0.821230\pi$
$174$		0			0
$175$		0			0
$176$	−2.50000	−	4.33013i	−0.188445	−	0.326396i
$177$		0			0
$178$	7.00000			0.524672
$179$	19.0000			1.42013			0.710063	−	0.704138i	$-0.248666\pi$
$179$	19.0000			1.42013			0.710063	+	0.704138i	$0.248666\pi$
$180$		0			0
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	−0.900794	−	0.434246i	$-0.857015\pi$
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	0.826465	+	0.562988i	$0.190348\pi$
$182$	−2.00000			−0.148250
$183$		0			0
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−18.0000			−1.30243			−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000			−1.30243			−0.651217	+	0.758891i	$0.725741\pi$
$192$		0			0
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	0.928986	−	0.370116i	$-0.120682\pi$
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	−0.785022	+	0.619467i	$0.787349\pi$
$194$	1.00000	−	1.73205i	0.0717958	−	0.124354i
$195$		0			0
$196$	3.00000	−	5.19615i	0.214286	−	0.371154i
$197$	−23.0000			−1.63868			−0.819341	−	0.573306i	$-0.805660\pi$
$197$	−23.0000			−1.63868			−0.819341	+	0.573306i	$0.805660\pi$
$198$	15.0000			1.06600
$199$	−12.0000	+	20.7846i	−0.850657	+	1.47338i	0.0299585	+	0.999551i	$0.490462\pi$
$199$	−12.0000	+	20.7846i	−0.850657	+	1.47338i	−0.880616	+	0.473831i	$0.842871\pi$
$200$		0			0
$201$		0			0
$202$	−10.0000			−0.703598
$203$	3.00000	−	5.19615i	0.210559	−	0.364698i
$204$		0			0
$205$		0			0
$206$	−6.50000	−	11.2583i	−0.452876	−	0.784405i
$207$	−1.50000	−	2.59808i	−0.104257	−	0.180579i
$208$	−2.00000			−0.138675
$209$	−2.50000	−	21.6506i	−0.172929	−	1.49761i
$210$		0			0
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	0.550743	−	0.834675i	$-0.314345\pi$
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$	2.50000	+	4.33013i	0.171701	+	0.297394i
$213$		0			0
$214$	2.00000	+	3.46410i	0.136717	+	0.236801i
$215$		0			0
$216$		0			0
$217$	−4.00000			−0.271538
$218$	2.00000	−	3.46410i	0.135457	−	0.234619i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−11.5000	−	19.9186i	−0.770097	−	1.33385i	−0.937509	−	0.347960i	$-0.886874\pi$
$223$	−11.5000	−	19.9186i	−0.770097	−	1.33385i	0.167412	−	0.985887i	$-0.446459\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$		0			0
$226$	6.00000	+	10.3923i	0.399114	+	0.691286i
$227$	10.0000			0.663723			0.331862	−	0.943328i	$-0.392323\pi$
$227$	10.0000			0.663723			0.331862	+	0.943328i	$0.392323\pi$
$228$		0			0
$229$	6.00000			0.396491			0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000			0.396491			0.198246	+	0.980152i	$0.436476\pi$
$230$		0			0
$231$		0			0
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	5.00000	+	8.66025i	0.327561	+	0.567352i	0.982027	−	0.188739i	$-0.0604400\pi$
$233$	5.00000	+	8.66025i	0.327561	+	0.567352i	−0.654466	+	0.756091i	$0.727107\pi$
$234$	3.00000	−	5.19615i	0.196116	−	0.339683i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	9.00000	−	15.5885i	0.579741	−	1.00414i	−0.415768	−	0.909471i	$-0.636487\pi$
$241$	9.00000	−	15.5885i	0.579741	−	1.00414i	0.995509	−	0.0946700i	$-0.0301796\pi$
$242$	7.00000	+	12.1244i	0.449977	+	0.779383i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−8.00000	−	3.46410i	−0.509028	−	0.220416i
$248$	−4.00000			−0.254000
$249$		0			0
$250$		0			0
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	−0.612159	−	0.790735i	$-0.709699\pi$
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	0.990876	+	0.134778i	$0.0430322\pi$
$252$	−1.50000	−	2.59808i	−0.0944911	−	0.163663i
$253$	2.50000	−	4.33013i	0.157174	−	0.272233i
$254$	−15.0000			−0.941184
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.00000	+	12.1244i	−0.436648	+	0.756297i	−0.997429	−	0.0716680i	$-0.977168\pi$
$257$	−7.00000	+	12.1244i	−0.436648	+	0.756297i	0.560781	+	0.827964i	$0.310501\pi$
$258$		0			0
$259$	−11.0000			−0.683507
$260$		0			0
$261$	9.00000	+	15.5885i	0.557086	+	0.964901i
$262$	0.500000	−	0.866025i	0.0308901	−	0.0535032i
$263$	5.50000	+	9.52628i	0.339145	+	0.587416i	0.984272	−	0.176659i	$-0.0565291\pi$
$263$	5.50000	+	9.52628i	0.339145	+	0.587416i	−0.645128	+	0.764075i	$0.723196\pi$
$264$		0			0
$265$		0			0
$266$	−3.50000	+	2.59808i	−0.214599	+	0.159298i
$267$		0			0
$268$	6.00000	+	10.3923i	0.366508	+	0.634811i
$269$	14.0000	+	24.2487i	0.853595	+	1.47847i	0.877942	+	0.478766i	$0.158916\pi$
$269$	14.0000	+	24.2487i	0.853595	+	1.47847i	−0.0243472	+	0.999704i	$0.507751\pi$
$270$		0			0
$271$	3.00000	+	5.19615i	0.182237	+	0.315644i	0.942642	−	0.333805i	$-0.108333\pi$
$271$	3.00000	+	5.19615i	0.182237	+	0.315644i	−0.760405	+	0.649449i	$0.775000\pi$
$272$		0			0
$273$		0			0
$274$	12.0000			0.724947
$275$		0			0
$276$		0			0
$277$	2.00000			0.120168			0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000			0.120168			0.0600842	+	0.998193i	$0.480863\pi$
$278$	−16.0000			−0.959616
$279$	6.00000	−	10.3923i	0.359211	−	0.622171i
$280$		0			0
$281$	7.50000	−	12.9904i	0.447412	−	0.774941i	−0.550804	−	0.834634i	$-0.685679\pi$
$281$	7.50000	−	12.9904i	0.447412	−	0.774941i	0.998217	+	0.0596933i	$0.0190123\pi$
$282$		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	$0.969939\pi$
$284$	6.00000			0.356034
$285$		0			0
$286$	10.0000			0.591312
$287$	−4.50000	−	7.79423i	−0.265627	−	0.460079i
$288$	−1.50000	−	2.59808i	−0.0883883	−	0.153093i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$		0			0
$292$	−14.0000			−0.819288
$293$	21.0000			1.22683			0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000			1.22683			0.613417	+	0.789760i	$0.289795\pi$
$294$		0			0
$295$		0			0
$296$	−11.0000			−0.639362
$297$		0			0
$298$	−2.00000	+	3.46410i	−0.115857	+	0.200670i
$299$	−1.00000	−	1.73205i	−0.0578315	−	0.100167i
$300$		0			0
$301$	−3.00000	−	5.19615i	−0.172917	−	0.299501i
$302$	−8.00000	−	13.8564i	−0.460348	−	0.797347i
$303$		0			0
$304$	−3.50000	+	2.59808i	−0.200739	+	0.149010i
$305$		0			0
$306$		0			0
$307$	−1.00000	−	1.73205i	−0.0570730	−	0.0988534i	0.836077	−	0.548612i	$-0.184843\pi$
$307$	−1.00000	−	1.73205i	−0.0570730	−	0.0988534i	−0.893150	+	0.449758i	$0.851510\pi$
$308$	2.50000	−	4.33013i	0.142451	−	0.246732i
$309$		0			0
$310$		0			0
$311$	4.00000			0.226819			0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000			0.226819			0.113410	+	0.993548i	$0.463823\pi$
$312$		0			0
$313$	−14.0000	+	24.2487i	−0.791327	+	1.37062i	0.133819	+	0.991006i	$0.457276\pi$
$313$	−14.0000	+	24.2487i	−0.791327	+	1.37062i	−0.925146	+	0.379612i	$0.876057\pi$
$314$	10.5000	−	18.1865i	0.592549	−	1.02633i
$315$		0			0
$316$	10.0000			0.562544
$317$	−13.5000	+	23.3827i	−0.758236	+	1.31330i	0.185514	+	0.982642i	$0.440605\pi$
$317$	−13.5000	+	23.3827i	−0.758236	+	1.31330i	−0.943750	+	0.330661i	$0.892728\pi$
$318$		0			0
$319$	−15.0000	+	25.9808i	−0.839839	+	1.45464i
$320$		0			0
$321$		0			0
$322$	−1.00000			−0.0557278
$323$		0			0
$324$	9.00000			0.500000
$325$		0			0
$326$	−5.00000	−	8.66025i	−0.276924	−	0.479647i
$327$		0			0
$328$	−4.50000	−	7.79423i	−0.248471	−	0.430364i
$329$		0			0
$330$		0			0
$331$	−25.0000			−1.37412			−0.687062	−	0.726599i	$-0.741100\pi$
$331$	−25.0000			−1.37412			−0.687062	+	0.726599i	$0.741100\pi$
$332$	7.00000	−	12.1244i	0.384175	−	0.665410i
$333$	16.5000	−	28.5788i	0.904194	−	1.56611i
$334$	−5.00000			−0.273588
$335$		0			0
$336$		0			0
$337$	3.00000	+	5.19615i	0.163420	+	0.283052i	0.936093	−	0.351752i	$-0.114414\pi$
$337$	3.00000	+	5.19615i	0.163420	+	0.283052i	−0.772673	+	0.634804i	$0.781081\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$		0			0
$340$		0			0
$341$	20.0000			1.08306
$342$	−1.50000	−	12.9904i	−0.0811107	−	0.702439i
$343$	13.0000			0.701934
$344$	−3.00000	−	5.19615i	−0.161749	−	0.280158i
$345$		0			0
$346$	−0.500000	+	0.866025i	−0.0268802	+	0.0465578i
$347$	9.00000	+	15.5885i	0.483145	+	0.836832i	0.999813	−	0.0193540i	$-0.00616095\pi$
$347$	9.00000	+	15.5885i	0.483145	+	0.836832i	−0.516667	+	0.856186i	$0.672828\pi$
$348$		0			0
$349$	−28.0000			−1.49881			−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000			−1.49881			−0.749403	+	0.662114i	$0.769659\pi$
$350$		0			0
$351$		0			0
$352$	2.50000	−	4.33013i	0.133250	−	0.230797i
$353$	−4.00000			−0.212899			−0.106449	−	0.994318i	$-0.533948\pi$
$353$	−4.00000			−0.212899			−0.106449	+	0.994318i	$0.533948\pi$
$354$		0			0
$355$		0			0
$356$	3.50000	+	6.06218i	0.185500	+	0.321295i
$357$		0			0
$358$	9.50000	+	16.4545i	0.502091	+	0.869646i
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	0.703382	−	0.710812i	$-0.251672\pi$
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	−0.967272	+	0.253741i	$0.918339\pi$
$360$		0			0
$361$	−18.5000	+	4.33013i	−0.973684	+	0.227901i
$362$	−2.00000			−0.105118
$363$		0			0
$364$	−1.00000	−	1.73205i	−0.0524142	−	0.0907841i
$365$		0			0
$366$		0			0
$367$	−2.00000	+	3.46410i	−0.104399	+	0.180825i	−0.913493	−	0.406855i	$-0.866625\pi$
$367$	−2.00000	+	3.46410i	−0.104399	+	0.180825i	0.809093	+	0.587680i	$0.199959\pi$
$368$	−1.00000			−0.0521286
$369$	27.0000			1.40556
$370$		0			0
$371$	−2.50000	+	4.33013i	−0.129794	+	0.224809i
$372$		0			0
$373$	−31.0000			−1.60512			−0.802560	−	0.596572i	$-0.796529\pi$
$373$	−31.0000			−1.60512			−0.802560	+	0.596572i	$0.796529\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.00000	+	10.3923i	0.309016	+	0.535231i
$378$		0			0
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$		0			0
$381$		0			0
$382$	−9.00000	−	15.5885i	−0.460480	−	0.797575i
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	0.949938	−	0.312437i	$-0.101145\pi$
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	−0.745548	+	0.666452i	$0.767812\pi$
$384$		0			0
$385$		0			0
$386$	−2.00000	+	3.46410i	−0.101797	+	0.176318i
$387$	18.0000			0.914991
$388$	2.00000			0.101535
$389$	−13.0000	+	22.5167i	−0.659126	+	1.14164i	0.321716	+	0.946836i	$0.395740\pi$
$389$	−13.0000	+	22.5167i	−0.659126	+	1.14164i	−0.980842	+	0.194804i	$0.937593\pi$
$390$		0			0
$391$		0			0
$392$	6.00000			0.303046
$393$		0			0
$394$	−11.5000	−	19.9186i	−0.579362	−	1.00348i
$395$		0			0
$396$	7.50000	+	12.9904i	0.376889	+	0.652791i
$397$	14.5000	+	25.1147i	0.727734	+	1.26047i	0.957839	+	0.287307i	$0.0927599\pi$
$397$	14.5000	+	25.1147i	0.727734	+	1.26047i	−0.230105	+	0.973166i	$0.573907\pi$
$398$	−24.0000			−1.20301
$399$		0			0
$400$		0			0
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	0.998350	−	0.0574304i	$-0.0182907\pi$
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	−0.548911	+	0.835881i	$0.684957\pi$
$402$		0			0
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$	−5.00000	−	8.66025i	−0.248759	−	0.430864i
$405$		0			0
$406$	6.00000			0.297775
$407$	55.0000			2.72625
$408$		0			0
$409$	5.50000	−	9.52628i	0.271957	−	0.471044i	−0.697406	−	0.716677i	$-0.745662\pi$
$409$	5.50000	−	9.52628i	0.271957	−	0.471044i	0.969363	+	0.245633i	$0.0789957\pi$
$410$		0			0
$411$		0			0
$412$	6.50000	−	11.2583i	0.320232	−	0.554658i
$413$		0			0
$414$	1.50000	−	2.59808i	0.0737210	−	0.127688i
$415$		0			0
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$		0			0
$418$	17.5000	−	12.9904i	0.855953	−	0.635380i
$419$	−7.00000			−0.341972			−0.170986	−	0.985273i	$-0.554695\pi$
$419$	−7.00000			−0.341972			−0.170986	+	0.985273i	$0.554695\pi$
$420$		0			0
$421$	4.00000	+	6.92820i	0.194948	+	0.337660i	0.946883	−	0.321577i	$-0.104213\pi$
$421$	4.00000	+	6.92820i	0.194948	+	0.337660i	−0.751935	+	0.659237i	$0.770879\pi$
$422$	6.50000	−	11.2583i	0.316415	−	0.548047i
$423$		0			0
$424$	−2.50000	+	4.33013i	−0.121411	+	0.210290i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−2.00000	+	3.46410i	−0.0966736	+	0.167444i
$429$		0			0
$430$		0			0
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$		0			0
$433$	1.00000	−	1.73205i	0.0480569	−	0.0832370i	−0.840996	−	0.541041i	$-0.818030\pi$
$433$	1.00000	−	1.73205i	0.0480569	−	0.0832370i	0.889053	+	0.457804i	$0.151364\pi$
$434$	−2.00000	−	3.46410i	−0.0960031	−	0.166282i
$435$		0			0
$436$	4.00000			0.191565
$437$	−4.00000	−	1.73205i	−0.191346	−	0.0828552i
$438$		0			0
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$		0			0
$441$	−9.00000	+	15.5885i	−0.428571	+	0.742307i
$442$		0			0
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	−0.0212481	−	0.999774i	$-0.506764\pi$
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	0.876454	−	0.481486i	$-0.159903\pi$
$444$		0			0
$445$		0			0
$446$	11.5000	−	19.9186i	0.544541	−	0.943172i
$447$		0			0
$448$	−1.00000			−0.0472456
$449$	−19.0000			−0.896665			−0.448333	−	0.893867i	$-0.647982\pi$
$449$	−19.0000			−0.896665			−0.448333	+	0.893867i	$0.647982\pi$
$450$		0			0
$451$	22.5000	+	38.9711i	1.05948	+	1.83508i
$452$	−6.00000	+	10.3923i	−0.282216	+	0.488813i
$453$		0			0
$454$	5.00000	+	8.66025i	0.234662	+	0.406446i
$455$		0			0
$456$		0			0
$457$	32.0000			1.49690			0.748448	−	0.663193i	$-0.230799\pi$
$457$	32.0000			1.49690			0.748448	+	0.663193i	$0.230799\pi$
$458$	3.00000	+	5.19615i	0.140181	+	0.242800i
$459$		0			0
$460$		0			0
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	0.968945	+	0.247276i	$0.0795353\pi$
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	−0.270326	+	0.962769i	$0.587131\pi$
$462$		0			0
$463$	−37.0000			−1.71954			−0.859768	−	0.510685i	$-0.829392\pi$
$463$	−37.0000			−1.71954			−0.859768	+	0.510685i	$0.829392\pi$
$464$	6.00000			0.278543
$465$		0			0
$466$	−5.00000	+	8.66025i	−0.231621	+	0.401179i
$467$	−34.0000			−1.57333			−0.786666	−	0.617379i	$-0.788195\pi$
$467$	−34.0000			−1.57333			−0.786666	+	0.617379i	$0.788195\pi$
$468$	6.00000			0.277350
$469$	−6.00000	+	10.3923i	−0.277054	+	0.479872i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	15.0000	+	25.9808i	0.689701	+	1.19460i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−7.50000	−	12.9904i	−0.343401	−	0.594789i
$478$	8.00000	+	13.8564i	0.365911	+	0.633777i
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	−0.583803	−	0.811895i	$-0.698436\pi$
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	0.995023	+	0.0996406i	$0.0317693\pi$
$480$		0			0
$481$	11.0000	−	19.0526i	0.501557	−	0.868722i
$482$	18.0000			0.819878
$483$		0			0
$484$	−7.00000	+	12.1244i	−0.318182	+	0.551107i
$485$		0			0
$486$		0			0
$487$	23.0000			1.04223			0.521115	−	0.853487i	$-0.325516\pi$
$487$	23.0000			1.04223			0.521115	+	0.853487i	$0.325516\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−13.5000	−	23.3827i	−0.609246	−	1.05525i	−0.991365	−	0.131132i	$-0.958139\pi$
$491$	−13.5000	−	23.3827i	−0.609246	−	1.05525i	0.382118	−	0.924113i	$-0.375195\pi$
$492$		0			0
$493$		0			0
$494$	−1.00000	−	8.66025i	−0.0449921	−	0.389643i
$495$		0			0
$496$	−2.00000	−	3.46410i	−0.0898027	−	0.155543i
$497$	3.00000	+	5.19615i	0.134568	+	0.233079i
$498$		0			0
$499$	19.5000	+	33.7750i	0.872940	+	1.51198i	0.858941	+	0.512074i	$0.171123\pi$
$499$	19.5000	+	33.7750i	0.872940	+	1.51198i	0.0139987	+	0.999902i	$0.495544\pi$
$500$		0			0
$501$		0			0
$502$	12.0000			0.535586
$503$	−16.5000	+	28.5788i	−0.735699	+	1.27427i	0.218718	+	0.975788i	$0.429813\pi$
$503$	−16.5000	+	28.5788i	−0.735699	+	1.27427i	−0.954416	+	0.298479i	$0.903521\pi$
$504$	1.50000	−	2.59808i	0.0668153	−	0.115728i
$505$		0			0
$506$	5.00000			0.222277
$507$		0			0
$508$	−7.50000	−	12.9904i	−0.332759	−	0.576355i
$509$	−7.00000	+	12.1244i	−0.310270	+	0.537403i	−0.978421	−	0.206623i	$-0.933753\pi$
$509$	−7.00000	+	12.1244i	−0.310270	+	0.537403i	0.668151	+	0.744026i	$0.267086\pi$
$510$		0			0
$511$	−7.00000	−	12.1244i	−0.309662	−	0.536350i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−14.0000			−0.617514
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−5.50000	−	9.52628i	−0.241656	−	0.418561i
$519$		0			0
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$	−9.00000	+	15.5885i	−0.393919	+	0.682288i
$523$	−21.0000	+	36.3731i	−0.918266	+	1.59048i	−0.116218	+	0.993224i	$0.537077\pi$
$523$	−21.0000	+	36.3731i	−0.918266	+	1.59048i	−0.802048	+	0.597259i	$0.796256\pi$
$524$	1.00000			0.0436852
$525$		0			0
$526$	−5.50000	+	9.52628i	−0.239811	+	0.415366i
$527$		0			0
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$		0			0
$531$		0			0
$532$	−4.00000	−	1.73205i	−0.173422	−	0.0750939i
$533$	18.0000			0.779667
$534$		0			0
$535$		0			0
$536$	−6.00000	+	10.3923i	−0.259161	+	0.448879i
$537$		0			0
$538$	−14.0000	+	24.2487i	−0.603583	+	1.04544i
$539$	−30.0000			−1.29219
$540$		0			0
$541$	10.0000	−	17.3205i	0.429934	−	0.744667i	−0.566933	−	0.823764i	$-0.691870\pi$
$541$	10.0000	−	17.3205i	0.429934	−	0.744667i	0.996867	+	0.0790969i	$0.0252036\pi$
$542$	−3.00000	+	5.19615i	−0.128861	+	0.223194i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−11.0000	+	19.0526i	−0.470326	+	0.814629i	−0.999424	−	0.0339321i	$-0.989197\pi$
$547$	−11.0000	+	19.0526i	−0.470326	+	0.814629i	0.529098	+	0.848561i	$0.322530\pi$
$548$	6.00000	+	10.3923i	0.256307	+	0.443937i
$549$		0			0
$550$		0			0
$551$	24.0000	+	10.3923i	1.02243	+	0.442727i
$552$		0			0
$553$	5.00000	+	8.66025i	0.212622	+	0.368271i
$554$	1.00000	+	1.73205i	0.0424859	+	0.0735878i
$555$		0			0
$556$	−8.00000	−	13.8564i	−0.339276	−	0.587643i
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	−0.945473	−	0.325701i	$-0.894400\pi$
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	0.754802	+	0.655953i	$0.227733\pi$
$558$	12.0000			0.508001
$559$	12.0000			0.507546
$560$		0			0
$561$		0			0
$562$	15.0000			0.632737
$563$	−32.0000			−1.34864			−0.674320	−	0.738440i	$-0.735563\pi$
$563$	−32.0000			−1.34864			−0.674320	+	0.738440i	$0.735563\pi$
$564$		0			0
$565$		0			0
$566$	7.00000	−	12.1244i	0.294232	−	0.509625i
$567$	4.50000	+	7.79423i	0.188982	+	0.327327i
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	45.0000			1.88650			0.943249	−	0.332086i	$-0.107752\pi$
$569$	45.0000			1.88650			0.943249	+	0.332086i	$0.107752\pi$
$570$		0			0
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$	5.00000	+	8.66025i	0.209061	+	0.362103i
$573$		0			0
$574$	4.50000	−	7.79423i	0.187826	−	0.325325i
$575$		0			0
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	−32.0000			−1.33218			−0.666089	−	0.745873i	$-0.732033\pi$
$577$	−32.0000			−1.33218			−0.666089	+	0.745873i	$0.732033\pi$
$578$	17.0000			0.707107
$579$		0			0
$580$		0			0
$581$	14.0000			0.580818
$582$		0			0
$583$	12.5000	−	21.6506i	0.517697	−	0.896678i
$584$	−7.00000	−	12.1244i	−0.289662	−	0.501709i
$585$		0			0
$586$	10.5000	+	18.1865i	0.433751	+	0.751279i
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	0.962872	−	0.269957i	$-0.0870095\pi$
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	−0.715226	+	0.698893i	$0.753676\pi$
$588$		0			0
$589$	−2.00000	−	17.3205i	−0.0824086	−	0.713679i
$590$		0			0
$591$		0			0
$592$	−5.50000	−	9.52628i	−0.226049	−	0.391528i
$593$	21.0000	−	36.3731i	0.862367	−	1.49366i	−0.00727173	−	0.999974i	$-0.502315\pi$
$593$	21.0000	−	36.3731i	0.862367	−	1.49366i	0.869638	−	0.493689i	$-0.164352\pi$
$594$		0			0
$595$		0			0
$596$	−4.00000			−0.163846
$597$		0			0
$598$	1.00000	−	1.73205i	0.0408930	−	0.0708288i
$599$	22.0000	−	38.1051i	0.898896	−	1.55693i	0.0699877	−	0.997548i	$-0.477704\pi$
$599$	22.0000	−	38.1051i	0.898896	−	1.55693i	0.828908	−	0.559385i	$-0.188963\pi$
$600$		0			0
$601$	21.0000			0.856608			0.428304	−	0.903635i	$-0.359111\pi$
$601$	21.0000			0.856608			0.428304	+	0.903635i	$0.359111\pi$
$602$	3.00000	−	5.19615i	0.122271	−	0.211779i
$603$	−18.0000	−	31.1769i	−0.733017	−	1.26962i
$604$	8.00000	−	13.8564i	0.325515	−	0.563809i
$605$		0			0
$606$		0			0
$607$	−13.0000			−0.527654			−0.263827	−	0.964570i	$-0.584985\pi$
$607$	−13.0000			−0.527654			−0.263827	+	0.964570i	$0.584985\pi$
$608$	−4.00000	−	1.73205i	−0.162221	−	0.0702439i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	0.999984	+	0.00563283i	$0.00179300\pi$
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	−0.495114	+	0.868828i	$0.664874\pi$
$614$	1.00000	−	1.73205i	0.0403567	−	0.0698999i
$615$		0			0
$616$	5.00000			0.201456
$617$	10.0000	−	17.3205i	0.402585	−	0.697297i	−0.591452	−	0.806340i	$-0.701445\pi$
$617$	10.0000	−	17.3205i	0.402585	−	0.697297i	0.994037	+	0.109043i	$0.0347785\pi$
$618$		0			0
$619$	−45.0000			−1.80870			−0.904351	−	0.426789i	$-0.859645\pi$
$619$	−45.0000			−1.80870			−0.904351	+	0.426789i	$0.859645\pi$
$620$		0			0
$621$		0			0
$622$	2.00000	+	3.46410i	0.0801927	+	0.138898i
$623$	−3.50000	+	6.06218i	−0.140225	+	0.242876i
$624$		0			0
$625$		0			0
$626$	−28.0000			−1.11911
$627$		0			0
$628$	21.0000			0.837991
$629$		0			0
$630$		0			0
$631$	11.0000	−	19.0526i	0.437903	−	0.758470i	−0.559625	−	0.828746i	$-0.689055\pi$
$631$	11.0000	−	19.0526i	0.437903	−	0.758470i	0.997528	+	0.0702759i	$0.0223880\pi$
$632$	5.00000	+	8.66025i	0.198889	+	0.344486i
$633$		0			0
$634$	−27.0000			−1.07231
$635$		0			0
$636$		0			0
$637$	−6.00000	+	10.3923i	−0.237729	+	0.411758i
$638$	−30.0000			−1.18771
$639$	−18.0000			−0.712069
$640$		0			0
$641$	5.00000	+	8.66025i	0.197488	+	0.342059i	0.947713	−	0.319123i	$-0.103388\pi$
$641$	5.00000	+	8.66025i	0.197488	+	0.342059i	−0.750225	+	0.661182i	$0.770055\pi$
$642$		0			0
$643$	−8.00000	−	13.8564i	−0.315489	−	0.546443i	0.664052	−	0.747686i	$-0.268835\pi$
$643$	−8.00000	−	13.8564i	−0.315489	−	0.546443i	−0.979541	+	0.201243i	$0.935502\pi$
$644$	−0.500000	−	0.866025i	−0.0197028	−	0.0341262i
$645$		0			0
$646$		0			0
$647$	3.00000			0.117942			0.0589711	−	0.998260i	$-0.481218\pi$
$647$	3.00000			0.117942			0.0589711	+	0.998260i	$0.481218\pi$
$648$	4.50000	+	7.79423i	0.176777	+	0.306186i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	5.00000	−	8.66025i	0.195815	−	0.339162i
$653$	25.0000			0.978326			0.489163	−	0.872192i	$-0.337302\pi$
$653$	25.0000			0.978326			0.489163	+	0.872192i	$0.337302\pi$
$654$		0			0
$655$		0			0
$656$	4.50000	−	7.79423i	0.175695	−	0.304314i
$657$	42.0000			1.63858
$658$		0			0
$659$	7.50000	−	12.9904i	0.292159	−	0.506033i	−0.682161	−	0.731202i	$-0.738960\pi$
$659$	7.50000	−	12.9904i	0.292159	−	0.506033i	0.974320	+	0.225168i	$0.0722932\pi$
$660$		0			0
$661$	−12.0000	+	20.7846i	−0.466746	+	0.808428i	−0.999278	−	0.0379819i	$-0.987907\pi$
$661$	−12.0000	+	20.7846i	−0.466746	+	0.808428i	0.532533	+	0.846410i	$0.321240\pi$
$662$	−12.5000	−	21.6506i	−0.485826	−	0.841476i
$663$		0			0
$664$	14.0000			0.543305
$665$		0			0
$666$	33.0000			1.27872
$667$	3.00000	+	5.19615i	0.116160	+	0.201196i
$668$	−2.50000	−	4.33013i	−0.0967279	−	0.167538i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−16.0000			−0.616755			−0.308377	−	0.951264i	$-0.599786\pi$
$673$	−16.0000			−0.616755			−0.308377	+	0.951264i	$0.599786\pi$
$674$	−3.00000	+	5.19615i	−0.115556	+	0.200148i
$675$		0			0
$676$	−9.00000			−0.346154
$677$	−27.0000			−1.03769			−0.518847	−	0.854867i	$-0.673639\pi$
$677$	−27.0000			−1.03769			−0.518847	+	0.854867i	$0.673639\pi$
$678$		0			0
$679$	1.00000	+	1.73205i	0.0383765	+	0.0664700i
$680$		0			0
$681$		0			0
$682$	10.0000	+	17.3205i	0.382920	+	0.663237i
$683$	44.0000			1.68361			0.841807	−	0.539779i	$-0.181492\pi$
$683$	44.0000			1.68361			0.841807	+	0.539779i	$0.181492\pi$
$684$	10.5000	−	7.79423i	0.401478	−	0.298020i
$685$		0			0
$686$	6.50000	+	11.2583i	0.248171	+	0.429845i
$687$		0			0
$688$	3.00000	−	5.19615i	0.114374	−	0.198101i
$689$	−5.00000	−	8.66025i	−0.190485	−	0.329929i
$690$		0			0
$691$	−15.0000			−0.570627			−0.285313	−	0.958434i	$-0.592098\pi$
$691$	−15.0000			−0.570627			−0.285313	+	0.958434i	$0.592098\pi$
$692$	−1.00000			−0.0380143
$693$	−7.50000	+	12.9904i	−0.284901	+	0.493464i
$694$	−9.00000	+	15.5885i	−0.341635	+	0.591730i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−14.0000	−	24.2487i	−0.529908	−	0.917827i
$699$		0			0
$700$		0			0
$701$	−3.00000	−	5.19615i	−0.113308	−	0.196256i	0.803794	−	0.594908i	$-0.202811\pi$
$701$	−3.00000	−	5.19615i	−0.113308	−	0.196256i	−0.917102	+	0.398652i	$0.869478\pi$
$702$		0			0
$703$	−5.50000	−	47.6314i	−0.207436	−	1.79645i
$704$	5.00000			0.188445
$705$		0			0
$706$	−2.00000	−	3.46410i	−0.0752710	−	0.130373i
$707$	5.00000	−	8.66025i	0.188044	−	0.325702i
$708$		0			0
$709$	−4.00000	+	6.92820i	−0.150223	+	0.260194i	−0.931309	−	0.364229i	$-0.881333\pi$
$709$	−4.00000	+	6.92820i	−0.150223	+	0.260194i	0.781086	+	0.624423i	$0.214666\pi$
$710$		0			0
$711$	−30.0000			−1.12509
$712$	−3.50000	+	6.06218i	−0.131168	+	0.227190i
$713$	2.00000	−	3.46410i	0.0749006	−	0.129732i
$714$		0			0
$715$		0			0
$716$	−9.50000	+	16.4545i	−0.355032	+	0.614933i
$717$		0			0
$718$	5.00000	−	8.66025i	0.186598	−	0.323198i
$719$	24.0000	+	41.5692i	0.895049	+	1.55027i	0.833744	+	0.552151i	$0.186193\pi$
$719$	24.0000	+	41.5692i	0.895049	+	1.55027i	0.0613050	+	0.998119i	$0.480474\pi$
$720$		0			0
$721$	13.0000			0.484145
$722$	−13.0000	−	13.8564i	−0.483810	−	0.515682i
$723$		0			0
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$		0			0
$726$		0			0
$727$	−8.00000	−	13.8564i	−0.296704	−	0.513906i	0.678676	−	0.734438i	$-0.262554\pi$
$727$	−8.00000	−	13.8564i	−0.296704	−	0.513906i	−0.975380	+	0.220532i	$0.929221\pi$
$728$	1.00000	−	1.73205i	0.0370625	−	0.0641941i
$729$	−27.0000			−1.00000
$730$		0			0
$731$		0			0
$732$		0			0
$733$	15.0000			0.554038			0.277019	−	0.960864i	$-0.410654\pi$
$733$	15.0000			0.554038			0.277019	+	0.960864i	$0.410654\pi$
$734$	−4.00000			−0.147643
$735$		0			0
$736$	−0.500000	−	0.866025i	−0.0184302	−	0.0319221i
$737$	30.0000	−	51.9615i	1.10506	−	1.91403i
$738$	13.5000	+	23.3827i	0.496942	+	0.860729i
$739$	15.5000	+	26.8468i	0.570177	+	0.987575i	0.996547	+	0.0830265i	$0.0264586\pi$
$739$	15.5000	+	26.8468i	0.570177	+	0.987575i	−0.426371	+	0.904549i	$0.640208\pi$
$740$		0			0
$741$		0			0
$742$	−5.00000			−0.183556
$743$	−7.50000	−	12.9904i	−0.275148	−	0.476571i	0.695024	−	0.718986i	$-0.255394\pi$
$743$	−7.50000	−	12.9904i	−0.275148	−	0.476571i	−0.970173	+	0.242415i	$0.922060\pi$
$744$		0			0
$745$		0			0
$746$	−15.5000	−	26.8468i	−0.567495	−	0.982931i
$747$	−21.0000	+	36.3731i	−0.768350	+	1.33082i
$748$		0			0
$749$	−4.00000			−0.146157
$750$		0			0
$751$	10.0000	−	17.3205i	0.364905	−	0.632034i	−0.623856	−	0.781540i	$-0.714435\pi$
$751$	10.0000	−	17.3205i	0.364905	−	0.632034i	0.988761	+	0.149505i	$0.0477681\pi$
$752$		0			0
$753$		0			0
$754$	−6.00000	+	10.3923i	−0.218507	+	0.378465i
$755$		0			0
$756$		0			0
$757$	−7.50000	−	12.9904i	−0.272592	−	0.472143i	0.696933	−	0.717137i	$-0.254548\pi$
$757$	−7.50000	−	12.9904i	−0.272592	−	0.472143i	−0.969525	+	0.244993i	$0.921214\pi$
$758$	−6.00000	−	10.3923i	−0.217930	−	0.377466i
$759$		0			0
$760$		0			0
$761$	−43.0000			−1.55875			−0.779374	−	0.626559i	$-0.784463\pi$
$761$	−43.0000			−1.55875			−0.779374	+	0.626559i	$0.784463\pi$
$762$		0			0
$763$	2.00000	+	3.46410i	0.0724049	+	0.125409i
$764$	9.00000	−	15.5885i	0.325609	−	0.563971i
$765$		0			0
$766$	−4.00000	+	6.92820i	−0.144526	+	0.250326i
$767$		0			0
$768$		0			0
$769$	13.0000	−	22.5167i	0.468792	−	0.811972i	−0.530572	−	0.847640i	$-0.678023\pi$
$769$	13.0000	−	22.5167i	0.468792	−	0.811972i	0.999364	+	0.0356685i	$0.0113561\pi$
$770$		0			0
$771$		0			0
$772$	−4.00000			−0.143963
$773$	22.5000	−	38.9711i	0.809269	−	1.40169i	−0.104102	−	0.994567i	$-0.533197\pi$
$773$	22.5000	−	38.9711i	0.809269	−	1.40169i	0.913371	−	0.407128i	$-0.133470\pi$
$774$	9.00000	+	15.5885i	0.323498	+	0.560316i
$775$		0			0
$776$	1.00000	+	1.73205i	0.0358979	+	0.0621770i
$777$		0			0
$778$	−26.0000			−0.932145
$779$	31.5000	−	23.3827i	1.12860	−	0.837772i
$780$		0			0
$781$	−15.0000	−	25.9808i	−0.536742	−	0.929665i
$782$		0			0
$783$		0			0
$784$	3.00000	+	5.19615i	0.107143	+	0.185577i
$785$		0			0
$786$		0			0
$787$	−18.0000			−0.641631			−0.320815	−	0.947142i	$-0.603957\pi$
$787$	−18.0000			−0.641631			−0.320815	+	0.947142i	$0.603957\pi$
$788$	11.5000	−	19.9186i	0.409671	−	0.709570i
$789$		0			0
$790$		0			0
$791$	−12.0000			−0.426671
$792$	−7.50000	+	12.9904i	−0.266501	+	0.461593i
$793$		0			0
$794$	−14.5000	+	25.1147i	−0.514586	+	0.891289i
$795$		0			0
$796$	−12.0000	−	20.7846i	−0.425329	−	0.736691i
$797$	−49.0000			−1.73567			−0.867835	−	0.496853i	$-0.834489\pi$
$797$	−49.0000			−1.73567			−0.867835	+	0.496853i	$0.834489\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−10.5000	−	18.1865i	−0.370999	−	0.642590i
$802$	−9.00000	+	15.5885i	−0.317801	+	0.550448i
$803$	35.0000	+	60.6218i	1.23512	+	2.13930i
$804$		0			0
$805$		0			0
$806$	8.00000			0.281788
$807$		0			0
$808$	5.00000	−	8.66025i	0.175899	−	0.304667i
$809$	−2.00000			−0.0703163			−0.0351581	−	0.999382i	$-0.511193\pi$
$809$	−2.00000			−0.0703163			−0.0351581	+	0.999382i	$0.511193\pi$
$810$		0			0
$811$	2.50000	−	4.33013i	0.0877869	−	0.152051i	−0.818788	−	0.574095i	$-0.805354\pi$
$811$	2.50000	−	4.33013i	0.0877869	−	0.152051i	0.906575	+	0.422044i	$0.138687\pi$
$812$	3.00000	+	5.19615i	0.105279	+	0.182349i
$813$		0			0
$814$	27.5000	+	47.6314i	0.963875	+	1.66948i
$815$		0			0
$816$		0			0
$817$	21.0000	−	15.5885i	0.734697	−	0.545371i
$818$	11.0000			0.384606
$819$	3.00000	+	5.19615i	0.104828	+	0.181568i
$820$		0			0
$821$	−25.0000	+	43.3013i	−0.872506	+	1.51122i	−0.0131101	+	0.999914i	$0.504173\pi$
$821$	−25.0000	+	43.3013i	−0.872506	+	1.51122i	−0.859396	+	0.511311i	$0.829160\pi$
$822$		0			0
$823$	−18.5000	+	32.0429i	−0.644869	+	1.11695i	0.339462	+	0.940620i	$0.389755\pi$
$823$	−18.5000	+	32.0429i	−0.644869	+	1.11695i	−0.984332	+	0.176327i	$0.943578\pi$
$824$	13.0000			0.452876
$825$		0			0
$826$		0			0
$827$	3.00000	−	5.19615i	0.104320	−	0.180688i	−0.809140	−	0.587616i	$-0.800067\pi$
$827$	3.00000	−	5.19615i	0.104320	−	0.180688i	0.913460	+	0.406928i	$0.133400\pi$
$828$	3.00000			0.104257
$829$	−52.0000			−1.80603			−0.903017	−	0.429604i	$-0.858653\pi$
$829$	−52.0000			−1.80603			−0.903017	+	0.429604i	$0.858653\pi$
$830$		0			0
$831$		0			0
$832$	1.00000	−	1.73205i	0.0346688	−	0.0600481i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	20.0000	+	8.66025i	0.691714	+	0.299521i
$837$		0			0
$838$	−3.50000	−	6.06218i	−0.120905	−	0.209414i
$839$	−13.0000	−	22.5167i	−0.448810	−	0.777361i	0.549499	−	0.835494i	$-0.314819\pi$
$839$	−13.0000	−	22.5167i	−0.448810	−	0.777361i	−0.998309	+	0.0581329i	$0.981485\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−4.00000	+	6.92820i	−0.137849	+	0.238762i
$843$		0			0
$844$	13.0000			0.447478
$845$		0			0
$846$		0			0
$847$	−14.0000			−0.481046
$848$	−5.00000			−0.171701
$849$		0			0
$850$		0			0
$851$	5.50000	−	9.52628i	0.188538	−	0.326557i
$852$		0			0
$853$	27.0000	+	46.7654i	0.924462	+	1.60122i	0.792424	+	0.609971i	$0.208819\pi$
$853$	27.0000	+	46.7654i	0.924462	+	1.60122i	0.132039	+	0.991245i	$0.457848\pi$
$854$		0			0
$855$		0			0
$856$	−4.00000			−0.136717
$857$	−14.0000	−	24.2487i	−0.478231	−	0.828320i	0.521458	−	0.853277i	$-0.325388\pi$
$857$	−14.0000	−	24.2487i	−0.478231	−	0.828320i	−0.999689	+	0.0249570i	$0.992055\pi$
$858$		0			0
$859$	24.5000	−	42.4352i	0.835929	−	1.44787i	−0.0573424	−	0.998355i	$-0.518263\pi$
$859$	24.5000	−	42.4352i	0.835929	−	1.44787i	0.893272	−	0.449517i	$-0.148404\pi$
$860$		0			0
$861$		0			0
$862$	−12.0000			−0.408722
$863$	−17.0000			−0.578687			−0.289343	−	0.957225i	$-0.593437\pi$
$863$	−17.0000			−0.578687			−0.289343	+	0.957225i	$0.593437\pi$
$864$		0			0
$865$		0			0
$866$	2.00000			0.0679628
$867$		0			0
$868$	2.00000	−	3.46410i	0.0678844	−	0.117579i
$869$	−25.0000	−	43.3013i	−0.848067	−	1.46889i
$870$		0			0
$871$	−12.0000	−	20.7846i	−0.406604	−	0.704260i
$872$	2.00000	+	3.46410i	0.0677285	+	0.117309i
$873$	−6.00000			−0.203069
$874$	−0.500000	−	4.33013i	−0.0169128	−	0.146469i
$875$		0			0
$876$		0			0
$877$	1.50000	+	2.59808i	0.0506514	+	0.0877308i	0.890239	−	0.455493i	$-0.150537\pi$
$877$	1.50000	+	2.59808i	0.0506514	+	0.0877308i	−0.839588	+	0.543224i	$0.817204\pi$
$878$	4.00000	−	6.92820i	0.134993	−	0.233816i
$879$		0			0
$880$		0			0
$881$	−35.0000			−1.17918			−0.589590	−	0.807703i	$-0.700711\pi$
$881$	−35.0000			−1.17918			−0.589590	+	0.807703i	$0.700711\pi$
$882$	−18.0000			−0.606092
$883$	−18.0000	+	31.1769i	−0.605748	+	1.04919i	0.386185	+	0.922422i	$0.373793\pi$
$883$	−18.0000	+	31.1769i	−0.605748	+	1.04919i	−0.991933	+	0.126765i	$0.959541\pi$
$884$		0			0
$885$		0			0
$886$	36.0000			1.20944
$887$	28.0000	−	48.4974i	0.940148	−	1.62838i	0.174962	−	0.984575i	$-0.444020\pi$
$887$	28.0000	−	48.4974i	0.940148	−	1.62838i	0.765186	−	0.643809i	$-0.222647\pi$
$888$		0			0
$889$	7.50000	−	12.9904i	0.251542	−	0.435683i
$890$		0			0
$891$	−22.5000	−	38.9711i	−0.753778	−	1.30558i
$892$	23.0000			0.770097
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$		0			0
$898$	−9.50000	−	16.4545i	−0.317019	−	0.549093i
$899$	−12.0000	+	20.7846i	−0.400222	+	0.693206i
$900$		0			0
$901$		0			0
$902$	−22.5000	+	38.9711i	−0.749168	+	1.29760i
$903$		0			0
$904$	−12.0000			−0.399114
$905$		0			0
$906$		0			0
$907$	−5.00000	−	8.66025i	−0.166022	−	0.287559i	0.770996	−	0.636841i	$-0.219759\pi$
$907$	−5.00000	−	8.66025i	−0.166022	−	0.287559i	−0.937018	+	0.349281i	$0.886426\pi$
$908$	−5.00000	+	8.66025i	−0.165931	+	0.287401i
$909$	15.0000	+	25.9808i	0.497519	+	0.861727i
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$		0			0
$913$	−70.0000			−2.31666
$914$	16.0000	+	27.7128i	0.529233	+	0.916658i
$915$		0			0
$916$	−3.00000	+	5.19615i	−0.0991228	+	0.171686i
$917$	0.500000	+	0.866025i	0.0165115	+	0.0285987i
$918$		0			0
$919$	10.0000			0.329870			0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000			0.329870			0.164935	+	0.986304i	$0.447259\pi$
$920$		0			0
$921$		0			0
$922$	−15.0000	+	25.9808i	−0.493999	+	0.855631i
$923$	−12.0000			−0.394985
$924$		0			0
$925$		0			0
$926$	−18.5000	−	32.0429i	−0.607948	−	1.05300i
$927$	−19.5000	+	33.7750i	−0.640464	+	1.10932i
$928$	3.00000	+	5.19615i	0.0984798	+	0.170572i
$929$	13.5000	+	23.3827i	0.442921	+	0.767161i	0.997905	−	0.0646999i	$-0.0206090\pi$
$929$	13.5000	+	23.3827i	0.442921	+	0.767161i	−0.554984	+	0.831861i	$0.687276\pi$
$930$		0			0
$931$	3.00000	+	25.9808i	0.0983210	+	0.851485i
$932$	−10.0000			−0.327561
$933$		0			0
$934$	−17.0000	−	29.4449i	−0.556257	−	0.963465i
$935$		0			0
$936$	3.00000	+	5.19615i	0.0980581	+	0.169842i
$937$	1.00000	−	1.73205i	0.0326686	−	0.0565836i	−0.849229	−	0.528025i	$-0.822933\pi$
$937$	1.00000	−	1.73205i	0.0326686	−	0.0565836i	0.881897	+	0.471441i	$0.156266\pi$
$938$	−12.0000			−0.391814
$939$		0			0
$940$		0			0
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	−0.681218	−	0.732081i	$-0.738549\pi$
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	0.974609	+	0.223912i	$0.0718827\pi$
$942$		0			0
$943$	9.00000			0.293080
$944$		0			0
$945$		0			0
$946$	−15.0000	+	25.9808i	−0.487692	+	0.844707i
$947$	−30.0000	−	51.9615i	−0.974869	−	1.68852i	−0.680367	−	0.732872i	$-0.738179\pi$
$947$	−30.0000	−	51.9615i	−0.974869	−	1.68852i	−0.294502	−	0.955651i	$-0.595154\pi$
$948$		0			0
$949$	28.0000			0.908918
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−18.0000	−	31.1769i	−0.583077	−	1.00992i	−0.995112	−	0.0987513i	$-0.968515\pi$
$953$	−18.0000	−	31.1769i	−0.583077	−	1.00992i	0.412035	−	0.911168i	$-0.364818\pi$
$954$	7.50000	−	12.9904i	0.242821	−	0.420579i
$955$		0			0
$956$	−8.00000	+	13.8564i	−0.258738	+	0.448148i
$957$		0			0
$958$	18.0000			0.581554
$959$	−6.00000	+	10.3923i	−0.193750	+	0.335585i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	22.0000			0.709308
$963$	6.00000	−	10.3923i	0.193347	−	0.334887i
$964$	9.00000	+	15.5885i	0.289870	+	0.502070i
$965$		0			0
$966$		0			0
$967$	−4.00000	−	6.92820i	−0.128631	−	0.222796i	0.794515	−	0.607244i	$-0.207725\pi$
$967$	−4.00000	−	6.92820i	−0.128631	−	0.222796i	−0.923147	+	0.384448i	$0.874392\pi$
$968$	−14.0000			−0.449977
$969$		0			0
$970$		0			0
$971$	10.0000	+	17.3205i	0.320915	+	0.555842i	0.980677	−	0.195633i	$-0.0626762\pi$
$971$	10.0000	+	17.3205i	0.320915	+	0.555842i	−0.659762	+	0.751475i	$0.729343\pi$
$972$		0			0
$973$	8.00000	−	13.8564i	0.256468	−	0.444216i
$974$	11.5000	+	19.9186i	0.368484	+	0.638233i
$975$		0			0
$976$		0			0
$977$	2.00000			0.0639857			0.0319928	−	0.999488i	$-0.489815\pi$
$977$	2.00000			0.0639857			0.0319928	+	0.999488i	$0.489815\pi$
$978$		0			0
$979$	17.5000	−	30.3109i	0.559302	−	0.968740i
$980$		0			0
$981$	−12.0000			−0.383131
$982$	13.5000	−	23.3827i	0.430802	−	0.746171i
$983$	10.5000	+	18.1865i	0.334898	+	0.580060i	0.983465	−	0.181097i	$-0.0579648\pi$
$983$	10.5000	+	18.1865i	0.334898	+	0.580060i	−0.648567	+	0.761157i	$0.724631\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	7.00000	−	5.19615i	0.222700	−	0.165312i
$989$	6.00000			0.190789
$990$		0			0
$991$	−9.00000	−	15.5885i	−0.285894	−	0.495184i	0.686931	−	0.726722i	$-0.258957\pi$
$991$	−9.00000	−	15.5885i	−0.285894	−	0.495184i	−0.972826	+	0.231539i	$0.925624\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$		0			0
$994$	−3.00000	+	5.19615i	−0.0951542	+	0.164812i
$995$		0			0
$996$		0			0
$997$	−26.5000	+	45.8993i	−0.839263	+	1.45365i	0.0512480	+	0.998686i	$0.483680\pi$
$997$	−26.5000	+	45.8993i	−0.839263	+	1.45365i	−0.890511	+	0.454961i	$0.849653\pi$
$998$	−19.5000	+	33.7750i	−0.617262	+	1.06913i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.e.f.501.1		2
5.2	odd	4		950.2.j.d.349.1		4
5.3	odd	4		950.2.j.d.349.2		4
5.4	even	2		190.2.e.a.121.1	yes	2
15.14	odd	2		1710.2.l.h.1261.1		2
19.11	even	3	inner	950.2.e.f.201.1		2
20.19	odd	2		1520.2.q.f.881.1		2
95.49	even	6		190.2.e.a.11.1	✓	2
95.64	even	6		3610.2.a.g.1.1		1
95.68	odd	12		950.2.j.d.49.1		4
95.69	odd	6		3610.2.a.c.1.1		1
95.87	odd	12		950.2.j.d.49.2		4
285.239	odd	6		1710.2.l.h.1531.1		2
380.239	odd	6		1520.2.q.f.961.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.e.a.11.1	✓	2	95.49	even	6
190.2.e.a.121.1	yes	2	5.4	even	2
950.2.e.f.201.1		2	19.11	even	3	inner
950.2.e.f.501.1		2	1.1	even	1	trivial
950.2.j.d.49.1		4	95.68	odd	12
950.2.j.d.49.2		4	95.87	odd	12
950.2.j.d.349.1		4	5.2	odd	4
950.2.j.d.349.2		4	5.3	odd	4
1520.2.q.f.881.1		2	20.19	odd	2
1520.2.q.f.961.1		2	380.239	odd	6
1710.2.l.h.1261.1		2	15.14	odd	2
1710.2.l.h.1531.1		2	285.239	odd	6
3610.2.a.c.1.1		1	95.69	odd	6
3610.2.a.g.1.1		1	95.64	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +5.00000 q^{11} +(1.00000 - 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +3.00000 q^{18} +(-0.500000 - 4.33013i) q^{19} +(2.50000 + 4.33013i) q^{22} +(0.500000 - 0.866025i) q^{23} +2.00000 q^{26} +(0.500000 - 0.866025i) q^{28} +(-3.00000 + 5.19615i) q^{29} +4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{36} +11.0000 q^{37} +(3.50000 - 2.59808i) q^{38} +(4.50000 + 7.79423i) q^{41} +(3.00000 + 5.19615i) q^{43} +(-2.50000 + 4.33013i) q^{44} +1.00000 q^{46} -6.00000 q^{49} +(1.00000 + 1.73205i) q^{52} +(2.50000 - 4.33013i) q^{53} +1.00000 q^{56} -6.00000 q^{58} +(2.00000 + 3.46410i) q^{62} +(-1.50000 + 2.59808i) q^{63} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{67} +(-3.00000 - 5.19615i) q^{71} +(-1.50000 + 2.59808i) q^{72} +(7.00000 + 12.1244i) q^{73} +(5.50000 + 9.52628i) q^{74} +(4.00000 + 1.73205i) q^{76} -5.00000 q^{77} +(-5.00000 - 8.66025i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{82} -14.0000 q^{83} +(-3.00000 + 5.19615i) q^{86} -5.00000 q^{88} +(3.50000 - 6.06218i) q^{89} +(-1.00000 + 1.73205i) q^{91} +(0.500000 + 0.866025i) q^{92} +(-1.00000 - 1.73205i) q^{97} +(-3.00000 - 5.19615i) q^{98} +(7.50000 - 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - 2 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + q^2 - q^4 - 2 * q^7 - 2 * q^8 + 3 * q^9	\( 2 q + q^{2} - q^{4} - 2 q^{7} - 2 q^{8} + 3 q^{9} + 10 q^{11} + 2 q^{13} - q^{14} - q^{16} + 6 q^{18} - q^{19} + 5 q^{22} + q^{23} + 4 q^{26} + q^{28} - 6 q^{29} + 8 q^{31} + q^{32} + 3 q^{36} + 22 q^{37} + 7 q^{38} + 9 q^{41} + 6 q^{43} - 5 q^{44} + 2 q^{46} - 12 q^{49} + 2 q^{52} + 5 q^{53} + 2 q^{56} - 12 q^{58} + 4 q^{62} - 3 q^{63} + 2 q^{64} + 12 q^{67} - 6 q^{71} - 3 q^{72} + 14 q^{73} + 11 q^{74} + 8 q^{76} - 10 q^{77} - 10 q^{79} - 9 q^{81} - 9 q^{82} - 28 q^{83} - 6 q^{86} - 10 q^{88} + 7 q^{89} - 2 q^{91} + q^{92} - 2 q^{97} - 6 q^{98} + 15 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^4 - 2 * q^7 - 2 * q^8 + 3 * q^9 + 10 * q^11 + 2 * q^13 - q^14 - q^16 + 6 * q^18 - q^19 + 5 * q^22 + q^23 + 4 * q^26 + q^28 - 6 * q^29 + 8 * q^31 + q^32 + 3 * q^36 + 22 * q^37 + 7 * q^38 + 9 * q^41 + 6 * q^43 - 5 * q^44 + 2 * q^46 - 12 * q^49 + 2 * q^52 + 5 * q^53 + 2 * q^56 - 12 * q^58 + 4 * q^62 - 3 * q^63 + 2 * q^64 + 12 * q^67 - 6 * q^71 - 3 * q^72 + 14 * q^73 + 11 * q^74 + 8 * q^76 - 10 * q^77 - 10 * q^79 - 9 * q^81 - 9 * q^82 - 28 * q^83 - 6 * q^86 - 10 * q^88 + 7 * q^89 - 2 * q^91 + q^92 - 2 * q^97 - 6 * q^98 + 15 * q^99

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